[
 {
  "mechanism": "GROUNDED ANSWER: in every permanent-medium growth system that actually produces spacing, the substitute for evaporation is not a second field — it is (a) measuring the RESOURCE instead of the DEPOSIT, and (b) putting the decay inside the READER (adaptation), and the pattern's length scale is set by HOW FAR THE TIP TRAVELS BETWEEN DECISIONS, not by how far it can sense.\n\nProposed rule for version six — \"clearance-driven self-avoidance with an adaptive readout on an anisotropic, persistence-limited tip\":\n\n1. Stop reading occupancy. Read CLEARANCE c(x) = distance from the tip to the nearest already-cut metal, clipped at the sensing radius R_s (a few mm). Occupancy is bounded above and saturates at 1; clearance is a field on the *un-consumed* set and stays graded until the free area is actually exhausted. This is exactly why DLA, dielectric breakdown, dendritic solidification and the Runions/Prusinkiewicz leaf-venation model need no evaporation: their field lives on the resource (free space / auxin sources / undercooled melt), which is consumed and never replenished, not on a deposit that accumulates. Physarum needs decay only because Tero-type models deposit.\n\n2. Make the reader forget, since the metal cannot. Steer on the adapted error e = c(tip) − ⟨c⟩_τ, where ⟨c⟩_τ is a running average over the last τ of PATH (not of wall time). This is growth-cone adaptation literally: Ming et al. 2002 showed a growth cone bathed in uniform netrin/BDNF goes blind (desensitization), then recovers gradient sensitivity after 60–90 min (resensitization, MAPK + local protein synthesis), which is what lets one 10 µm sensor work across orders of magnitude of background. The evaporation-equivalent is a high-pass on the readout, and it is legal here because it touches no metal.\n\n3. Threshold, not proportional turning. Below a kill distance d_k (< R_s) the rule turns away hard; above it, it goes straight. Contact-triggered repulsion with a threshold is what makes spacing in the systems where the structure is permanent: Dscam1 isoform-specific homophilic repulsion in Drosophila da/PVD dendrites (filopodial contact → contact-induced retraction within minutes), gamma-protocadherin self-recognition, MEGF10-dependent dendrite–soma exclusion in mouse starburst amacrine mosaics. None of these has a diffusible field at all; the interaction range is a molecular contact (~20 nm), yet the mosaic period is ~26–28 µm (1290–1495 cells/mm², soma 10 µm). No decay anywhere.\n\n4. Keep the anisotropy and add a turn-rate limit. Solvability theory is unambiguous: with zero interfacial anisotropy the Mullins–Sekerka instability gives tip splitting and scale-free \"seaweed\"/DLA morphology (D≈1.71, branch gaps power-law, NO characteristic spacing); above a threshold anisotropy you get stable needles with a selected tip radius and sidebranch spacing. The polar machine already has anisotropy for free (0.38 mm tangential quantum at the rim vs 0.02 mm at r=10, plus the anisotropic groove-floor roughness) — that is very likely why version four bought a factor of ten. Do not remove it; couple to it deliberately, and add an explicit minimum turn radius so the tip has a persistence length.\n\n5. Exploit the premise that pass two cuts nothing. A retrace is INVISIBLE. Therefore the never-lift constraint does not forbid branching: the stroke can walk the doubled graph (Euler tour of the tree with each edge traversed twice) and render a genuine 3-valent arbor, paying only path time. This unlocks the axon/venation family, not just loop networks.\n\nJudgement on the stigmergy reframing: \"the collective is its own past selves\" is doing real work only after step 1 and 2. With a saturating deposit readout, past selves leave a message that reads 1 everywhere — the channel has zero capacity and the phrase is decoration. With clearance + adaptation the past selves are transmitting a graded, signed, non-saturating message, and the metal is a real communication channel. So: currently a nice sentence; the fix is to change what is written and how it is read, not to rename it.",
  "minimal_ingredients": [
   {
    "ingredient": "Read the resource, not the deposit: clearance (distance to nearest cut) instead of occupancy fraction",
    "why_essential": "Occupancy is bounded in [0,1] and saturates the instant a neighbourhood is marked; clearance is defined on the un-consumed set and stays graded until the free area is genuinely exhausted. This is the single structural difference between Physarum models (deposit -> needs evaporation) and DLA / dielectric breakdown / leaf venation / solidification (resource -> needs nothing). All five previous failures read a saturating deposit.",
    "can_it_be_dropped": "No. This is the whole diagnosis. Any variant that keeps a bounded accumulating readout will re-derive the closed orbit, faster or slower."
   },
   {
    "ingredient": "Adaptation in the reader: steer on clearance minus its running average over the last tau of PATH",
    "why_essential": "Puts the decay where it is legal. Ming et al. 2002: a growth cone in uniform cue desensitizes (goes blind) and resensitizes after 60-90 min, which is what lets a 10 um sensor detect 0.24-0.3% per 10 um gradients across a huge concentration range. Mathematically identical to a spatial high-pass of length v*tau along the trajectory; the metal stays permanent while the readout does not.",
    "can_it_be_dropped": "Only if clearance alone stays informative, which it does not past ~50% coverage: everything reads 'close to a groove'. Keep it. It is also the cheapest of all the ingredients to implement."
   },
   {
    "ingredient": "Threshold self-avoidance (kill distance d_k), not proportional turning on error size",
    "why_essential": "Characteristic spacing in every permanent-medium biological case comes from a contact-triggered binary decision, not a graded one: Dscam1 homophilic repulsion -> contact-induced filopodial retraction (minutes); gamma-protocadherin self-recognition; MEGF10 dendrite-soma exclusion setting the starburst mosaic period. Turning by the SIZE of the error (versions one to four) is a linear controller and linear controllers have fixed points; a threshold gives a bistable, hysteretic step that cannot be servoed to zero.",
    "can_it_be_dropped": "No, not if characteristic spacing is wanted. Drop it and you get either the old orbit or scale-free tip splitting with no periodicity."
   },
   {
    "ingredient": "Tip transport longer than the sensor: an explicit persistence length L_p = v / kappa_max (minimum turn radius)",
    "why_essential": "This is the answer to the length-scale question. In the retinal mosaic the interaction range is a molecular contact (~20 nm) and the exclusion zone is ~26-28 um: the scale is set by how far the dendrite CARRIES the rule, not by the range of the rule. Same in dendritic solidification, where the selected tip radius R = sqrt(2*d0*l_D/sigma*) with sigma*~0.0195 is a geometric mean of a ~1 nm capillary length and a 1-100 um diffusion length, i.e. ~700x the microscopic scale. A local rule plus long transport gives a large scale; a local rule plus local transport gives a sensor-sized pattern.",
    "can_it_be_dropped": "No. Without it the emergent lambda will simply equal 2*d_k <= 2*R_s and the result is a pattern at the sensor scale, i.e. exactly the criticism the project is trying to escape."
   },
   {
    "ingredient": "Anisotropy above threshold (keep the polar quantisation; couple to it on purpose)",
    "why_essential": "Solvability theory: at zero anisotropy Mullins-Sekerka produces tip splitting and seaweed/DLA morphology which is SCALE-FREE (D approx 1.71, power-law branch gaps, no periodicity); above a threshold anisotropy stable needles appear with a selected tip radius and sidebranch spacing. DBM/DLA mapping puts the non-fractal transition at a tip-split angle near 74 deg (eta = 4.0 +/- 0.3). The disc already supplies anisotropy: 0.38 mm tangential quantum at the rim vs 0.02 mm at r=10, plus anisotropic groove-floor roughness. Version four's factor of ten is most plausibly this effect.",
    "can_it_be_dropped": "It can be dropped, at a stated cost: branching without characteristic spacing (a Lichtenberg figure, not a leaf). If 'veins with spacing' is the goal, keep it."
   },
   {
    "ingredient": "Invisible retrace as the branching primitive (Euler tour of the doubled graph)",
    "why_essential": "The premise that pass two finds nothing left to cut means a retrace deposits nothing. So a single unlifted stroke can render any connected graph, including 3-valent trees, by traversing each edge twice. This is what makes the axon / venation / dendrite-tiling family available at all rather than only 4-valent loop networks. It also gives the machine biology's other move: contact-induced RETRACTION, which is how Dscam self-avoidance actually works.",
    "can_it_be_dropped": "Yes, but then restrict the target morphology to reticulate loop networks with 4-valent crossings (mature Physarum, leaf areoles), which are natively single-stroke and still show cells, veins and spacing."
   },
   {
    "ingredient": "A genuinely depletable resource and therefore an end",
    "why_essential": "DLA, invasion percolation and space colonization terminate or slow because the resource runs out; that finite budget is what makes the pattern rather than a limit cycle. Free area on the disc is the budget. The rule must be able to notice the budget shrinking (clearance maxima collapsing), which it can, locally.",
    "can_it_be_dropped": "No, but it is free: it is a consequence of ingredient 1, not extra machinery. It does mean the honest run length is set by area, not by hours - which is consistent with '80 hours changed nothing'."
   }
  ],
  "what_sets_the_length_scale": "THREE distinct scale-setting mechanisms appear in the permanent-medium literature; only two of them beat the sensing radius, and by very different factors.\n\n(1) CONTACT REPULSION CARRIED BY A MOVING TIP -- scale = tip reach/persistence, NOT interaction range. Factor: enormous, because the numerator and denominator are unrelated quantities. Mouse starburst amacrine mosaic: MEGF10-dependent dendrite-soma contact exclusion, soma 10 um, density 1290-1495 cells/mm^2 -> mean spacing 26-28 um, while the molecular homophilic interaction range is ~20 nm and the exclusion zone is set by the DENDRITIC TERRITORY (the paper's conclusion is literally \"dendrite-soma contact determines exclusion zone size\"). Ratio spacing / interaction-range ~ 10^3. Drosophila da/PVD dendrites: filopodial contact range ~1-5 um, resulting inter-branch spacing tens of um, tiled field 50-300 um -> factor 10-100. Transferable law: lambda = (distance the tip travels between avoidance decisions), so in the machine lambda ~ L_p = v/kappa_max, freely choosable at 20-60 mm against a 3 mm sensing box: factor 7-20x.\n\n(2) SENSOR ADAPTATION -- scale = v * tau, the path length over which the reader's baseline updates. Growth cone: sensing aperture ~10-20 um, gradient compared across ~10 um, detection threshold 0.24-0.3% per 10 um; desensitization then resensitization at 60-90 min; growth 20-60 um/h -> adaptation window 20-90 um = 2-9x the sensing aperture. So biology's own adaptation factor is only about 3-10x. Modest but real, and it is the ingredient that removes saturation rather than the one that sets a big scale.\n\n(3) THRESHOLD INSTABILITY WITH TWO SCALES -- scale = geometric mean, amplification = sqrt(long/short). Dendritic solidification: selection criterion sigma* = 2*D*d0/(R^2*V) approx 0.0195 gives tip radius R = sqrt(2*d0*l_D/sigma*) approx 10*sqrt(d0*l_D) with l_D = D/V. With d0 ~ 1 nm and l_D ~ 10 um, R ~ 1 um and primary spacing ~ l_D: three orders above the microscopic scale, amplification sqrt(l_D/d0)/sqrt(sigma*) ~ 700. The general recipe: one SHORT stabilising scale plus one LONG transport scale, pattern at their geometric mean. In the machine the short scale is the 0.6 mm step / 0.38 mm quantum and the long scale must be the persistence length; predicted lambda ~ sqrt(0.6 mm * 50 mm) ~ 5.5 mm, or sqrt(R_s * L_p) ~ sqrt(3 * 50) ~ 12 mm. Note the warning: version four's 10 mm ring already sits in this range, so lambda alone proves nothing -- only its SCALING does (see signatures).\n\nWHAT DOES NOT SET A SCALE: DLA and the dielectric breakdown model. They are the cleanest permanent, non-decaying, binary-occupancy systems there are -- and they produce branching with NO characteristic length. D approx 1.71 in 2D, self-similar, branch-gap distribution a power law, active zone thickness proportional to cluster radius. Their non-saturation comes from the growth field being HARMONIC: the probability of growth is the normal derivative of a Laplacian field, so screening keeps interior sites permanently quiet and tips permanently active without anything evaporating. That is the deep result to take: saturation is defeated by a field that decays in SPACE and carries a sign, not by one that decays in time. But the machine has no Laplacian field it can physically sense at the tip (no diffusion, no potential), so it cannot borrow DLA's trick directly -- and even if it could, DLA alone would give it branching with no spacing. Hence the recommendation is (1)+(2)+(3), with anisotropy supplying what DLA lacks.",
  "needs_decay": "not-needed",
  "decay_free_variants": [
   "Diffusion-limited aggregation (Witten-Sander): permanent binary deposit, no decay whatsoever; non-saturating because the growth field is harmonic and screening is a spatial, signed effect. Gives branching, D approx 1.71, but no characteristic spacing.",
   "Dielectric breakdown model / Lichtenberg figures / electrical trees: same, with eta tuning the tip-splitting angle; non-fractal above ~74 deg (eta = 4.0 +/- 0.3). Permanent damage tracks, no evaporation.",
   "Dendritic and needle-crystal solidification: permanent solid, no decay; spacing selected by the Mullins-Sekerka threshold plus interfacial anisotropy (sigma* approx 0.0195). Zero anisotropy -> tip splitting and scale-free seaweed; above threshold -> needles with selected tip radius and sidebranch spacing.",
   "Snow crystals: same mechanism, anisotropy-selected, permanent.",
   "Dscam1 dendrite self-avoidance in Drosophila da and PVD neurons: 19,008 isoforms, isoform-specific homophilic binding -> contact-induced retraction of sibling filopodia. Purely contact-based, no diffusible or decaying field; produces even spacing of self-arbors while heterotypic arbors freely intermingle.",
   "Gamma-protocadherin filopodial self-recognition (retinal starburst amacrine, cerebellar Purkinje): contact-based self-avoidance, no field at all.",
   "MEGF10/MEGF11-dependent retinal mosaics: exclusion zones set by dendrite-soma contact; mutant arbors enclose more homotypic somata. Contact, not diffusion.",
   "Leaf venation by space colonization / auxin-source competition (Runions, Fowler, Prusinkiewicz): sources are CONSUMED (removed inside the kill distance) rather than evaporating; veins are permanent. Produces veins, areoles and characteristic spacing with no decay term. The closest existing algorithmic analogue to this machine.",
   "Auxin canalization (Mitchison-type flux positive feedback): permanent strands, structure from a consumed/transported resource plus positive feedback.",
   "Winner-take-all competition for a finite molecular pool: cadherin/catenin among spines, target-derived neurotrophins among axons, NMJ occupancy among motor axon terminals. The resource is depleted and reallocated, never evaporated; produces one-per-territory outcomes and pruning.",
   "Invasion percolation and Eden growth: permanent occupation of the strongest available site; non-saturating because the readout is the ranking of the remaining resource, not the amount deposited.",
   "Growth-cone adaptation itself (Ming et al. 2002): the field need not decay because the READER does - desensitization plus resensitization moves the decay into the sensor."
  ],
  "compatible_with_one_stroke": "YES, and more strongly than the framing assumes -- because of the premise that pass two finds nothing left to cut.\n\nTopological facts. A never-lifting tool traces a walk. The visible mark set is the edge set of the graph it traverses. A graph is drawable in one stroke with no repeated edge only if it has an Eulerian path (all vertices even degree except at most two), so 4-valent CROSSINGS are native and 3-valent BRANCH POINTS are not. That alone would restrict the machine to reticulate loop networks -- which is not a bad place to be: mature Physarum networks and leaf areoles are reticulate with 4-valent junctions, and cells / veins / characteristic spacing all live there.\n\nBut retrace is free and invisible here. Depth is set by the spring load and does not accumulate, so re-traversing an existing groove deposits nothing new. Therefore the machine can walk the DOUBLED graph -- every edge twice, which makes every degree even and guarantees an Euler tour -- and render an arbitrary connected graph, including genuine 3-valent trees, axon-like arbors and DLA-like dendrites. Cost is bounded by 2x path length, and only on the tree part; loops need no doubling. Given that 7200 m already gets cut in 80 h, a factor of two in path is affordable.\n\nRetrace also hands the machine the second half of the biological move it currently lacks: contact-induced RETRACTION. Dscam self-avoidance is not \"turn away\", it is \"touch, then withdraw and try elsewhere\". A machine that can back down its own groove invisibly can implement exactly that.\n\nTwo physical cautions, both testable on a coupon before the run. (a) Self-railing: a diamond tip re-entering a ~16 um groove is mechanically captured and guided by it. This is useful (accurate retrace for free, no closed-loop tracking needed) and dangerous (the tip may refuse to leave, which is a hardware-level mechanism for exactly the closed-orbit failure being fought). Measure the lateral force needed to exit the groove and require the rail to exceed it with margin. (b) Shallow-angle crossings deflect the tip: below some crossing angle the groove wins and the trajectory jumps. Characterise the critical angle and make the rule forbid crossings below it -- which, usefully, is itself a self-avoidance constraint with a real physical basis, and a source of the anisotropy that ingredient 5 needs.\n\nOne honest asymmetry: biology's tip is one-way (an axon does not un-lay itself, a dendrite retracts a branch it has not yet consolidated). The machine's retrace is invisible but the metal stays. So the machine can emulate retraction of the DECISION but never of the MARK. Failed exploratory branches are permanent. Design for that: keep exploratory excursions short compared with lambda, or accept that the finished plate records its own hesitation, which is arguably the more interesting object.",
  "measurable_signatures": [
   "THE DECISIVE ONE -- scaling exponent of lambda against the sensing radius. Run three configurations with the sensing box at 1.5, 3 and 6 mm, everything else fixed, and fit d(log lambda)/d(log R_s) from the first peak of the segment pair-correlation. Exponent ~1.0 means the pattern IS the sensor (a smoothing-kernel artefact, the same class of result as the 10 mm ring). Exponent ~0.0 (transport-dominated) or ~0.5 (geometric-mean selection) means the scale is emergent. Report with error bars; nothing else in this list can substitute for it.",
   "POSITIVE CONTROL on transport. Sweep the minimum turn radius / persistence length L_p over 4x and the adaptation path window v*tau over 4x. Emergence predicts lambda tracks these with slope ~1 (or 0.5 in the geometric-mean regime) while being flat in R_s. If lambda ignores both, the scale is coming from something unmodelled.",
   "SPACING STATISTICS with an exclusion zone. Compute the density recovery profile of cut segments (5 mm annuli, following the retinal-mosaic convention) and the nearest-neighbour regularity index = mean/SD of nearest-groove distance. A Poisson pattern gives ~1.9; real orderly mosaics give 3-8. Target > 3, plus a resolved exclusion zone whose radius exceeds R_s. Ratio lambda / R_s >= 5 and lambda / step(0.6 mm) >= 30 are the headline numbers.",
   "AREOLE STATISTICS -- does a cell size exist. Count closed loops per unit area and take the distribution of enclosed areas. A real length scale gives a peaked distribution with CV ~0.3-0.6. A power-law with no peak means DLA-class scale-free branching: structure, but no spacing, and the anisotropy ingredient failed.",
   "BOX-COUNTING DIMENSION with a crossover. D approx 1.0 = the old closed-orbit failure. D approx 1.71 = DLA/seaweed, scale-free (branching achieved, spacing not). D approx 1.8-2.0 with a clean crossover length = veins plus spacing, which is the target. Report D over at least a decade and the crossover explicitly.",
   "NON-SATURATION, stated in the same currency as the five failures. The published failure signature is the readout error falling to 1/34, 1/73, 1/195 of its morning value. Require instead that the variance of the adapted readout falls by less than 2x while coverage rises from 0 to 60%, and that the mutual information between the readout and the executed turn (bits per step) stays above a fixed floor for the whole run. A run whose information rate is stationary while its coverage climbs is the actual claim being made.",
   "GROWTH LOCALISATION (harmonic-measure analogue). Fraction of new cutting occurring in the outermost 10% of the pattern's current radius, and the distribution of new cut per unit of existing frontier. Screened, tip-dominated growth is the signature that the resource field is still doing work; uniform infill means the rule has become a space-filling scan.",
   "EVAPORATION-EQUIVALENCE TEST. Simulate the same rule on a field that DOES decay with time constant tau_sim, and compare g(r), areole CV and D against the real run. If the adaptive-readout run matches the decaying-field run within error, the claim 'adaptation substitutes for evaporation' is measured rather than asserted -- and the matching tau_sim tells you what v*tau you actually realised.",
   "SELF-RAILING / groove-capture audit. Log every event where the tip enters an existing groove, and the path length before it exits. A heavy tail here is the hardware-level version of the closed orbit and would explain a collapse without any failure of the rule. Also log the crossing-angle histogram against the measured critical deflection angle."
  ],
  "sources": [
   "https://www.nature.com/articles/nature745 -- Ming et al., Adaptation in the chemotactic guidance of nerve growth cones, Nature 417:411-418 (2002): desensitization then resensitization at 60-90 min, MAPK and local protein synthesis dependent",
   "https://www.med.upenn.edu/minglab/assets/user-content/documents/Nature_May2002.pdf -- full text of the above",
   "https://www.nature.com/articles/nn1380 -- endocytosis-dependent desensitization and protein-synthesis-dependent resensitization in retinal growth cone adaptation",
   "http://www.goodhill.org/pub/mortimer08.pdf -- Mortimer et al., Growth cone chemotaxis (review): gradient comparison across ~10 um, detection thresholds",
   "https://goodhill.org/pub/mortimer09.pdf -- Mortimer et al., A Bayesian model predicts the response of axons to molecular gradients: steepnesses of 0.24-0.3% per 10 um, receptor-binding noise as the limiting constraint",
   "https://www.jneurosci.org/content/23/1/193 -- Gradient steepness influences the pathfinding decisions of neuronal growth cones in vivo",
   "https://www.cell.com/fulltext/S0092-8674(07)00470-9 -- Matthews et al., Dendrite self-avoidance is controlled by Dscam",
   "https://pubmed.ncbi.nlm.nih.gov/17481394/ -- Drosophila sensory neurons require Dscam for dendritic self-avoidance and dendritic field organization",
   "https://pubmed.ncbi.nlm.nih.gov/20573716/ -- Grueber & Sagasti, Self-avoidance and tiling: mechanisms of dendrite and axon spacing",
   "https://www.biorxiv.org/content/10.1101/2022.11.23.517768.full.pdf -- gamma-protocadherins regulate filopodia self-recognition and dynamics to drive dendrite self-avoidance",
   "https://pmc.ncbi.nlm.nih.gov/articles/PMC10680827/ -- Retinal neurons establish mosaic patterning by excluding homotypic somata from their dendritic territory: soma 10 um, 1290-1495 cells/mm^2, MEGF10-dependent, dendrite-soma contact determines exclusion zone size",
   "https://www.cell.com/cell-reports/fulltext/S2211-1247(24)00965-3 -- journal version of the above",
   "https://www.damtp.cam.ac.uk/user/eglen/papers/raven2003.pdf -- Raven & Eglen, Determinants of the exclusion zone in dopaminergic amacrine cell mosaics; density recovery profile methodology",
   "https://www.frontiersin.org/journals/neuroanatomy/articles/10.3389/fnana.2014.00113/full -- regularity index conventions: ~1.9 for random sampling, 3-8 for retinal mosaics",
   "https://pubmed.ncbi.nlm.nih.gov/8730986/ -- Spatial properties of retinal mosaics: empirical evaluation of existing measures",
   "https://algorithmicbotany.org/papers/colonization.egwnp2007.large.pdf -- Runions, Lane, Prusinkiewicz, Modeling trees with a space colonization algorithm: auxin sources removed inside the kill distance; spacing from consumed resource, no decay term",
   "https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3240471/ -- The impact of resource competition on neurite outgrowth",
   "https://pmc.ncbi.nlm.nih.gov/articles/PMC4668927/ -- Sculpting neural circuits by axon and dendrite pruning: competition for limited target-derived factors",
   "https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3383746/ -- Axons compete for neuromuscular junctions",
   "https://english.cas.cn/newsroom/archive/research_archive/rp2015/201508/t20150807_151221.shtml -- winner-take-all competition for a limited cadherin/catenin pool in circuit pruning",
   "https://www.ncbi.nlm.nih.gov/pubmed/12059377 -- Tip splittings and phase transitions in the dielectric breakdown model, mapping to DLA: eta = 4.0 +/- 0.3 at a ~74 deg tip-split angle",
   "https://arxiv.org/pdf/cond-mat/0403527 -- Effects of the screening breakdown in the diffusion-limited aggregation model",
   "https://arxiv.org/pdf/cond-mat/0401384 -- Growth by random walker sampling and scaling of the dielectric breakdown model (harmonic measure formulation)",
   "https://www.sciencedirect.com/science/article/pii/B9780080925233500277 -- Fundamentals of dendritic solidification I: steady-state tip growth; stability criterion 2*alpha*d0/(V*R^2) = 0.0195",
   "https://arxiv.org/pdf/2111.05658 -- In-situ measurements of dendrite tip shape selection: sigma* = 2*D*d0/(R^2*V)",
   "https://www.sciencedirect.com/science/article/abs/pii/S0927796X03000366 -- Atomistic and continuum modeling of dendritic solidification: anisotropy threshold, tip splitting and seaweed morphology at zero anisotropy, DLA as the isotropic limit",
   "https://arxiv.org/pdf/cond-mat/0206179 -- Dynamics of low anisotropy morphologies in directional solidification",
   "https://arxiv.org/pdf/1910.06389 -- Libbrecht, Snow crystals (anisotropy-selected permanent growth)",
   "https://royalsocietypublishing.org/doi/10.1098/rsos.190225 -- Testing the limits of pheromone stigmergy in high-density robot swarms: environmental saturation with social information nullifies stigmergic coordination; faster decay required at higher density (i.e. the failure mode the five previous versions hit)"
  ]
 },
 {
  "mechanism": "SENSOR-SIDE DIAGNOSIS FIRST: the five failures are not caused by permanence. They are caused by reading an AREA FRACTION through a box 81 groove-widths wide.\n\nChecked against your own code ({repo_path}/only-surprise/engine/polar.py, scribe.py, stylus.py):\n- groove = 61.8 um wide, 15.907 um deep (recomputed from stylus.py: 120 deg cone, 12.5 um apex, 300 gf)\n- SENSE_MM = 2.5 mm, so the sensing box is 5 mm across = 81:1 versus the mark it is trying to see\n- CELL = 1.0 mm (flat) = 16.2:1; DS = 0.6 mm = 9.7:1\nThe sensor is a low-pass filter whose cutoff deletes every structure at the only scale where structure exists. Occupancy through that filter reaches 1 long before the metal does.\n\nQuantitatively: the 8 h flat run laid 720 m over the A3 plate, i.e. groove length density lambda = 5.8 mm/mm^2. The Boolean-strip estimate of TRUE areal coverage is 1-exp(-lambda*w) = 30.0%. The machine reported 82% and called it a plateau. It announced saturation while 70% of the mirror was untouched. THE SATURATION WAS IN THE MEASUREMENT, NOT YET IN THE METAL.\n\nSecond diagnosis: LOOKAHEAD_MM = 7.0 with left/right probes at +/-0.62 rad is not a stylus. It reads density 7 mm ahead of the tip. Your own constraint (\"at or near the tip\") forbids it. A real tip reads only where it is — which shortens the loop from \"predict the metal 7 mm ahead, verify in 12 steps\" to \"predict the next millisecond of force, verify now\", and moves the decision rate from 41.7 Hz to kHz. Groove-crossing transit is w/v = 2.47 ms (405 Hz); 1 um lay features are 25 kHz. The machine has been sampling a kHz world at 41.7 Hz through an 81:1 box. THE UNEXPLOITED AXIS IS BANDWIDTH — not time, not number, not body, not novelty-seeking.\n\n(a) ADAPTATION AS A HIGH-PASS, AND THE RESULT THAT KILLS THE OBVIOUS FIX.\nSpike-frequency adaptation is subtractive feedback: an adaptation variable a leaks toward u with time constant tau, output y = u - a. Transfer function s*tau/(1+s*tau) — a leaky differentiator. Numerically verified (dt = 1 ms, tau = 1 s):\n  - monotone ramp u = kt, k = 0.5  ->  y(end) = 0.4995, exactly k*tau. NON-ZERO FOREVER.\n  - saturating u = 1-exp(-t/2)     ->  y(end) = 0.00005. DEAD.\n  - log ramp                        ->  y(end) = 0.048, dying slowly.\nSo habituation CANNOT rescue an occupancy reading. It differentiates, and the derivative of a saturated signal is zero. Adaptation is only useful bolted onto a genuinely unbounded accumulator. This is the single most important design statement, and it is why \"just add habituation\" would have been the sixth failure.\nThe divisive family behaves differently and better: Weber (delta_u/u), log compression, and Naka-Rushton R = u^n/(u^n + sigma^n) with sigma tracking a running local mean of u. Light adaptation is exactly this — adaptation is a horizontal shift of the response curve along the log axis, sigma ~= the average level. Divisive normalisation discards the level and keeps the relative pattern. On occupancy it still dies (1/1 = 1, contrast 0). On an unbounded field it never dies, because sigma chases u forever. Failure mode to name honestly: if the field becomes spatially uniform, normalisation amplifies noise.\n\n(b)+(c) RANKED CANDIDATE SCALAR READINGS (physical realisability stated for each; ranked by structure carried at 90% marked).\n\n1. CROSSING RATE nu — groove-crossing transients per mm of travel. UNBOUNDED, because it measures groove LENGTH DENSITY lambda (mm of groove per mm^2), which has no ceiling even after area occupancy hits 1. Cauchy/Buffon: nu = (2/pi)*lambda for isotropic grooves, nu = lambda*|sin(dtheta)| against a parallel bundle. At lambda = 8 mm/mm^2 (125 um spacing): 0.00 crossings/mm travelling along a bundle, 8.00 across, 5.09 in isotropic felt. That is a 1:8 readable contrast that IS the local texture.\nREADABLE? YES, cheaply. A crossing is a 2.47 ms drop-and-climb: an impulsive normal acceleration plus a drag spike. Accelerometer or AE sensor on the drag holder. AE discriminates rubbing/ploughing/cutting in single-grit scratch tests in the 0.03-1 MHz band, so this is standard instrumentation, not speculation.\nHARD LIMIT: crossings merge and stop being countable when mean spacing = groove width, i.e. lambda = 1/w = 16.2 mm/mm^2. See the horizon below.\n\n2. DRAG-FORCE ANISOTROPY WITH HEADING — the local lay direction and its strength, read as the difference in tangential force between travelling along and across the local texture. NON-SATURATING because it is a DIRECTION, not an accumulation: each pass re-smears the floor in the new direction of travel and OVERWRITES the previous lay. This is the one genuine forgetting channel in a permanent medium, and it lives at the roughness scale (tens of nm), not the groove scale. Your commit e37629b already found the anisotropy; it is the sensor answer as much as the optics answer.\nREADABLE? YES. Textured surfaces have a friction TENSOR with two principal coefficients; random untextured surfaces are direction-independent. Force magnitudes here are large: normal load 2.942 N; ploughing a virgin cut costs H*A = 0.707 N; friction-only riding costs ~0.44 N at mu = 0.15 — a 2.6:1 tangential-force contrast between cutting and riding. Re-cutting work-hardened metal reaches 9.96 um instead of 15.907 um, another force-visible difference. Strain-gauge flexure in the holder, few-kHz bandwidth.\nCAVEAT: the SIGN of the along/across friction difference is regime-dependent in the literature (narrow grooves under light load can give higher friction PARALLEL). Calibrate on the real machine; do not assume.\n\n3. NEMATIC ORDER OF THE LOCAL GROOVE FIELD, S = |<exp(2*i*theta)>| in [0,1], with its axis. Lives on a compact manifold with no absorbing state, and is NON-MONOTONE: it FALLS when grooves arrive at new angles. Your groove_field.py already computes exactly this (band_cos2/band_sin2, radial_order, alignment_strength) — as an analysis tool. Promote it to the sensor.\nREADABLE? YES, as the derived quantity behind readings 1 and 2 (crossing rate versus heading gives both axis and magnitude). Not directly, but reconstructible at the tip.\nCAVEAT, stated honestly: S also has a saturating attractor, at S = 0 (isotropic felt). It survives only because the machine's own habit is locally coherent — parallel bundles keep S high where they are laid. That is the whole bet.\n\n4. CROSSING-ANGLE DISTRIBUTION. Experimentally grounded: when a tool crosses a previous scratch, cutting forces drop locally, and the lowest crossing angle (10 deg) gives the lowest forces. So the force signature encodes the angle, not just the presence.\nREADABLE? YES, same channel as 2. Adds the second moment that distinguishes crosshatch (two modes) from felt (many).\n\n5. GROOVE CAPTURE / GUIDANCE. Walls at 30 deg from the surface plane, aspect w/d = 3.89: below a critical crossing angle the tip is captured and steered along the groove, producing lateral force on the rail (readable as radial-axis motor current or a flexure). This is the ONE-STROKE VERSION OF PHYSARUM TRAIL-FOLLOWING and it is free — mechanical, not computed.\n\n6. AE ENVELOPE / SPECTRAL CENTROID — distinguishes cutting virgin metal from rubbing a worked plateau. Survives groove merging (unlike 1). Bounded but non-monotone.\n\n7. RIDING HEIGHT (spring deflection, capacitive or eddy-current). Bounded by 15.907 um, and swamped by disc runout and thermal drift on a 400 mm plate. Only the AC part is trustworthy — the physics FORCES the high-pass whether you want it or not. Low rank as a standalone reading.\n\n8. PASS COUNT n. Unbounded in principle (measured up to 85 in your burned ring) and USELESS, because nothing readable tracks it: depth is fixed by load at pass 1 (40 passes add exactly zero); work hardening has a ~3-pass time constant and saturates at 450 HV; pile-up ridges get shaved off. Weber contrast 1/n at n = 85 is 1.2%. The count-based-exploration bonus beta/sqrt(N) is the mathematically correct decay-free habituation, and there is no sensor for N.\n\n9. GROOVE DEPTH. Dead on arrival, by your own metal calculation. 15.907 um at pass 1 and pass 40.\n\nTHE MECHANISM THAT FOLLOWS. Steer on divisively normalised crossing rate and lay anisotropy, both read at the tip at kHz, both normalised against a running local mean (Naka-Rushton with sliding sigma). Turn toward low crossing rate: travelling along a bundle costs almost no crossings, so a bundle self-reinforces IN LENGTH AND NOT IN WIDTH — that is a vein. Where the machine has already crossed itself at many angles, S -> 0, crossing rate is isotropic and high, no direction is preferred, and the region behaves as a boundary the line skirts. Domains of coherent lay meeting at mismatch boundaries is GRAIN GROWTH, which is the canonical decay-free network former: the state variable is a permanent orientation, and it produces a cellular network with a characteristic grain size and no evaporating field anywhere in the model.\n\nJUDGEMENT ON THE STIGMERGY REFRAMING, since you asked. It is doing real work ONLY under a specific test: every reading must be one that A SECOND, NAIVE MACHINE ARRIVING WITH NO MEMORY COULD ALSO OBTAIN FROM THE PLATE ALONE. Occupancy passes that test and carries no information after the first hour — which is why, for versions 1-5, \"the collective is its own past selves\" was indeed only a nice sentence: the channel had zero capacity. An internal per-cell pass-count map would FAIL the test — that is internal memory with extra steps, and the metal stops being the medium. Lay orientation, lambda via crossing rate, and drag anisotropy all PASS it. The reframing becomes true the moment the reading changes, and not before.",
  "minimal_ingredients": [
   {
    "ingredient": "A sensing scale within an order of magnitude of the mark width (target <= 10:1; currently 81:1)",
    "why_essential": "This is the diagnosed cause of all five failures. A 5 mm box over a 61.8 um groove is a low-pass filter that deletes the only scale at which structure exists, and it manufactures saturation: reported 82% coverage versus a true areal coverage of 30.0% at 8 h flat.",
    "can_it_be_dropped": "NO. Nothing else in this list works without it. It is also the cheapest fix and requires no new physics — only reading closer to the tip and at a shorter integration length."
   },
   {
    "ingredient": "An unbounded accumulator readable at the tip: groove length density lambda, sensed as crossing rate",
    "why_essential": "Area occupancy has a ceiling at 1; length per unit area does not, because grooves overlap. Verified numerically: a first-order high-pass on a ramp settles at k*tau = 0.4995 (alive forever), on a saturating input at 5e-5 (dead). Adaptation differentiates, so it can only rescue a signal that keeps growing.",
    "can_it_be_dropped": "NO. Dropping it and keeping adaptation is exactly the sixth failure — habituation applied to a saturated field yields zero."
   },
   {
    "ingredient": "Reader-side divisive adaptation: Naka-Rushton R = u^n/(u^n + sigma^n) with sigma tracking a running local mean of u",
    "why_essential": "lambda grows ~60x over a long run, so any fixed-gain reading of it clips. Divisive normalisation with sliding semi-saturation is how light adaptation preserves sensitivity at any background level — it shifts the operating point instead of letting the background fade. This is where the medium's inability to forget is compensated: the READER forgets.",
    "can_it_be_dropped": "NO if lambda is the reading. It could be replaced by Weber contrast (delta_u/u) or log compression, which are weaker versions of the same operator. It must NOT be replaced by subtractive spike-frequency adaptation alone, which throws away the level entirely and is noise-dominated once the field is uniform."
   },
   {
    "ingredient": "A directional, non-scalar reading: local lay axis and nematic order S = |<exp(2*i*theta)>|",
    "why_essential": "A scalar density field can only make stripes at the filter scale. Cells, territories and boundaries require a state variable with an internal direction, so that two regions can DISAGREE without either being denser. Orientation lives on a compact manifold with no absorbing state, so it does not ramp to a ceiling — it falls again when grooves arrive at new angles.",
    "can_it_be_dropped": "Only by giving up the wanted result. Without it there is no mechanism for territories, only for spacing."
   },
   {
    "ingredient": "kHz force / acoustic-emission sensing at the tip (strain-gauge flexure plus accelerometer or AE piezo)",
    "why_essential": "The informative signal is at 405 Hz (2.47 ms groove-crossing transit) and up to 25 kHz (1 um lay features). The current loop runs at 41.7 Hz. Tangential-force contrast between cutting virgin metal and riding an existing groove is ~2.6:1 (0.707 N ploughing versus 0.44 N friction at 2.942 N load) — a large, robust, standard measurement.",
    "can_it_be_dropped": "Only downward, at the cost of the reading. Below a few hundred Hz there is nothing left to read. AE can be dropped if force alone is used, at the cost of the cutting/rubbing discrimination."
   },
   {
    "ingredient": "Removal of the 7 mm lookahead",
    "why_essential": "It violates the stated constraint (read at or near the tip) and is the reason the loop is 42 Hz. A real stylus reads only where it is, which forces a reactive kHz loop and is what opens the bandwidth axis.",
    "can_it_be_dropped": "It must be dropped, not kept. Keeping it means the piece is not about a physical stylus."
   },
   {
    "ingredient": "Anisotropic capture geometry of the tool (walls 30 deg from the surface plane, aspect w/d = 3.89)",
    "why_essential": "Below a critical crossing angle the groove guides the tip, giving mechanical trail-following with no computation. This is the one-stroke analogue of Physarum following its own trail, and it is the physical origin of vein reinforcement in length rather than width.",
    "can_it_be_dropped": "It cannot be removed — it is the tip's geometry, and it is a gift rather than a cost."
   },
   {
    "ingredient": "A hard stop at the groove-merge horizon (~1930 m on the disc, ~21.5 h at 25 mm/s), or a finer tip",
    "why_essential": "Beyond lambda = 1/w = 16.2 mm/mm^2 the mean groove spacing equals the groove width, individual grooves cease to exist, and crossing-based readings die. The 80 h runs reached lambda = 60 mean and 446 in the ring: 3.7x and 27x past the horizon. Your own metal calculation already found the endpoint — a flat matte plane 12.8 um down, no mirror, no ridges, 85 passes, same 15.907 um.",
    "can_it_be_dropped": "Only by accepting the ring. lambda_merge = 1/w, so a 6 um tip buys 10x more run; a bigger disc buys area proportionally. Time alone buys nothing, which is now explained rather than merely observed."
   },
   {
    "ingredient": "NOT NEEDED: an evaporating field, several machines, a goal or reward, more hours, or error-seeking",
    "why_essential": "Each was tried and ruled out. The new content is entirely in the sensor's scale, bandwidth and algebra.",
    "can_it_be_dropped": "Already dropped. Adding any of them back would obscure the test of the actual hypothesis."
   }
  ],
  "what_sets_the_length_scale": "Not a decay rate. Five independent handles, in order of how much control they give:\n\n1. ADVECTIVE ADAPTATION LENGTH v*tau — the direct substitute for the Physarum diffusion length sqrt(D/k). The reader's adaptation time constant times tool speed. At 25 mm/s: tau = 5 ms -> 125 um, 20 ms -> 500 um, 40 ms -> 1.0 mm, 100 ms -> 2.5 mm, 400 ms -> 10 mm. This is the primary tunable, and unlike a decay rate it belongs to the machine, not the metal.\n\n2. THE DIVISIVE NORMALISATION POOL RADIUS — the spatial version of the same, and what actually sets vein spacing if the pool is spatial rather than temporal. DANGER: if the emergent spacing simply equals the pool radius, the \"pattern\" is the filter's impulse response and nothing has emerged. This is the first thing to test (see signatures).\n\n3. THE MERGE LENGTH 1/lambda, floored by the groove width w = 61.8 um. At the merge horizon lambda = 1/w = 16.2 mm/mm^2 the mean spacing IS the groove width. So 61.8 um is the finest structure that can ever exist on this plate with this tool, and the usable band is roughly 62 um to a few mm — under two decades. Narrow, and worth stating plainly.\n\n4. REGENERATIVE CHATTER WAVELENGTH v/f_resonance of the drag holder's flexure — and this one is FREE, requiring no rule at all. 80 Hz -> 312 um, 200 Hz -> 125 um, 500 Hz -> 50 um, 1200 Hz -> 21 um. This is how washboard road ripples, brake judder and chatter marks acquire characteristic spacing in permanently deformed media with nothing forgetting anywhere. If the flexure is left compliant, the machine will produce characteristic spacing whether or not the rule asks for it — which is both an opportunity and a confound that must be measured and subtracted before claiming emergence.\n\n5. THE GROOVE CAPTURE ANGLE, set by the wall inclination (30 deg from the surface plane, aspect 3.89). This fixes the angular width of the \"vein\" attractor and therefore how straight a bundle must be to keep guiding the tip — i.e. the persistence length of a vein, not its spacing.\n\nPhysarum's decay does two things: prevents saturation, and sets the scale via sqrt(D/k). Both are recovered above (reader-side adaptation; v*tau). It also does a third thing that CANNOT be recovered here: it lets weak trails die, which prunes the network. You cannot un-cut metal. The best available substitute is masking — the reader stops responding to a region, so it functionally leaves the dynamics while remaining in the metal. Selection by inattention rather than selection by evaporation. And the flux-reinforcement loop of the Tero adaptive-conductance model is genuinely unavailable: it needs a conserved flow through a network with back-pressure, and a single pen carries unit flux through exactly one place at a time. Say that out loud rather than papering over it.",
  "needs_decay": "helpful",
  "decay_free_variants": [
   "GRAIN GROWTH / ORIENTATION-FIELD PHASE-FIELD MODELS — the closest match and the strongest reference. The state variable is a crystal ORIENTATION: permanent, never erased, living on a compact manifold with no absorbing state, so it cannot saturate the way a concentration can. Produces exactly the wanted vocabulary — cells, territories, boundaries, characteristic grain size, coarsening — with no evaporating field anywhere in the model. Orientation-field models use a single-well potential and let boundary energy and mobility depend on misorientation. This is the decay-free template for the lay-orientation reading.",
   "DIFFUSION-LIMITED AGGREGATION — permanent deposit, irreversible, branching networks, no decay. Non-saturation comes from SCREENING rather than evaporation: interior sites become unreachable rather than uninformative, with a measured exponential screening length (~22.7 lattice units), power-law branch lengths (tau ~ 2.1) and preferred branching angles (~72 deg). The analogue here is that the tool's own continuity and its capture in grooves screen the interior of a worked region.",
   "REGENERATIVE CHATTER, BRAKE JUDDER AND WASHBOARD ROAD CORRUGATIONS — self-organised periodic structure in a permanently deformed medium where the length scale is v/f_resonance and absolutely nothing forgets. Directly applicable: the drag holder has a flexure resonance, so this mechanism is already present in the machine and must be measured before any claim of emergence.",
   "CRACK NETWORKS — mud cracks, columnar basalt, craquelure. Permanent, cellular, characteristic spacing set by layer thickness and stress relaxation length. The archetype of a permanent cellular pattern with no decaying field.",
   "COUNT-BASED EXPLORATION BONUSES beta/sqrt(N) (Bellemare et al., Unifying Count-Based Exploration and Intrinsic Motivation) — habituation implemented DIVISIVELY on a permanent, monotone, never-decaying count. Mathematically it is Weber-Fechner, and it is the proof that decay-free habituation is coherent. Noted here as the correct formalism that this machine unfortunately has no sensor for: nothing on the plate reports N.",
   "NAKA-RUSHTON LIGHT ADAPTATION WITH SLIDING SEMI-SATURATION — R = u^n/(u^n + sigma^n) with sigma tracking the mean level. The sensory proof that sensitivity can be preserved at ANY background without the background fading: adaptation is a horizontal shift of the response curve along the log axis. This is the operator that replaces evaporation in the proposal.",
   "BTW SANDPILE / SELF-ORGANISED CRITICALITY and EDEN/KPZ GROWTH — additive, conservative, no decay term, and still long-range correlated structure. Included to make the general point: decay is one way to avoid a fixed point, not the only way. Thresholds and conservation laws also work."
  ],
  "compatible_with_one_stroke": "YES, and more compatible than the previous versions were — with three consequences that must be accepted rather than worked around.\n\nCOMPATIBLE. Every reading proposed is taken at the point of contact while moving. Nothing requires lifting, nothing requires erasing, nothing requires revisiting a place on purpose, nothing requires a second sensor away from the tip. Crossing rate, drag anisotropy, lay axis, crossing angle and capture are all things that happen TO the tip as it travels, which is why they suit a tool that never lifts: they are free by-products of contact. The previous versions' 7 mm lookahead was the part that was NOT compatible with a single continuous stroke on real metal, and removing it is a simplification.\n\nBETTER THAN COMPATIBLE — the one-stroke constraint supplies the mechanism. Groove capture means a bundle of near-parallel grooves mechanically STEERS the tip along itself below a critical crossing angle. That is Physarum trail-following implemented in the tool's geometry rather than in the rule, and it only exists because the tool is permanently in contact. A pen that lifted would lose it.\n\nTHREE CONSEQUENCES.\n1. The loop becomes reactive, not predictive-at-distance. Sensing at the tip means the machine can only make claims about the next millisecond along its current heading. Decision rate rises from 41.7 Hz to kHz; the \"predict, be surprised, turn\" structure survives intact but the horizon shrinks from 7 mm to ~25 um. Turning authority must be rate-limited accordingly or the line becomes noise (TURN_CLAMP = 0.30 rad per 0.6 mm step no longer means what it meant).\n2. The run has an end, and it is about 21.5 hours, not 80. After lambda = 16.2 mm/mm^2 the grooves merge and the crossing-based readings die; the piece after that point is about a matte plateau, not a network. This is a decision to make deliberately: stop at the horizon, or use a finer tip (lambda_merge = 1/w, so 6 um buys 10x), or make the disc bigger. It is not a decision to make by running longer and hoping.\n3. Pruning is unavailable. A single stroke on permanent metal can add a vein but never remove one, so the network can coarsen by MASKING (the reader ceases to respond) but not by dying. Expect structure that accretes and competes for attention, not structure that is selected and cleaned up. Physarum's characteristic pruned elegance is the one reference behaviour that will not transfer, and the honest version of this work says so instead of implying otherwise.",
  "measurable_signatures": [
   "SPACING-TO-SENSOR RATIO, the primary test. Report (characteristic pattern spacing) / (sensing integration length). If it is near 1, the 'structure' is the filter's impulse response and nothing emerged. Require > 10. For reference, the current sensor fails in the other direction: sensing length / mark width = 81:1.",
   "FILTER-SCALING TEST, the decisive one. Change the adaptation constant tau (or pool radius) by 4x and remeasure the spacing. If spacing scales as 4x, the scale is set by the FILTER. If it scales sublinearly (say 1.5-2x) and then plateaus, the scale is set by the INTERACTION. Report the log-log slope; emergence means a slope well below 1. Also vary tool speed v independently of tau: a pure v*tau artefact scales with the product, a real interaction scale does not.",
   "CHATTER SUBTRACTION. Measure the drag holder's flexure resonance f and report v/f (25 mm/s at 80-1200 Hz gives 312 down to 21 um). Any spectral peak at v/f is mechanics, not intelligence, and must be subtracted before claiming a characteristic spacing. This is the confound most likely to produce a convincing false positive.",
   "TRUE COVERAGE VERSUS CELL COVERAGE, reported side by side, always. Give 1-exp(-lambda*w) alongside the grid figure. The 8 h flat run reads 30.0% versus 82% reported. If they differ by more than a few points, the grid figure is meaningless and every conclusion drawn from a coverage plateau is void.",
   "SPATIAL VARIANCE OF THE NEMATIC ORDER, Var(S(x)), versus path length. This is the direct saturation test for the new reading, and the exact analogue of the error-decay curves that condemned versions 1-5. Failure signature: Var(S) -> 0 (the whole plate becomes isotropic felt). Success: Var(S) holds or rises while lambda keeps growing. Report both curves on one axis.",
   "BIMODALITY OF THE S HISTOGRAM. A genuine domain structure gives two lobes — high S inside veins, near 0 at boundaries. A sensor-scale pattern gives one lobe. Report the histogram and a dip statistic, not just the mean.",
   "DOMAIN COARSENING EXPONENT. If the lay-domain structure is really grain growth, mean domain area should grow as a power law in path length. Fit and report the exponent; grain growth predicts roughly linear in time. An exponent of 0 means frozen, and frozen is the failure mode of every previous version.",
   "CROSSING-RATE ANISOTROPY RATIO nu_across / nu_along, measured in situ. Cauchy predicts nu = lambda*|sin(dtheta)|: at lambda = 8 mm/mm^2 that is 8.00 crossings/mm across a bundle, 0.70 at 5 deg, and 5.09 for isotropic felt. A real vein gives a large ratio; felt gives 1. This is the cheapest single number that distinguishes texture from mush, and it is measured by the machine itself, live.",
   "GROOVE-SCALE HEALTH: report lambda(x) against the merge threshold 1/w = 16.2 mm/mm^2 as a map, with the fraction of the plate already past it. This replaces 'coverage' as the honest progress metric and makes the 21.5 h horizon visible while the run is happening.",
   "PERSISTENCE LENGTH OF THE HEADING, replacing 'straight fraction'. Straight fraction went to 93% and meant nothing because a closed orbit is mostly straight. Persistence length must show a PLATEAU at an intermediate value — much greater than the step, much less than the disc. A plateau at the disc scale is the orbit; a plateau at the step scale is noise.",
   "EXPLICIT TESTS AGAINST THE KNOWN FAILURE SIGNATURES. Radius histogram flatness (versus 69% of length in one 10 mm ring); standard deviation of radius over the last third of the run (versus 177.4 +/- 2.9 mm for 64 of 80 hours); and the autocorrelation of the trajectory at the orbit period. Report all three every run, so a sixth closed orbit is detected within the hour rather than at hour eighty.",
   "THE NAIVE-READER TEST, which is the operational test of whether the stigmergy claim is true. Hand the finished plate to a second machine with no memory and let it map the same readings. Correlate its reading field with the first machine's internal field. High correlation means the information is genuinely in the metal and the past-selves framing is real. Low correlation means the machine was reading its own memory and the metal was decoration."
  ],
  "sources": [
   "Local code, recomputed rather than quoted: {repo_path}/only-surprise/engine/stylus.py (groove 15.907 um deep, 61.8 um wide, 360.4 um^2 cross-section, walls 30 deg from the surface plane, ploughing force 0.707 N against 2.942 N normal load, hardened re-cut reach 9.96 um)",
   "{repo_path}/only-surprise/engine/polar.py (SENSE_MM = 2.5, LOOKAHEAD_MM = 7.0, PROBE_SPREAD, CELL = 0.5, DS = 0.6 — the 81:1 sensing-to-mark ratio and the physically unavailable lookahead)",
   "{repo_path}/only-surprise/engine/scribe.py (GROOVE = 0.10 assumed during running versus 0.0618 actual, CELL = 1.0, SCRIBE_MM_S = 25.0)",
   "{repo_path}/only-surprise/engine/groove_field.py (already computes the nematic order parameter as an analysis tool: band_cos2/band_sin2, radial_order, alignment_strength — the proposal promotes this to the sensor)",
   "{repo_path}/only-surprise/engine/depth_disc.py and README.md (no depth accumulation; the burned ring as a flat matte plane 12.8 um down, 85 passes, no ridges, no mirror left)",
   "Derived and numerically verified in this session: lambda_merge = 1/w = 16.2 mm/mm^2 -> 1932 m on the disc annulus (119381 mm^2) = 21.5 h at 25 mm/s; true areal coverage 1-exp(-lambda*w) = 30.0% at 8 h flat versus 82% reported; first-order high-pass settles at k*tau = 0.4995 on a ramp and 5e-5 on a saturating input",
   "Cauchy/Buffon line-intersection formula: expected crossings per unit path = (2/pi)*lambda isotropic, lambda*|sin(dtheta)| against a parallel bundle",
   "https://www.nature.com/articles/srep00988 — Friction Anisotropy with Respect to Topographic Orientation (narrow grooves under light load can give HIGHER friction parallel; sign is regime-dependent)",
   "https://link.springer.com/article/10.1007/s12046-008-0013-6 — Friction tensor concept for textured surfaces (two principal friction coefficients; random untextured surfaces are direction-independent)",
   "https://www.sciencedirect.com/science/article/abs/pii/S0043164804002170 — Surface lay effect on rough friction in roller contact (optimal contact lay angle, symmetrical effect of sliding direction)",
   "https://www.sciencedirect.com/science/article/abs/pii/S0043164819302807 — Study of angular cutting conditions using multiple scratch tests onto low carbon steel: crossing a previous groove reduces cutting forces locally, lowest angle (10 deg) gives lowest forces. The direct experimental basis for reading crossing angle from force.",
   "https://link.springer.com/article/10.1007/s00170-015-7081-7 and https://www.mdpi.com/2076-3417/12/13/6724 — acoustic emission in single-grit scratch tests; rubbing/ploughing/cutting discriminated in the 0.03-1 MHz band",
   "https://www.sciencedirect.com/science/article/pii/S1000936121003046 — Interference mechanism and damage accumulation in high-speed cross scratches (damage radius increases as crossing angle decreases)",
   "https://journals.plos.org/ploscompbiol/article?id=10.1371/journal.pcbi.1002889 — Temporal Adaptation Enhances Efficient Contrast Gain Control (adaptation as a horizontal shift of the response curve; Naka-Rushton semi-saturation tracking the mean level)",
   "https://opg.optica.org/josaa/abstract.cfm?uri=josaa-30-10-2066 — Visual adaptation reinterpreted; near-logarithmic Naka-Rushton compression with gain control equivalent to modifying the half-saturation constant",
   "https://papers.nips.cc/paper/6383-unifying-count-based-exploration-and-intrinsic-motivation.pdf — Bellemare et al., count-based exploration bonus beta/sqrt(N): decay-free divisive habituation on a permanent monotone count",
   "https://phasefield.hu/ori and https://www.sciencedirect.com/science/article/abs/pii/S135964542200550X — orientation-field and anisotropic phase-field models of grain growth: permanent orientation state, cellular network, characteristic grain size, no decaying field",
   "https://arxiv.org/pdf/0906.0301 and https://pubmed.ncbi.nlm.nih.gov/17358103/ — DLA harmonic measure and screening (screening length ~22.7 lattice units): non-saturation by screening rather than evaporation",
   "https://arxiv.org/html/2412.19790 and https://arxiv.org/pdf/2305.12244 — Physarum agent models: trail evaporation rate mu_T ~ 0.7 is a critical parameter controlling trail persistence and network quality. The explicit statement of what this medium cannot provide."
  ]
 },
 {
  "mechanism": "Two different model families, and they answer different questions — conflating them is the main way this route gets mis-borrowed.\n\n(1) JONES' MULTI-AGENT MODEL (Artificial Life 16(2):127-153, 2010) is the one that actually GENERATES a length scale. Thousands of particle-agents on a lattice, one agent per cell (hard exclusion). Each agent has three forward sensors FL/F/FR at offset distance SO, at angle +/-SA from heading. Motor stage: every agent attempts one forward step of SS in its current heading; IF THE NEXT CELL IS OCCUPIED THE MOVE FAILS, the agent deposits NOTHING and takes a new random heading. If the move succeeds it deposits depT into the trail map. Sensory stage: rotate by +/-RA toward the strongest of the three sensor readings. The trail map is then convolved with a 3x3 mean filter and multiplied by (1-decayT). That is the whole rule. Network formation is autocrine chemotaxis: agents secrete and follow the same field, so a positive feedback loop forms along used paths; the forward-only sensor bias plus deposit-only-on-successful-move is what prevents the population collapsing into a static cluster. The macroscopic result is a reticular network with lacunae that continuously remodels (small loops contract and vanish, new sprouts bifurcate across large loops, junctions behave as if under surface tension).\n\n(2) TERO/NAKAGAKI FLOW-CONDUCTIVITY MODEL (Tero 2006; Tero et al., Science 327:439, 2010) DOES NOT GENERATE A LENGTH SCALE AT ALL — it prunes a graph you already supplied. Hagen-Poiseuille flux Q_ij = D_ij (p_i - p_j)/c_ij, Kirchhoff conservation at every node with +/-I0 injected at source/sink, giving a global Poisson solve for the pressures; then conductivity adapts as dD_ij/dt = f(|Q_ij|) - mu*D_ij, with f(Q) = |Q|^gamma / (1 + |Q|^gamma). gamma is the tree/loop knob: gamma > 1 concentrates flow into few thick tubes (tree, Steiner-like), gamma < 1 (and gamma near 1) keeps multiple parallel paths alive (loops, redundancy). Edges below a threshold D are cut. Bonifaci/Mehlhorn/Varma and Miyaji proved convergence to the shortest path only for the special case f(|Q|)=|Q|, mu=1. The mesh spacing of the output is simply the spacing of the input lattice — this model has no intrinsic wavelength, and it needs a NONLOCAL linear solve over the whole graph, so a single sensing tip cannot run it.\n\nFor the plotter, only family (1) is a candidate rule, and family (2) is only useful as a source of one idea: selection driven by competition for a CONSERVED, FINITE budget (I0), not by forgetting.",
  "minimal_ingredients": [
   {
    "ingredient": "A field with GRADED values, compared as a 3-way argmax at an offset (Jones: FL/F/FR at SO)",
    "why_essential": "The entire steering signal is argmax over three samples of a real-valued concentration. This is exactly the ingredient the current machine lacks: a binary-occupancy box filter that saturates at 1 makes all three samples equal, and argmax over ties is a coin flip. Jones' model, given a binary clipped trail, would also die — the diagnosis in the brief is correct and it is not a decay problem in the first instance, it is a QUANTISATION problem.",
    "can_it_be_dropped": "No. But it can be satisfied without decay: a box or Gaussian kernel over sparse permanent lines is graded provided local area fraction stays well below 1. With a 50 um groove and 3 mm spacing that is 1.7% coverage — hugely informative. What killed v1-v5 was that an ATTRACTIVE rule drove coverage to 82%; the field did not saturate because it is permanent, it saturated because the rule was cohesive. Sparsity has to be produced by the dynamics, and only a repulsive/exclusion sign does that."
   },
   {
    "ingredient": "Sensor offset SO large relative to the body and to the step (default SO = 9 px, SS = 1 px)",
    "why_essential": "SO is the indirect coupling range between distinct agents — 'the sensory input of one agent can be strongly affected by the actions of nearby agents'. Jones states explicitly that a MINIMUM SO OF 3 CELLS is necessary for the complex behaviour to emerge at all; below that the agent only smells its own deposit and the population never couples.",
    "can_it_be_dropped": "No — and this is the single most transferable number. SO/SS ~ 9 is the ratio that makes a 1-step-local rule produce structure at ~10-50 steps. In plotter units: step 0.6 mm, so the sensor look-ahead must be several mm, i.e. roughly where their existing few-mm box already sits. Keep the box, change what it measures."
   },
   {
    "ingredient": "Simultaneity — a POPULATION acting at the same time, with a lag between movement and the diffusion of what was deposited",
    "why_essential": "The network is a crowd phenomenon. Cohesion comes from mutual attraction between agents that are moving NOW; the 'built-in lag between agent movement and the production and diffusion of sol flux' is what makes the dynamics complex rather than a follow-the-leader ratchet. Jones tracks a single agent (Fig. 8 right) precisely to show that one agent's trajectory is NOT the network — it wanders and takes ~10^4 steps to cover a 100x100 lattice.",
    "can_it_be_dropped": "This is the ingredient the one-stroke machine cannot have, and it is where the 'past selves are the collective' reframing breaks. See compatible_with_one_stroke."
   },
   {
    "ingredient": "Hard exclusion (one agent per cell) + deposit only on SUCCESSFUL move",
    "why_essential": "This is the only inhibition in the model — Jones notes there is no explicit Turing-style inhibitor. Blocked agents stop reinforcing and re-randomise, which is what converts crowding into pattern instead of into a blob. At high density (%p 60-90) the pattern INVERTS: it is carried by 'vacancy islands' — regions of empty space surrounded by solidly packed immobile agents — and their spacing grows with SO. That is a published example of structured, scale-carrying pattern in a medium that is saturated everywhere else.",
    "can_it_be_dropped": "No, and it is FREE on permanent metal: 'already cut' is exactly an occupancy exclusion, and it never expires. This is the ingredient the medium gives you rather than takes away."
   },
   {
    "ingredient": "Diffusion (3x3 mean filter each step)",
    "why_essential": "Without it, 'the patterning would be dependent to a large extent on the initial distribution and orientation of the agents' (Jones, sec. on RD analogy). Diffusion is what makes a deposit felt at a distance and what smooths the argmax; it is the 'reaction-diffusion without an inhibitor' half of the mechanism.",
    "can_it_be_dropped": "No, but it needs no physical diffusing substance — the spatial averaging kernel of the tip sensor IS the diffusion operator. A few-mm read box applied to permanent marks is a one-shot blur, mathematically the steady state of diffuse+decay rather than an iterated one. This is a real difference: an iterated filter has memory of the field's own history; a read box does not."
   },
   {
    "ingredient": "decayT (default 0.1 per step) — evaporation of the trail",
    "why_essential": "It does TWO separable jobs, which is why the literature conflates them. (a) It bounds the field: a continuously reinforced cell equilibrates at ~depT/decayT = 5/0.1 = 50, so contrast between used and unused stays finite and RENEWABLE. (b) It sets the field's own reach: for a 3x3 mean filter the effective diffusivity is D = sigma^2/2 = (2/3)/2 = 1/3 px^2/step, so the screening length is ell = sqrt(D/decayT) = sqrt(3.33) = 1.8 px [MY DERIVATION, not published]. Note that 1.8 px << SO = 9 px — so in the multi-agent model the decay length is NOT what sets the mesh scale. Decay's load-bearing job here is (a): keeping the field re-writable so the network can REMODEL. Jones reports decay only shifts edge coarseness — higher decay gives coarser edges, very low decay gives stronger attraction and REDUCED connectivity (i.e. toward blob).",
    "can_it_be_dropped": "Job (b) can be dropped — SO already carries the scale. Job (a) cannot be dropped for an ATTRACTIVE rule. With decay = 0 and an integrating field, every cell's value grows monotonically, the relative contrast between an old trail and a new one tends to 1, and because steering is a bare argmax the SIGN survives but is dominated by the deepest historical trail: the network freezes onto its initial random condition and thereafter only deepens. That is a hysteresis ratchet, and it is functionally identical to the closed orbit the machine has found five times. [Derivation, not published — I found no published decay-free variant of the multi-agent model.]"
   },
   {
    "ingredient": "SA/RA relation — the pattern-class knob",
    "why_essential": "Jones' 500x500 SA x RA sweep (0-180 deg, 22.5 deg steps) classifies the output as reticular / labyrinthine / island-like, connectivity falling monotonically as SA and RA rise together. The specific relation matters more than either value: RA > SA (default RA 45, SA 22.5) puts the sensors off the path of travel and gives SPONTANEOUS BRANCHING and endless remodeling — network length is sacrificed for connectivity. RA = SA (45/45) gives a MINIMISING network that converges to an approximate HEXAGONAL TILING that is stable while continuously turning over its components. RA < SA increases contraction (blob).",
    "can_it_be_dropped": "No — this is the free structural dial and it costs nothing on metal. RA > SA is the setting for 'never stops exploring'; RA = SA is the setting for 'characteristic-spacing mesh with 120-degree junctions'. Note the third state (stable-but-turning-over) is impossible on permanent metal: turnover requires erasure."
   },
   {
    "ingredient": "Population density %p (3-15% typical)",
    "why_essential": "Sets vein thickness and lacuna count: higher %p thickens boundaries and reduces the number of lacunae. Above ~%p 60 the pattern inverts to vacancy islands. Interacts with SO: at high %p and large SO, patterning shifts from network-with-lacunae to stripes and spots, because most agents cannot move.",
    "can_it_be_dropped": "It has no direct plotter analogue (one pen), which is the same problem as simultaneity. The nearest analogue is the local density of already-cut metal, i.e. the machine's own coverage — which makes coverage a control parameter rather than a score to maximise."
   }
  ],
  "what_sets_the_length_scale": "DIRECT ANSWER: in the Jones multi-agent model it is the SENSOR OFFSET SO, not the decay rate, not the deposition rate. Jones is explicit: 'The parameter SO ... acts as a scaling factor. Smaller SO values exhibit a more fine-grained structure, while large values show wider patterns and coarser network paths.' The mechanism given is that SO is the range of indirect coupling between distinct agents: small SO = weak coupling = fine grain; large SO = strong coupling between distant agents = coarse veins and thick paths. Reported bands: SO 3-7 fine-grained; SO 9 default; SO 15 and 25 progressively coarser (Fig. 10, all at %p 15, SA 45, RA 45, 500 steps). Minimum SO 3 for any complex behaviour. In the saturated/vacancy-island regime the same holds inversely: as SO increases, the number of vacancy islands DECREASES and their spacing INCREASES (Fig. 9, SO 9/13/19/23/28/38).\n\nNO PUBLISHED FORMULA. I searched for a scaling law (lambda vs SO) for this model and there is none — Jones reports it qualitatively with figure panels, and the follow-up literature (the 2015 Parallel Processing Letters paper, the 2023 vein-network review) repeats the same qualitative statement: 'increasing SO results in thicker networks, faster network adaptation, and coarser-grained networks'. From Fig. 5 (hexagonal tiling, 200x200 lattice, SO 9) the cell pitch reads as roughly 2-3 x SO, so lambda ~ (2-3) SO is a reasonable working estimate but IT IS MY READ OF A FIGURE, not a published relation. It should be measured, not assumed.\n\nThe other three candidates, ranked:\n- DEPOSITION RATE depT: sets field AMPLITUDE only (equilibrium ~ depT/decayT), not scale. Because steering is a scale-free argmax, depT is close to a nuisance parameter. It matters only through the ratio depT/decayT relative to the sensitivity threshold sMin (default 0).\n- DECAY decayT: second-order for scale. It controls edge coarseness and connectivity (high decay -> coarser edges; very low decay -> stronger cohesion, fewer connections), and it sets the field's own reach ell = sqrt(D/decayT) ~ 1.8 px at default, which is FIVE TIMES SMALLER THAN SO. In this model family the decay length is subdominant.\n- AGENT DENSITY %p: sets vein WIDTH and lacuna COUNT, and above ~60% flips which phase carries the pattern. It modulates the SO-set scale rather than setting it.\n\nWHERE 'DECAY SETS THE SCALE' IS LITERALLY TRUE: continuum reaction-diffusion, not the agent model. For a single diffusing-decaying morphogen the reach is ell = sqrt(D/k); for a two-species Turing system the selected wavelength comes from linear stability, lambda = 2 pi / k_c with k_c set by the ratio of the two diffusivities and the reaction rates — decay appears in both. This is the source of the belief that Physarum-like patterning 'needs decay'. It is true of the RD formulation and only weakly true of the agent formulation. That distinction is the most useful single result of this whole search.\n\nAND IN TERO: nothing sets a length scale. The flow model inherits the spacing of the graph it is given. gamma sets topology (tree vs loops), I0 sets total flux, mu sets pruning speed. If you want a characteristic spacing out of a flow model you must import it: from the FLUCTUATION correlation length of the load (Corson, PRL 2010; Katifori, Szollosi & Magnasco, PRL 104:048704, 2010 — loops appear at a size set by damage statistics or by the sparsity of simultaneously-open sinks), or from a fixed material budget (Bohn & Magnasco, PRL 2007), or from domain GROWTH (Ronellenfitsch & Katifori, PRL 2016 — growth of the domain is what generates hierarchy in an otherwise scale-free local adaptation rule).",
  "needs_decay": "essential",
  "decay_free_variants": [
   "NEGATIVE RESULT FIRST, because it is the most important finding: I could not find ANY published decay-free variant of the Jones multi-agent model, and no published analysis of the decayT -> 0 limit. What is published points the other way: Jones reports that very low decay strengthens attraction and REDUCES connectivity (toward blob), and that removing the diffusion mechanism makes the pattern hostage to the initial condition. The decay = 0 limit for a chemoATTRACTIVE integrating field is, by my derivation, a hysteresis ratchet: contrast ratios tend to 1, the argmax locks onto the deepest historical trail, the network freezes into its initial random configuration and only deepens. Anyone who tells you Physarum agent models work without evaporation is extrapolating.",
   "CHEMOREPULSION + EXCLUSION (Jones 2010, sec. 3.5, Figs 15-16). This IS the escape, and it is in the same paper. Invert the sensory rule — orient AWAY from the strongest reading — and you get regularly spaced Turing-like structures: honeycomb domains (%p 20, RA 45, SA 45, SO 40) and stripes (%p 20, RA 67.5, SA 112.5, SO 13). Spacing is again set by SO. Two properties make this decay-tolerant in a way attraction is not: (i) a repulsive rule is SELF-SPARSIFYING — it drives the agent to where the field is weakest, i.e. exactly where the field is still informative, so local coverage equilibrates at roughly (line width / spacing) instead of climbing to saturation; (ii) the pattern is carried by the UNMARKED space, and unmarked space on a permanent medium is still a real, measurable, non-degenerate quantity. Jones also shows the chemorepulsion pattern REPAIRS synthetic damage and regenerates its original spacing (Fig. 22, SO 27, %p 10) — self-healing spacing without any appeal to erasure. Caveat to be honest about: Jones' repulsive runs still had decayT on. The claim that repulsion survives decay = 0 is my inference from the self-sparsification argument, not a published result. It is cheap to test in simulation before touching metal.",
   "VACANCY-ISLAND / NEGATIVE-SPACE PATTERNING (Jones 2010, sec. 3.2-3.3, Fig. 9, Fig. 11 at %p 90 / SO 27). Published, and a direct answer to 'the field saturates': at high occupancy the informative variable stops being where the deposit IS and becomes where it IS NOT. Island spacing is set by SO and grows with it. This says a saturating occupancy sensor is not automatically dead — the same sensor read as a vacancy detector still carries a length scale. What it does NOT give you is remodeling: the islands are dissipative in the model because agents keep moving.",
   "SCREENING / LAPLACIAN GROWTH (DLA, dielectric breakdown). The canonical permanent-deposit, zero-decay system that nonetheless produces branching networks. The deposit never evaporates; what keeps the growth field informative is that the guiding field is HARMONIC and set by geometry plus boundary conditions, so protruding tips capture flux and interiors are screened — growth probability falls off exponentially with screening depth. A field defined by geometry cannot saturate, because it is not an accumulation. Locally sensable proxy for a tip: not 'how much metal is nearby' but 'how far can I travel before I meet metal' — a free-path or distance-to-nearest-groove reading. That is measurable at the tip and it is unbounded above and never saturates on a sparse pattern. Cost: pure DLA has no characteristic spacing (it is scale-free / fractal), so screening alone gives branching WITHOUT a mesh; you need noise reduction or a finite surface tension to get a tip radius and a branch pitch.",
   "CONSERVED-BUDGET COMPETITION instead of evaporation. Tero's model already has one conserved quantity doing real work: total flux I0 is fixed, so flow that goes one way does not go another — selection by scarcity. The optimal-network literature makes the bound explicit and drops evaporation entirely: Bohn & Magnasco (PRL 2007) and Ronellenfitsch & Katifori (PRL 2016) derive local adaptation dynamics as descent on a transport cost under a FIXED TOTAL MATERIAL constraint (sum over edges of length x cross-section = const). No decay term is needed because reinforcing one edge necessarily de-reinforces others through the constraint. For the plotter the conserved budget is obvious and physical: ONE STROKE OF FINITE LENGTH. Path length spent here is path length not spent there. This is a legitimate, non-mystical replacement for evaporation, and unlike evaporation it is already true of the machine.",
   "FLUCTUATING LOAD / DAMAGE as the source of loops and of loop SIZE (Katifori, Szollosi & Magnasco, PRL 104:048704, 2010; Corson, PRL 2010; and the later Nat. Commun. 2020 discontinuous loop-formation transition, PNAS 2024 breakthrough-induced loops). Cost-optimal networks under a STATIC load are trees; loops appear when the load fluctuates (most sinks closed at any instant) or when links can fail. No decay anywhere in this argument. The characteristic loop size is inherited from the statistics of the fluctuation, not from an evaporation rate. Transfer: if the machine's local 'demand' varies in space at some correlation length, it gets a mesh at that length — but then the scale comes from the drive, and you must be able to say honestly where the drive comes from and that it is not a disguised hand-drawn wavelength.",
   "BOUNDED ARCHIVE INSTEAD OF EVAPORATION (P-ACO, Guntsch & Middendorf 2002). Explicitly removes pheromone evaporation: pheromone is defined by a fixed-size FIFO population of recent good solutions; a solution entering adds its trail, a solution leaving removes it. Boundedness from finite MEMORY LENGTH rather than from a physical decay. Also MAX-MIN Ant System bounds pheromone by explicit tau_min/tau_max CLIPPING. Both are proof that stigmergic search does not require an evaporating medium. BUT: for this machine the forgetting has migrated into the agent's own head. A finite-memory internal map of its own past is legal (it is odometry, not clairvoyance) — however it is no longer the METAL that carries the information, and therefore the stigmergy claim, and the 'past selves are the collective' framing, collapse into 'a robot with a short memory'. Worth naming rather than smuggling.",
   "CURRENT-REINFORCED RANDOM WALKS (Ma, Johansson, Tero, Nakagaki & Sumpter, J. R. Soc. Interface 10:20120864, 2013). Reinforcement by CURRENT (net traffic) rather than by accumulated visits. This is the closest thing in the literature to a fix for the specific pathology in v1-v5: reinforcing on a signed, conserved flow rather than on an accumulating count is what 'avoids the self-reinforcing loops seen in standard models'. The relevance is precise — the machine's five failures were all self-reinforcing loops. A signed quantity does not saturate the way a count does."
  ],
  "compatible_with_one_stroke": "PARTIALLY, AND THE REFRAMING IS DOING LESS WORK THAN IT LOOKS. Blunt assessment, since it was asked for.\n\nWHAT SURVIVES CONTACT WITH ONE PEN:\n- The sensor geometry: three offset readings at SO with rotation RA and sensor angle SA is a one-tip rule. It is already almost what the machine does. SO/SS ~ 9 (a few mm look-ahead against a 0.6 mm step) is directly usable and is the model's real gift.\n- Exclusion: 'already cut' is a permanent occupancy exclusion, for free, forever. In Jones' model exclusion is the ONLY inhibition mechanism, and the metal supplies it natively.\n- The SA/RA dial: RA > SA for sustained branching, RA = SA for a minimising hexagonal-tiling mesh with ~120 degree junctions. Free, and it is the difference between a network and a scribble.\n- The finite one-stroke length as the conserved budget replacing evaporation.\n\nWHAT DOES NOT SURVIVE, AND THIS IS THE HONEST ANSWER TO THE STIGMERGY QUESTION:\nJones' network is a CROWD phenomenon and its cohesion comes from SIMULTANEITY — the sensory input of one agent being altered by another agent that is moving right now, with a short lag between motion and the diffusion of what was laid down. Jones tracks one agent explicitly (Fig. 8 right) to show that a single agent's trajectory is not the network: it wanders, and needs ~10^4 steps to cover a 100x100 lattice. Replace the crowd with a single pen and every interaction acquires a lag equal to the whole elapsed history. Lateral competition — the thing that makes small loops contract while large ones sprout — requires two flows to push on each other within one relaxation time. A pen cannot push against something it did an hour ago; it can only follow it or avoid it.\n\nSo: 'the collective is the machine's own past selves' is TRUE AS BOOKKEEPING and FALSE AS MECHANISM, for the attractive rule. With attraction plus a permanent medium it is strictly a ratchet — follow the deepest thing you can smell — which is precisely the closed orbit found five times, and note that the eight-machine experiment already demonstrated the converse half of this: real simultaneity with identical rules and no mutual sensing also produced no territories. Neither number nor time is the axis, as stated. The axis is the SIGN of the interaction and the ORDER of the quantity being sensed.\n\nThe reframing DOES do real work for the repulsive rule, and only there. Self-avoidance needs no simultaneity: a mark laid an hour ago is exactly as good an obstacle as one laid a second ago, because the information is geometric (where is it) and not dynamic (how fresh is it). Permanence stops being a defect and becomes the correct substrate — this is dendrite/axon self-avoidance and tiling, where the spacing signal is contact-based and never expires, and it is Jones' own chemorepulsion result where regular spacing is set by SO. The bill for this: repulsion alone gives spacing but no VEINS — no thick trunks, no hierarchy, no flow. A repulsive-only rule produces a labyrinth of characteristic pitch, which is beautiful and is honestly a lamellar phase, not a Physarum network. To get hierarchy you need reinforcement of successful traffic, which is attraction, which needs erasure. THAT is the real conflict, stated cleanly:\n\n  characteristic spacing  <- repulsion / exclusion  <- works on permanent metal\n  vein hierarchy          <- flux reinforcement     <- needs pruning, i.e. erasure\n\nThe one place they can be reconciled without erasure is a two-scale rule where the two signs act at two DIFFERENT sensor offsets — short-range attraction (join the nearest existing groove) plus long-range repulsion (stay away from the bulk of what you have cut). Short-range attraction, long-range inhibition is the generic recipe for a fixed wavelength, it needs no decay whatsoever because both terms are geometric, and the wavelength is set by the ratio of the two offsets. Jones' model contains both halves separately, in one paper, at the same SO. I found no published variant combining them at two offsets on a permanent field. That is the gap this piece would sit in, and it should be simulated before it is cut.\n\nFINAL CAVEAT ON PHYSICS, since 'may not read anything it could not physically sense' is a hard constraint: everything above assumes the tip can read a GRADED few-mm neighbourhood function of the groove field. Binary occupancy will not do it — that is the confirmed cause of the collapse. Candidates that are physically at the tip and do not saturate on a sparse pattern: distance/free-path to the nearest groove ahead; groove ORIENTATION in the neighbourhood (a permanent groove field that reads 1 everywhere in occupancy still has a nematic director and topological defects, and orientation does not saturate); crossing COUNT per unit length; and the anisotropic floor roughness already noted in this project's own history. Orientation is the strongest of these — it is the one quantity that stays informative at 100% coverage.",
  "measurable_signatures": [
   "STRUCTURE FACTOR PEAK AT FIXED k. Radially average the 2D power spectrum of the cut pattern. A blob gives power piling up at k -> 0; a scribble gives a flat/featureless S(k); a real mesh gives a peak at finite k_0 = 2 pi / lambda. THE DISCRIMINATING TEST IS TIME: the peak must SHARPEN while k_0 STAYS PUT. If k_0 drifts to lower k as a power law (t^(1/3) is the Cahn-Hilliard/coarsening signature) there is no intrinsic scale and the pattern will eventually be one big domain — a slow blob.",
   "SCALE SEPARATION RATIOS, reported as bare numbers. lambda / step (0.6 mm) should be >= 5, ideally 10-50. lambda / sensor box (a few mm) MUST be > ~2, or the 'emergent' spacing is just the sensor's own kernel width printed onto the disc — this is the single most likely way to fool yourself, and it is the number a critic will ask for first. In Jones the mesh pitch reads as roughly 2-3 x SO, so a plotter with a 3 mm box should be looking for 6-10 mm spacing; if it produces 3 mm spacing, that is the box, not emergence.",
   "PARAMETER-SCALING TEST (the real proof of emergence). Vary the sensor offset SO alone, holding the step size, the deposit and everything else fixed, and confirm lambda scales with SO. Then vary the STEP SIZE alone and confirm lambda does NOT change. A rule whose output wavelength tracks the coupling range but not the integration step contains a length it was not given; a rule whose output tracks the step size is a drawing machine with a fixed stride.",
   "SENSOR-READING ENTROPY / VARIANCE OVER TIME — the direct instrument for the saturation failure. Log the histogram of the raw sensor value every N steps. The v1-v5 death signature is variance -> 0 with mass piling at 1 (saturation) and it will be visible in the first hour, long before the closed orbit is visible in the plot. Set a hard gate: if the interquartile range of the sensor reading falls below some fraction of its first-hour value, the run has already failed. Also track local area coverage: it must PLATEAU FAR BELOW saturation, near the geometric prediction (groove width / spacing) — 50 um / 6 mm ~ 0.8%, not 82%.",
   "LOOP DENSITY (first Betti number per unit area) AND ITS TIME COURSE. Skeletonise, then count independent cycles. Trees have beta_1 = 0; a Steiner-like optimum has beta_1 = 0; a real vein network has a stable, nonzero loop density. Also count sprouting and closure EVENTS per hour separately: Jones' living network is defined by small loops contracting while new sprouts bifurcate across large ones. A pattern with loops but zero events per hour is a finished picture; a pattern with a steady, non-decaying event rate is a live process. On permanent metal contraction is impossible, so honestly expect sprouting-only, and report the sprout rate as the aliveness metric.",
   "JUNCTION ANGLE DISTRIBUTION. A minimising mesh (Jones RA = SA = 45, approximate hexagonal tiling; also Plateau/Physarum) concentrates junction angles near 120 degrees with three-way nodes dominating. A scribble gives a broad angle distribution and mostly four-way crossings (which is what a non-lifting tool produces by accident). Fraction of 3-way vs 4-way nodes is a cheap, sharp discriminator between structure and traffic.",
   "NEAREST-NEIGHBOUR SPACING CV. Measure gaps between adjacent groove segments along many radial and tangential transects. Poisson/scribble gives coefficient of variation ~ 1; a genuine characteristic spacing gives a unimodal distribution with CV ~ 0.2-0.4. Report CV, not just a mean spacing — a mean spacing exists for random lines too.",
   "ORIENTATIONAL CORRELATION LENGTH xi. Compute the nematic order parameter field from local groove direction and its correlation length. Emergence at a much larger scale than the rule means xi >> step and ideally xi >> lambda, with a countable, sparse set of topological defects. This doubles as the fallback sensor: if occupancy saturates, orientation does not.",
   "TURN-RATE POWER SPECTRUM (the closed-orbit detector, and it should be running live). A locked orbit shows a sharp line at the orbit frequency plus harmonics; an exploring rule shows a broadband spectrum. This is a far earlier and less ambiguous alarm than watching coverage plateau — the previous runs' orbits would have shown as a growing spectral line hours before the coverage curve flattened. Log peak-to-broadband ratio continuously.",
   "RADIUS-OCCUPANCY DISTRIBUTION, given the polar geometry and the specific v4/v5 failures (69% of 7200 m in one 10 mm ring; radius locked to 177.4 +/- 2.9 mm for 64 hours). Report the entropy of the visited-radius histogram against the uniform-in-area expectation, and the maximum fraction of path length inside any 10 mm annulus. These two numbers alone would have flagged both prior collapses, and they must be gates on the next run, not post-mortem statistics."
  ],
  "sources": [
   "Jones, J. (2010) Characteristics of Pattern Formation and Evolution in Approximations of Physarum Transport Networks. Artificial Life 16(2):127-153 — the primary source for the agent rule, Table 1 parameter defaults (%p 3-15, diffK 3, decayT 0.1, SA 22.5/45, RA 45, SO 9, SW 1, SS 1, depT 5), the SO scaling section 3.2, the decay/density section 3.3, the SA x RA pattern-class sweep 3.4, and the chemorepulsion regular-spacing results 3.5. Full text: https://uwe-repository.worktribe.com/output/980579/characteristics-of-pattern-formation-and-evolution-in-approximations-of-physarum-transport-networks (a readable copy that WebFetch could not parse but pdftotext could: extracted text left at {temporary_worktree}/scratchpad/jones2010.txt)",
   "https://pubmed.ncbi.nlm.nih.gov/20067403/ — Jones 2010 abstract/record",
   "https://arxiv.org/pdf/2305.12244 — Formation and Optimisation of Vein Networks in Physarum (2023 review): restates the minimum SO of 3 cells, 'increasing SO results in thicker networks, faster network adaptation, and coarser-grained networks', and the alpha (rotation) vs beta (sensor) interplay — alpha > beta gives spontaneous branching, alpha < beta increases contraction",
   "https://arxiv.org/abs/1511.05869 — Jones, Mechanisms Inducing Parallel Computation in a Model of Physarum polycephalum Transport Networks (Parallel Processing Letters 25(1):1540004, 2015)",
   "https://arxiv.org/pdf/1712.02910 — Physarum-inspired Network Optimization: A Review. Source for the exact Tero flow-conductivity equations: Q_ij = D_ij (p_i - p_j)/c_ij; D_ij = pi r^4 / 8 xi; dD_ij/dt = f(|Q_ij|) - mu D_ij; the network Poisson equation with +/- I0 at source/sink; threshold-based edge cutting; and the note that the Miyaji and Bonifaci et al. convergence proofs hold only for f(|Q|) = |Q| and mu = 1",
   "https://markfricker.org/wp-content/uploads/2015/12/tero_et_al-2010-science-327-439.pdf — Tero et al., Rules for Biologically Inspired Adaptive Network Design, Science 327:439-442 (2010): f(Q) = |Q|^gamma / (1 + |Q|^gamma), gamma as the tree-vs-loops knob (low gamma keeps parallel paths and loops, high gamma concentrates into a tree), gamma = 2, 3, 4 tested",
   "https://link.springer.com/article/10.1007/s00285-016-1036-y and https://arxiv.org/abs/1606.04225 — Bonifaci, A revised model of fluid transport optimization in Physarum polycephalum (J. Math. Biol. 2016): argues the controlling variable is the flow's PRESSURE GRADIENT rather than flux amount, extending the class of admissible response functions",
   "https://royalsocietypublishing.org/rsif/article/10/80/20120864/35084/Current-reinforced-random-walks-for-constructing — Ma, Johansson, Tero, Nakagaki & Sumpter, Current-reinforced random walks for constructing transport networks, J. R. Soc. Interface 10:20120864 (2013): reinforcement by current rather than by visit count, which 'avoids the self-reinforcing loops seen in standard models'",
   "https://arxiv.org/abs/0906.0006 and https://link.aps.org/doi/10.1103/PhysRevLett.104.048704 — Katifori, Szollosi & Magnasco, Damage and Fluctuations Induce Loops in Optimal Transport Networks, PRL 104:048704 (2010): loops (hence a mesh) arise from damage-averaging or sparse fluctuating sinks, with no decay term anywhere",
   "http://www.lps.ens.fr/~corson/pdf/prl-10.pdf — Corson, Fluctuations and Redundancy in Optimal Transport Networks, PRL (2010): the independent derivation of the same result",
   "https://web.sas.upenn.edu/katifori/publications/ — index for Bohn & Magnasco, Structure, Scaling, and Phase Transition in the Optimal Transport Network, PRL (2007) and Ronellenfitsch & Katifori, Global Optimization, Local Adaptation, and the Role of Growth in Distribution Networks, PRL (2016): local adaptation under a FIXED TOTAL MATERIAL constraint, i.e. bounded by conservation rather than evaporation, with domain growth generating hierarchy",
   "https://www.nature.com/articles/s41467-020-19567-2 — Discontinuous transition to loop formation in optimal supply networks, Nat. Commun. (2020)",
   "https://www.pnas.org/doi/abs/10.1073/pnas.2401200121 — Breakthrough-induced loop formation in evolving transport networks, PNAS (2024)",
   "https://link.springer.com/chapter/10.1007/3-540-46004-7_8 and https://cgi.cse.unsw.edu.au/~odiessel/papers/fpt02guntsch.pdf — Guntsch & Middendorf, A Population Based Approach for ACO (2002): pheromone evaporation REPLACED by insertion into / removal from a fixed-size population of good solutions — a genuinely evaporation-free stigmergic search, where boundedness comes from finite memory length",
   "https://cshperspectives.cshlp.org/content/2/9/a001750 — Self-avoidance and Tiling: Mechanisms of Dendrite and Axon Spacing (Cold Spring Harb. Perspect. Biol.): contact-based self-avoidance and tiling as a spacing mechanism that requires no decaying field",
   "https://link.springer.com/book/10.1007/978-3-319-16823-4 — Jones, From Pattern Formation to Material Computation: Multi-agent Modelling of Physarum Polycephalum (Springer 2015), the book-length treatment of the model",
   "NOT FOUND, searched for specifically: (a) any closed-form or fitted scaling law for mesh wavelength vs SO in the multi-agent model — only qualitative statements and figure panels exist; (b) any published decay-free (decayT = 0) variant of the Jones multi-agent model or analysis of that limit. The decay-length estimate ell = sqrt(D/decayT) = sqrt((2/3)/2 / 0.1) = 1.8 px, and the conclusion that it is ~5x smaller than the default SO of 9 px, are MY derivations from the stated 3x3 mean filter and decayT = 0.1, not published results."
  ]
 },
 {
  "mechanism": "REACTION-DIFFUSION / LALI, GROUNDED — AND WHAT SURVIVES CONTACT WITH A MEDIUM THAT CANNOT FORGET.\n\n1. THE CLASSICAL TURING MECHANISM, AND WHY DECAY IS FORCED IN IT.\nFor u_t = f(u,v) + Du∇²u, v_t = g(u,v) + Dv∇²v, perturbations ~exp(λt+ik·x) give λ² − λ[trJ − k²(Du+Dv)] + h(k²) = 0 with h(K) = DuDv·K² − (Dv·f_u + Du·g_v)K + detJ. The four conditions are: trJ = f_u+g_v < 0; detJ = f_u g_v − f_v g_u > 0 (uniform state stable); Dv·f_u + Du·g_v > 0; and (Dv·f_u + Du·g_v)² > 4 DuDv detJ (h dips below zero).\nConditions 1 and 3 together, with Du,Dv > 0, FORCE f_u and g_v to have opposite signs. The standard resolution is f_u > 0 (short-ranged species self-activates) and g_v < 0 with |g_v| > f_u (long-ranged species self-removes) and Dv > Du. So in the two-species local-kinetics form, decay of the inhibitor is not a modelling convenience — it is a necessary condition. Gray–Scott needs both its feed F(1−u) and its removal −(F+k)v; without the removal v accumulates without bound and the reactor has no steady state at all. Gierer–Meinhardt needs its −μa and −νh explicitly. (Caveat, honestly: the strict activator/inhibitor sign structure is a two-species artefact; with ≥3 species Turing instability exists without a canonical activator-inhibitor pair — see the \"generalised Turing mechanism\" work. It does not rescue the decay-free case, but it does mean \"one must self-activate, one must self-decay\" is not a law of nature.)\n\n2. DOES LALI NEED DECAY, OR ONLY TWO RANGES WITH OPPOSITE SIGN? — THE ANSWER SPLITS INTO THREE JOBS.\nThis is the crux and the literature is unambiguous once you separate what decay is doing. Decay does three logically distinct jobs, and each has a decay-free substitute:\n (a) It supplies the long range. A diffusive range is ℓ = √(D/rate). A range built out of diffusion cannot exist without a rate. THIS is why RD needs decay — not because inhibition needs decay, but because diffusion-plus-decay is how RD manufactures a length. If instead the two ranges are written EXPLICITLY into the operator — a Mexican-hat / difference-of-Gaussians kernel with widths σ1 < σ2, or the −ν∇² − κ∇⁴ pair — then no rate is needed and no decay is needed. Two ranges of opposite sign is genuinely sufficient for the instability. Siebert & Schöll show Turing patterns induced purely by Mexican-hat nonlocal feedback; neural-field/Amari models and Swift–Hohenberg are the same statement.\n (b) It prevents saturation. Substitutes: divisive normalization (Weber-law read), or hard bounds on the field (MAX–MIN Ant System's τ_min/τ_max is exactly this — bounding pheromone, not evaporating it, is what actually kills stagnation in ACO).\n (c) It selects and freezes a finite wavelength, and arrests coarsening. This is where decay-free schemes genuinely pay. Pure mass-conserving RD (McRD, wave-pinning) patterns with NO production or degradation at all — mass redistribution alone — but the Frey-group review is explicit that pure McRD systems COARSEN INDEFINITELY, winner-takes-all, down to a single domain; wavelength selection requires weakly broken conservation, i.e. a little production/degradation, which sets Λ_stop and Λ_split. Independently, the Turing formula says the same thing: λ_c = 2π(DuDv/detJ)^(1/4), and as removal rates → 0, detJ → 0 and λ_c → ∞. Two different literatures, one conclusion: WITHOUT A RATE THE PATTERN STILL FORMS, BUT ITS LENGTH SCALE DIVERGES.\n\n3. THE DECISIVE QUESTION: DoG READ OF A MONOTONICALLY GROWING DEPOSIT.\nWorked through properly, because the answer is not one of the three offered options — it is all three, depending on one thing.\nLet N(x,t) ≥ 0 be the deposit, w = G_σ1 − G_σ2 with both Gaussians unit-mass, so ∫w = 0 and ŵ(0) = 0 (DC-balanced bandpass). R = w*N.\n CASE A — BOUNDED DEPOSIT (the current sensor: binary occupancy, ceiling 1). As the neighbourhood fills, N → const, and R → 0 EXACTLY. A zero-mean kernel does NOT rescue a bounded field. DoG on binary occupancy dies the same death as the present read, only more elegantly. This must be said plainly: the fix is not the kernel, it is the quantity.\n CASE B — UNBOUNDED, UNIFORM ADDITIVE GROWTH, N = N₀(x) + ct. R is EXACTLY INVARIANT: the constant is annihilated. This is the one real and unconditional gain of a zero-mean read — indifference to how much total metal has been cut.\n CASE C — UNBOUNDED, PROPORTIONATE GROWTH, N = t·ρ(x). R = t·(w*ρ) GROWS LINEARLY AND WITHOUT BOUND. It does not go to zero and it does not stay finite. Zero crossings and sign structure are time-invariant; magnitude diverges, so any controller consuming R raw will hard-saturate — a different death from the same cause.\n CASE D — UNBOUNDED BUT ONLY STOCHASTICALLY STRUCTURED, N = t·ρ̄ + √t·ξ. R grows as √t (finite, never zero) but RELATIVE contrast decays as t^(−1/2). Absolutely informative, relatively useless.\n THE FIX IS TO DIVIDE, NOT TO SUBTRACT. Use C = (G_σ1*N)/(G_σ2*N) − 1, equivalently a DoG of log N. Then: uniform multiplicative growth adds a constant to log N and is annihilated exactly; C is bounded below by −1; and in Case C, C is STATIONARY IN TIME — a non-saturating, structured, fixed-length-scale field out of a strictly permanent, strictly growing deposit. This is the honest positive answer to the hard part. Divisive normalization is the arithmetic that evaporation was doing physically. Nothing is erased; the read is simply made scale-free in deposit amplitude. Retinal ON/OFF centre-surround plus divisive contrast normalization is precisely this design, and it is what lets an eye work across ~10 decades of luminance without any \"decay of light\".\n BUT IT CARRIES A HARD SIDE CONDITION, which is the real design constraint: Case D shows that relative contrast washes out as t^(−1/2) unless deposition is MULTIPLICATIVE (self-reinforcing) rather than additive-random. So local positive feedback — cut preferentially where the accumulator is already locally high — is not decoration; it is what keeps a Weber-normalized read of a permanent medium alive forever. Three jobs, three decay-free substitutes: explicit kernel ranges for the scale, divisive normalization for saturation, local self-reinforcement for contrast persistence.\n\n4. YES — THERE IS A KNOWN FORMULATION WHERE THE PATTERN-FORMING FIELD IS THE DERIVATIVE OF AN ACCUMULATING QUANTITY. THIS IS THE STRONGEST HIT IN THE WHOLE SEARCH.\n (i) KPZ / noisy Burgers \"tilt\" formulation. h(x,t) grows without bound forever; the dynamics closes on u = ∇h, and u HAS A GENUINE STATIONARY STATE. Stated directly in the surface-growth literature: the height gradients can be stationary even though the height field itself grows with time. Structurally exactly what is needed. Weakness: KPZ is self-affine and SCALE-FREE — no characteristic length. Non-saturation without a length scale.\n (ii) KURAMOTO–SIVASHINSKY — the one that has both. h_t = ν∇²h − κ∇⁴h + ½(∇h)², with ν destabilizing. There is NO −αh term: h has no decay and drifts/grows without bound. The instability and the pattern live entirely in the derivatives. Dispersion ω(k) = |ν|k² − κk⁴, most-unstable k_max = √(|ν|/2κ), λ_max = 2π√(2κ/|ν|). In the unit-coefficient form k = 1/√2 and λ = 2√2π ≈ 8.89. κ/ν has units of length² and CONTAINS NO TIME CONSTANT AT ALL. This is the existence proof: a fixed length scale out of a monotonically growing, decay-free accumulator, because the scale comes from the ratio of two spatial-derivative orders rather than from √(D/rate).\n (iii) BRADLEY–HARPER ION-BEAM EROSION — the same equation, in a physically irreversible material-removal medium. Curvature-dependent sputter yield gives a negative effective surface tension (roughening), surface self-diffusion gives a ∇⁴ smoothing, and a wavelength is selected: λ = 2π√(2B/|ν|). Material only ever leaves; nothing is restored; and a clean periodic pattern with a fixed spacing emerges anyway. It is the closest physical precedent to a diamond point in steel, and it is the right thing to cite when someone says \"reaction-diffusion needs evaporation\".\n (iv) Abelian sandpile / critical-slope models. Height accumulates without bound, local toppling rules only, no decay, and large-scale self-similar patterns with proportionate growth emerge (Dhar & Sadhu). Again: the controlled variable is the SLOPE of an unbounded accumulator. Scale-free, like KPZ.\n (v) Laplacian growth / DLA / dielectric-breakdown. Permanent aggregate; growth rate ∝ |∇φ|^η — the pattern-forming field is the gradient of a harmonic field, never the deposit. Branching networks, screening, characteristic finger width from destabilizing gradient vs stabilizing curvature. Decay-free. Weakness for this machine: needs a global Laplace solve, which no tip sensor can provide locally.\n\n5. THE HONEST CAVEATS, stated because they will bite.\n (a) Undamped KS is SPATIOTEMPORALLY CHAOTIC. The ion-erosion literature is explicit that a damping term (−αh, a decay of the accumulated height) is what stabilizes and freezes an ordered ripple; without it the late-time state is chaotic with no long-range order. So decay-free KS gives a persistent CHARACTERISTIC CELL SIZE forever, with cells continually born, merging and dying — not a frozen periodic lattice. For an artwork asking for \"veins, networks, cells\" rather than a crystal, that is arguably the desired outcome, but it must be chosen knowingly, not discovered at hour 60.\n (b) In Bradley–Harper the stabilizing ∇⁴ term is a PHYSICAL relaxation — atoms actually migrate; the surface does slowly forget. Room-temperature steel does not. So the machine must supply the ∇⁴ itself, in the controller (a small-σ blur in the read, or a hard turn-rate/curvature limit on the stroke). That is legitimate — it is a computation, not a physical claim — but it means the short range is imported, not found.\n (c) DEEPEST CAVEAT, and it goes to the brief's own criterion. Every decay-free wavelength-selecting mechanism gets its length from a ratio of two EXPLICIT ranges in the rule (σ2/σ1, or κ/ν). So under any of these routes the characteristic spacing will be something the rule does contain, roughly proportional to σ2. The length scale will not be emergent in the strict sense demanded. What CAN be genuinely emergent, and is the honest target: TOPOLOGY AND HIERARCHY — branch points, loop-area distributions, vein-thickness hierarchy, junction angles, Voronoi-like cell walls — none of which appear anywhere in a statement about two blur radii. And a length scale can become emergent if it arises from a NONLINEAR balance (coarsening arrest, state-dependent ν) rather than sitting in the kernel; the test for that is whether λ scales as σ¹ (imported) or sub-linearly (selected). That test is cheap and should be run first.\n\n6. ON THE STIGMERGY REFRAMING — is it doing real work?\nPartly, and the part that is real is not the part usually claimed. If the machine reads a DoG of its own LOGGED path, the metal mediates nothing: the writing is deterministic and known, so this is ordinary memory wearing a nicer word, and calling it stigmergy is only a sentence. It becomes real exactly where the commanded path and the cut path DISAGREE. Version 4 already measured this: the rotary quantisation means about a fifth of the requested shape never reaches the metal. That discrepancy field is information ONLY the metal has, it is not in any log, it is spatially structured (0.38 mm at the rim, 0.02 mm at r=10), and it does not saturate. That is the one channel where the medium genuinely carries information from past selves to the present one, and it is also the axis that already bought a factor of ten. Point the sensor at the DISCREPANCY, not at the occupancy.",
  "minimal_ingredients": [
   {
    "ingredient": "Two spatial ranges of opposite sign, both explicit in the rule (short-range positive, long-range negative) — a zero-mean/DC-balanced kernel w = G_σ1 − G_σ2, or its differential-operator equivalent −ν∇² − κ∇⁴",
    "why_essential": "This IS the instability. Nothing else in the LALI family generates structure. And making both ranges explicit is precisely what removes the need for decay: a diffusive range is √(D/rate) and cannot exist without a rate, whereas a kernel width is just a number. Siebert & Schöll get Turing patterns from Mexican-hat nonlocal feedback alone; Swift-Hohenberg and neural-field models are the same statement.",
    "can_it_be_dropped": "No. Drop it and there is no mechanism at all. It can be REALISED differently — kernel, ∇²/∇⁴ pair, or depletion of a fast-spreading conserved substrate — but the opposite-sign two-range structure itself is non-negotiable."
   },
   {
    "ingredient": "An UNBOUNDED (or very high ceiling) accumulator as the written field — pass count, integrated path length in cell, groove-edge crossings per unit length — never a binary occupancy bit",
    "why_essential": "A zero-mean kernel annihilates constants, so it is immune to uniform additive growth (exactly invariant). But it tracks absolute contrast, and a BOUNDED field must lose contrast as it approaches its ceiling, so DoG on binary occupancy goes to zero exactly as the present read does. The kernel is not the fix; the quantity is. Physically readable candidate: groove-edge crossings per unit scan length has roughly 50-60x the dynamic range of occupancy fraction at ~50 um groove width in a ~3 mm box.",
    "can_it_be_dropped": "No — this is the single load-bearing change. Every one of the five failures is this ceiling. Note that depth cannot supply it (spring-loaded, non-accumulating), so it must be crossing/line density read geometrically, or an internal counter."
   },
   {
    "ingredient": "Divisive (Weber) normalization of the read: C = (G_σ1*N)/(G_σ2*N) − 1, equivalently a DoG of log N",
    "why_essential": "This is the arithmetic substitute for evaporation. It makes the read exactly invariant under uniform multiplicative growth of the deposit, bounds it below by −1, and makes it stationary in time when the deposit grows proportionately (N = t·ρ). Without it, an unbounded accumulator makes the raw DoG response grow linearly without bound and the controller saturates — a different death from the same cause. MAX-MIN Ant System's τ_min/τ_max bounds are the crude version of the same idea, and are what actually kills stagnation in ACO.",
    "can_it_be_dropped": "Only if the deposit were bounded AND something erased it. Neither holds here. Ratio, never difference."
   },
   {
    "ingredient": "Local self-reinforcement at the small scale (deposit preferentially where the accumulator is already locally high)",
    "why_essential": "The hidden side condition on the whole scheme. If deposition is additive-random, N = t·ρ̄ + √t·ξ and RELATIVE contrast decays as t^(−1/2) — the normalized read fades even though the deposit is unbounded. Only multiplicative, self-reinforcing accumulation keeps relative contrast O(1) forever. Positive feedback is doing decay's contrast-maintaining job.",
    "can_it_be_dropped": "No. Dropping it reintroduces the same slow fade, just with exponent 0.5 instead of a hard ceiling. It is also the 'local activation' half of LALI, so dropping it breaks ingredient 1 anyway."
   },
   {
    "ingredient": "A stabilizing SHORT-scale term supplied by the controller: the inner blur σ1, or equivalently a hard turn-rate/curvature limit on the stroke (the ∇⁴ of Kuramoto-Sivashinsky)",
    "why_essential": "Without a short-wavelength sink the fastest-growing mode is the smallest resolvable one and the output is noise at the 0.6 mm step. In Bradley-Harper this term is physical (surface self-diffusion actually smooths the eroded surface). Room-temperature steel does not do that, so the machine must compute it. λ = 2π√(2κ/|ν|) is entirely this ratio, with no time constant in it.",
    "can_it_be_dropped": "No, if a finite characteristic spacing is wanted. It can be dropped if scale-free/self-affine structure (KPZ, sandpile) is acceptable instead."
   },
   {
    "ingredient": "Read the DISCREPANCY between commanded and actual cut, not the occupancy",
    "why_essential": "This is the only quantity the metal knows that the machine's own log does not, so it is the only channel that makes the stigmergy claim literally true rather than decorative. Version 4 already measured it: ~1/5 of the commanded shape never reaches the metal, structured by radius (0.38 mm at rim, 0.02 mm at r=10), and it bought a factor of ten in error survival. It does not saturate.",
    "can_it_be_dropped": "Yes, mechanically — the scheme runs on an internal accumulator alone. But then the metal is not a medium, it is an output, and 'collective intelligence of past selves' is only a nice sentence."
   },
   {
    "ingredient": "Noise / symmetry breaking",
    "why_essential": "Any Turing-type instability needs something to amplify. Deterministic quantisation error is enough and is already present in abundance on the polar machine.",
    "can_it_be_dropped": "Effectively yes — it is free here. Do not add explicit randomness before checking whether the rotary quantisation already supplies it; version 4 suggests it does."
   },
   {
    "ingredient": "Decay / turnover / weakly broken conservation",
    "why_essential": "Not needed for the instability — mass-conserving reaction-diffusion patterns with zero production and degradation, and Kuramoto-Sivashinsky has no −αh term at all. It is needed only to ARREST COARSENING and freeze long-range order. Pure mass-conserving systems coarsen indefinitely to a single domain (winner-takes-all); the Turing formula agrees, since λ_c = 2π(DuDv/detJ)^(1/4) diverges as removal rates → 0. Undamped KS keeps a characteristic cell size forever but stays spatiotemporally chaotic.",
    "can_it_be_dropped": "YES — and this is the finding that matters. The cost is specific and must be chosen deliberately: either indefinite coarsening (mass-conserving route) or a persistent characteristic cell size with no long-range order (KS route). For veins, networks and cells rather than a lattice, the chaotic-cellular outcome is probably what is wanted."
   }
  ],
  "what_sets_the_length_scale": "FOUR DIFFERENT ANSWERS, AND THEY ARE NOT EQUIVALENT — one needs a rate and three do not.\n\n(1) CLASSICAL TWO-SPECIES TURING. h(K) = DuDv·K² − (Dv f_u + Du g_v)K + detJ is minimised at K = (Dv f_u + Du g_v)/(2DuDv); at onset h = 0 at its minimum, which gives (Dv f_u + Du g_v)² = 4DuDv·detJ and therefore\n  k_c = (detJ / (DuDv))^(1/4),  λ_c = 2π (DuDv / detJ)^(1/4).\nUnits check: detJ is rate², DuDv is length⁴·rate⁻², ratio is length⁴, fourth root is a length. Equivalently λ_c = 2π√(ℓ_u ℓ_v) — 2π times the GEOMETRIC MEAN of the two diffusion lengths ℓ_i = √(D_i / rate_i). It depends on BOTH diffusivities (as the fourth root of their product — so a 16x change in a diffusivity moves the wavelength only 2x; this is why real Turing wavelengths are hard to tune) and on the reaction rates through detJ. The rates in the denominator are REMOVAL rates. This is the precise sense in which decay sets the scale: as decay → 0, detJ → 0 and λ_c → ∞. Reported empirically in nanometric Turing patterns as a (Ka/Kb)^(1/4) dependence of the most unstable wavenumber.\n\n(2) NONLOCAL / DIFFERENCE-OF-GAUSSIANS KERNEL. For w = G_σ1 − A·G_σ2, ŵ(k) = exp(−σ1²k²/2) − A·exp(−σ2²k²/2), maximised at\n  k_max² = 2 ln(A σ2²/σ1²) / (σ2² − σ1²),  λ = 2π/k_max, which is O(σ2).\nNO TIME CONSTANT APPEARS. The scale is pure kernel geometry. This is the cheapest decay-free route and the most directly buildable on this machine: σ1 and σ2 are just two read radii. Price: the scale is imported, not emergent.\n\n(3) KURAMOTO-SIVASHINSKY / BRADLEY-HARPER (the derivative-of-an-accumulator route).\n  ω(k) = |ν|k² − κk⁴,  k_max = √(|ν|/2κ),  λ = 2π√(2κ/|ν|).\nIn the unit-coefficient KS form k = 1/√2, λ = 2√2π ≈ 8.886. For ion-beam ripples λ = 2π√(2B/|ν|) with |ν| the curvature-dependent erosion coefficient (∝ ion flux) and B the surface-diffusion smoothing; experimentally λ ~ (fT)^(−1/2)exp(−ΔE/2k_BT). κ/ν has units of length² and contains no rate. The height erodes/accumulates without bound while λ stays fixed. This is the route to cite when told that pattern formation requires evaporation.\n\n(4) MASS-CONSERVING REACTION-DIFFUSION. NOTHING sets the scale: pure McRD coarsens indefinitely by mass-competition instability. A scale appears only when conservation is WEAKLY BROKEN, which arrests coarsening above Λ_stop and splits domains above Λ_split. The one intrinsic length is the interface width ℓ_int ~ √(D_m τ_r) with τ_r the reactive turnover time — again a diffusion length over a rate. Interfacial tension σ ~ ℓ_int, curvature shift δη ~ ℓ_int·κ.\n\nCONSEQUENCE FOR THIS MACHINE. If the scale is wanted at, say, 8 mm on a plate whose step is 0.6 mm and whose read box is ~3 mm, route (2) sets σ2 ≈ 3-4 mm and route (3) sets κ/ν ≈ (1.3 mm)². Both are single numbers in the rule, which means the SPACING will not be an emergent quantity. The emergent quantities have to be sought in topology (branch density, loop-area distribution, junction angles, thickness hierarchy) and in whether λ scales sub-linearly with σ2, which would prove a nonlinear selection is doing work the kernel does not contain.",
  "needs_decay": "helpful",
  "decay_free_variants": [
   "MASS-CONSERVING REACTION-DIFFUSION (McRD) / WAVE PINNING — Mori, Jilkine & Edelstein-Keshet; Halatek & Frey; the 2025 'Pattern Formation Beyond Turing' review. Zero production, zero degradation. Patterns form purely by redistribution of a conserved mass between a slow (membrane-bound) and a fast (cytosolic) state; a negative reactive-nullcline slope dc*/dm < 0 is the instability condition; stationary interfaces satisfy a flux-balance construction c + d·m = eta_stat with d = D_m/D_c. PROOF that LALI does not need decay. CAVEAT, explicit in the review: pure McRD coarsens indefinitely, winner-takes-all, to a single domain — no wavelength selection.",
   "SUBSTRATE DEPLETION (activator-depleted-substrate, Gierer-Meinhardt variant; Schnakenberg) — the long-range negative signal is CONSUMPTION of a fast-spreading finite pool, not decay of an inhibitor. Directly instantiable here: UNCUT METAL is a real, finite, depletable substrate and cutting consumes it irreversibly. Note the honest limit: it is depletion, so it runs out, and it runs out locally at the read-box scale long before the plate is globally exhausted — which is exactly the observed 82% plateau.",
   "NONLOCAL MEXICAN-HAT / DIFFERENCE-OF-GAUSSIANS FEEDBACK — Siebert & Schoell (EPL 2015) get fronts and Turing patterns from sign-changing nonlocal coupling alone; the neural-field (Amari/Wilson-Cowan) and Swift-Hohenberg families are the same idea. The Mexican-hat kernel is not positive definite and has negative second moment. Both ranges are explicit numbers, so NO RATE AND NO DECAY IS REQUIRED to set the wavelength. Cheapest route to build on this machine: two read radii.",
   "KURAMOTO-SIVASHINSKY — h_t = nu*grad^2 h - kappa*grad^4 h + (grad h)^2/2. NO -alpha*h term: the accumulated field h has no decay and grows/drifts without bound, while the instability and the selected wavelength live entirely in its derivatives. lambda = 2*pi*sqrt(2*kappa/|nu|), a pure ratio of two spatial operators with no time constant. THE existence proof for 'fixed length scale from a monotonically growing, decay-free accumulator'. Caveat: the undamped equation is spatiotemporally chaotic — a persistent characteristic CELL SIZE, not a frozen lattice; the ion-erosion literature is explicit that the damping term is what freezes an ordered ripple.",
   "BRADLEY-HARPER ION-BEAM SPUTTERING / EROSION RIPPLES (and the Cuerno-Barabasi KS-type nonlinear extension) — the closest PHYSICAL precedent: an irreversible material-removal medium that cannot be un-cut, producing a clean fixed-wavelength pattern, lambda = 2*pi*sqrt(2B/|nu|), from curvature-dependent removal against short-range smoothing. Caveat: the smoothing B is real surface self-diffusion, i.e. the material does slowly forget. Room-temperature steel does not, so this machine must supply the grad^4 term in its controller (inner blur, or a turn-rate/curvature limit).",
   "KPZ / NOISY BURGERS 'TILT' FORMULATION — the height grows forever, but the dynamics closes on u = grad h and the GRADIENT FIELD HAS A GENUINE STATIONARY STATE (stated in exactly those terms in the surface-growth literature; Fogedby's soliton/domain-wall picture of the stationary morphology). Structurally the answer to 'can the pattern-forming field be the derivative of an accumulating quantity'. Weakness: self-affine and scale-free, so non-saturation WITHOUT a length scale.",
   "ABELIAN SANDPILE / CRITICAL-SLOPE MODELS (Dhar & Sadhu, 'Pattern formation in growing sandpiles' / 'fast-growing sandpiles') — unbounded accumulation, purely local toppling rules, no decay anywhere, and large-scale self-similar patterns with proportionate growth. The controlled variable is the SLOPE of an unbounded pile. Again scale-free rather than wavelength-selecting.",
   "LAPLACIAN GROWTH / DLA / DIELECTRIC-BREAKDOWN MODEL — permanent aggregate, growth probability proportional to |grad phi|^eta: the pattern-forming field is the gradient of a harmonic potential, never the deposit itself. Gives branching networks, screening, and a characteristic finger width from destabilizing gradient against stabilizing curvature, with no decay. Weakness for this machine: requires a global Laplace solve, which a tip sensor cannot supply locally.",
   "DIVISIVE / WEBER NORMALIZATION AND HARD BOUNDS as arithmetic substitutes for evaporation — DC-balanced bandpass plus divisive contrast normalization (the retinal ON/OFF centre-surround design, and adaptive local contrast normalization in vision) makes a read scale-free in signal amplitude across many decades without anything decaying. MAX-MIN Ant System's [tau_min, tau_max] clamping is the crude discrete version, and in ACO it is the bounding, not the evaporation, that demonstrably prevents search stagnation and premature convergence — which is precisely the failure mode all five previous versions exhibit."
  ],
  "compatible_with_one_stroke": "YES, with four specific consequences that have to be designed for rather than discovered.\n\n1. RETRACING IS FREE, AND THAT IS WHAT MAKES A NETWORK DRAWABLE IN ONE STROKE. Depth does not accumulate — pass two finds nothing left to cut — so re-traversing an existing groove costs nothing and is invisible. A vein network is therefore reachable by a single non-lifting stroke: traverse the graph, retrace edges as needed to get between branches, and the retraced edges add no mark. This is the single most useful physical fact in the brief for this route, and it is the one thing that lets a LALI/network target be honest about the one-stroke constraint. (Formally: no Eulerian condition is needed, because a walk that repeats edges is indistinguishable from one that does not.)\n\n2. THE FIELD MUST BE READ FROM AN INTERNAL MAP, WITH THE SENSOR USED FOR DISCREPANCY ONLY — and this is where the stigmergy claim has to be earned. A DoG needs its outer lobe at several millimetres; a tip sensor can only report the neighbourhood it is in, so the machine cannot read metal at radius sigma2 that it has not physically visited. The workable arrangement is: keep an internal accumulator map (the machine knows where it commanded the tool to go), evaluate the normalized DoG on that map, and use the tip sensor for the one thing the map cannot contain — WHETHER THE CUT ACTUALLY LANDED. On the polar machine that discrepancy is large (about a fifth of the commanded shape never reaches the metal), spatially structured by radius (0.38 mm quantisation at the rim, 0.02 mm at r=10), unbounded, and non-saturating. If the sensor reads occupancy, the metal is only an output and 'communication with past selves' is decoration. If it reads discrepancy, the metal genuinely carries information no log has, and the reframing is doing real work.\n\n3. THE READABLE ACCUMULATOR IS CROSSING DENSITY, NOT DEPTH AND NOT OCCUPANCY. Depth is set by spring load and cannot encode 'how much'. Occupancy saturates at 1 — the diagnosed cause of all five deaths, and a zero-mean kernel does not rescue a bounded field. What IS physically readable at the tip and roughly unbounded is the number of groove EDGES crossed per unit scan length: with ~50 um grooves in a ~3 mm read box that is roughly 50-60x the dynamic range of occupancy fraction, on a machine that currently plateaus at 82% coverage. It saturates eventually; it does not saturate in eighty hours. Feed log(crossing density) to the DoG and divide by the outer blur.\n\n4. THE PATTERN IS SAMPLED ALONG A CURVE, NOT SOLVED ON A PLANE — so this is not reaction-diffusion and should not be described as such. Every cited mechanism evolves a field everywhere simultaneously; here a single walker writes and reads along a 1-D trajectory through a 2-D field. Two real consequences. First, the effective 'diffusion' of the pattern is the walker's own transport, so the pattern can only organise as fast as the tool covers ground — the KS/BH growth rate omega(k_max) = nu^2/4kappa has to be slow compared to the coverage time of one wavelength squared, or the machine will be committing to structure in regions it has not yet informed. Second, the 0.6 mm step and the sigma1 inner blur are close enough (a factor of ~5) that the short-scale stabilizing term is nearly at the resolution limit; the turn-rate/curvature limit is the safer way to supply it than a blur. Set sigma2 at 3-4 mm, sigma1 at 1 mm or use a curvature cap, expect spacing around 8-10 mm, and check that lambda_peak/step is at least 15-20 before believing any of it.",
  "measurable_signatures": [
   "SPACING vs SENSOR SCALE — the primary fraud test. Compute the radial power spectrum of the marked-metal field over the whole disc and locate lambda_peak. Require lambda_peak / sigma_outer >= 4 and lambda_peak / step(0.6 mm) >= 15. If lambda_peak lands in [1.5, 3] x sigma_outer you have photographed the filter's own scale, not a pattern: a DoG with sigma2 = 3 mm will always report something near 8 mm whether or not the metal organised. This number alone separates the two outcomes and costs nothing to compute.",
   "THE SCALING EXPONENT d(log lambda_peak)/d(log sigma2) — the test for whether the length scale is IMPORTED or SELECTED. Run three short jobs at sigma2, 1.5*sigma2, 2*sigma2. Exponent ~1.0 means the scale is simply the kernel width restated and the rule does contain the answer. Exponent < 0.7, or saturation of lambda_peak, means a nonlinear balance (coarsening arrest, state-dependent nu) is selecting the scale and something genuinely emergent is happening. This is the single most decisive experiment in the whole programme and it can be done in hours, not eighty of them.",
   "WEBER CONTRAST PERSISTENCE C(t) = mean|(G_s1*N)/(G_s2*N) - 1|, logged hourly. The signature shared by all five failures is C(t) -> 0. Fit C ~ t^(-alpha) over the last 80% of the run. alpha ~ 0.5 means additive/diffusive washout — deposition is not self-reinforcing and the run will fade on schedule. alpha ~ 0 (C within a factor of 2 across the final 60 hours) is the pass condition. alpha > 0.5 means a hard ceiling is still in the read path somewhere.",
   "ACCUMULATOR HEADROOM, reported alongside C(t): mean and 95th-percentile crossing density per read box, as a fraction of the geometric maximum (~60 lines per 3 mm at 50 um groove pitch). Two curves must diverge: mean N growing steadily while normalized C stays flat. If the 95th percentile reaches ~0.8 of maximum anywhere, that region is dead regardless of what the spectrum says, and the collapse will start there.",
   "TOPOLOGY INVARIANTS — where genuine emergence has to show up, since the spacing may be imported. Skeletonise the marked field and report: (a) branch points per cm^2; (b) mean vertex degree — Physarum and leaf-vein networks sit near 3, a grid gives 4, a closed orbit gives ~2; (c) junction-angle histogram, with a peak near 120 degrees indicating real three-way/Steiner-like junctions that no statement about two blur radii contains; (d) loop-area distribution tested for a power law over at least 1.5 decades. None of these are in the rule. All are in slime mould.",
   "SPECTRAL PARTICIPATION RATIO / NUMBER OF LIVE MODES: count Fourier modes above 10% of peak power, and report the participation ratio (sum P)^2 / sum P^2, hourly. Kuramoto-Sivashinsky-like cellular chaos sustains O(L/lambda) ~ 30-40 live modes on an A3-scale plate indefinitely. A closed orbit collapses to a handful. This is the direct quantitative replacement for the qualitative observation 'it found a closed orbit' and it will show the collapse tens of hours before a human sees it.",
   "RECURRENCE-TIME DISTRIBUTION: for each step, the distribution of times since the tool was last within lambda_peak/4 of that position. A closed orbit gives a sharp peak at the orbit period (version 5's radius locked to 177.4 +/- 2.9 mm for 64 hours would show as a delta). A living network gives a broad, heavy-tailed distribution. Report the coefficient of variation; require CV > 1.",
   "COMMANDED-vs-ACTUAL DISCREPANCY FIELD statistics, binned by radius: mean and variance of (commanded arc - delivered arc) per cell. This is the only channel where the metal carries information the log does not, so its variance is a direct measure of whether the stigmergy claim is true rather than decorative. It must stay non-zero and structured; if it collapses (e.g. the walker settles into a radius band where quantisation is uniform, which is exactly what version 4's 10 mm tangential ring did) the medium has stopped speaking even if the pattern still looks alive.",
   "STRAIGHT FRACTION AND ERROR ARE NOT PASS CRITERIA AND SHOULD BE DEMOTED. Every previous version reported falling error (1/34, 1/73, 1/195) and rising straight fraction (93%) while dying, and version 5 reported FLAT error at 0.12 while its radius locked for 64 hours. Both metrics are compatible with total collapse. Report them for continuity, but gate the run on lambda_peak/sigma_outer, the sigma-scaling exponent, C(t) flatness, participation ratio and mean vertex degree."
  ],
  "sources": [
   "https://arxiv.org/html/2512.12558v1 — 'Pattern Formation Beyond Turing: Physical Principles of Mass-Conserving Reaction-Diffusion Systems' (review). THE key source: patterns with zero production/degradation, but indefinite coarsening; wavelength selection requires weakly broken conservation (Lambda_stop, Lambda_split); interface width l_int ~ sqrt(D_m tau_r).",
   "https://arxiv.org/pdf/1802.07169 — Halatek & Frey, 'Self-organization principles of intracellular pattern formation' (local-equilibria / reactive-nullcline framework for mass-conserving RD).",
   "https://arxiv.org/pdf/2010.03900 — 'Surface-tension-driven coarsening in mass-conserved reaction-diffusion systems' (the coarsening that decay-free patterning cannot avoid).",
   "https://arxiv.org/pdf/1012.0337 — Mori, Jilkine & Edelstein-Keshet, asymptotic and bifurcation analysis of WAVE PINNING: mass-conserved, no degradation, stable sharp interface.",
   "https://arxiv.org/html/2410.12213v2 — bistability of travelling waves and wave-pinning states in a mass-conserved RD system.",
   "https://pmc.ncbi.nlm.nih.gov/articles/PMC9884266/ — 'General conditions for Turing and wave instabilities in reaction-diffusion systems' (critical-wavenumber conditions in general form).",
   "https://pubmed.ncbi.nlm.nih.gov/10918306/ — Meinhardt & Gierer, 'Pattern formation by local self-activation and lateral inhibition' — the LALI statement itself, including the activator-depleted-substrate alternative.",
   "https://arxiv.org/pdf/1803.07886 — 'Beyond activator-inhibitor networks: the generalised Turing mechanism' (the strict opposite-sign diagonal requirement is a two-species artefact).",
   "https://pmc.ncbi.nlm.nih.gov/articles/PMC11436923/ — 'Widespread biochemical reaction networks enable Turing patterns without imposed feedback'.",
   "https://www.nature.com/articles/s41598-021-84313-7 — 'Wavelength of a Turing-type mechanism regulates the morphogenesis of MESHWORK patterns' — directly relevant: how wavelength controls whether you get spots, stripes or a vein/network mesh. lambda = 2*pi/k_c, fourth-root dependence on diffusivities.",
   "https://arxiv.org/pdf/1411.6561 — Siebert & Schoell, 'Front and Turing patterns induced by Mexican-hat-like nonlocal feedback' (EPL 2015). Turing patterns from a sign-changing nonlocal KERNEL: two explicit ranges, no decay needed to set the scale.",
   "https://www.chebfun.org/examples/pde/Kuramoto.html — Kuramoto-Sivashinsky: most-amplified k = 1/sqrt(2), wavelength 2*sqrt(2)*pi ~ 8.89; dispersion omega(k) = -nu k^2 - kappa k^4 with k_m = sqrt(-nu/2kappa). No -alpha*h term; h unbounded.",
   "https://johncarlosbaez.wordpress.com/2021/10/17/conjectures-on-the-kuramoto-sevashinsky-equation/ — accessible account of KS cell-size selection and the balance of long-wavelength instability against short-wavelength dissipation.",
   "https://doi.org/10.3390/ma3104811 — 'Ion-Induced Nanoscale Ripple Patterns on Si Surfaces: Theory and Experiment' (Materials 2010). Bradley-Harper linear theory, curvature-dependent erosion vs surface-diffusion smoothing, wavelength selection in an IRREVERSIBLE material-removal medium, and Cuerno-Barabasi's KS-type nonlinear extension. (Landing page 403s to WebFetch; content obtained via search snippets.)",
   "https://www.hzdr.de/publications/Publ-12691 — 'Ripple rotation in the anisotropic Kuramoto-Sivashinsky equation'. Source of the honest caveat: the DAMPED KSE's damping coefficient is what stabilizes the pattern; without it the late-time state is chaotic with no order.",
   "https://arxiv.org/pdf/cond-mat/0007354 — Makeev, Cuerno & Barabasi, 'Morphology of Ion-Sputtered Surfaces' (the standard reference for the erosion-KS equation and its coefficients).",
   "https://arxiv.org/abs/1711.09652 — 'KPZ models: height-gradient fluctuations and the tilt method'. Explicit: the height GRADIENTS can be stationary even though the height field itself grows with time; one studies Burgers for u = d_x h.",
   "https://arxiv.org/pdf/cond-mat/9809238 — Fogedby, 'Aspects of the Noisy Burgers Equation': subtracting the global growth velocity / working with the slope yields a unique stationary state described by a gas of left/right domain-wall solitons.",
   "https://arxiv.org/abs/1109.2908 and https://arxiv.org/pdf/0808.1732 — Sadhu & Dhar, pattern formation in (fast-)growing SANDPILES: unbounded local accumulation, no decay, large-scale self-similar patterns; slope is the controlled variable.",
   "https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8599479/ — 'Population receptive fields of human primary visual cortex organised as DC-BALANCED BANDPASS filters' — the zero-DC property that makes a DoG read exactly invariant to uniform additive growth.",
   "https://arxiv.org/pdf/2004.07945 — 'ALCN: Adaptive Local Contrast Normalization' — divisive normalization giving invariance to intensity transformations; the arithmetic substitute for decay.",
   "https://www.researchgate.net/publication/277284831_MAX-MIN_ant_system — Stuetzle & Hoos, MAX-MIN Ant System: bounding pheromone to [tau_min, tau_max] is what prevents search stagnation and premature convergence. The discrete precedent for 'bound/normalize instead of evaporate', and the closest existing description of the five observed failures.",
   "https://arxiv.org/pdf/1304.2050 and https://softologyblog.wordpress.com/2019/04/11/physarum-simulations/ — standard Physarum agent models, confirming that the canonical implementations DO include an evaporation step (a small subtraction from every trail cell each tick), i.e. the brief's statement of the hard part is correct about the reference behaviour.",
   "https://arxiv.org/pdf/1511.05779 — 'Towards Lateral Inhibition and Collective Perception in Unorganised Non-Neural Systems' — directly on point for implementing LALI with simple local agents rather than chemistry, but NOT READ: the PDF would not decode through WebFetch. Flagging as unverified rather than citing its content."
  ]
 }
]