[
 {
  "ranking": [
   {
    "proposal": "4 — YIELD/BREAK (compliance-switched stigmergy)",
    "verdict": "strong",
    "why": "The only one of the four with NO internal map and NO length in its rule. Its two readings are forces the past self exerts on the present self right now (capture reaction through a 30 deg wall; a 2.47 ms crossing impulse), so the collective-intelligence claim is mechanical rather than metaphorical — and unlike a field, a contact reaction genuinely does not fade or accumulate, which is the only clean answer anyone gave to 'how do you get non-saturating information out of a permanent deposit'. It also contains the single best diagnosis-to-fix in the whole set: v4's rim ring and v5's 177.4 mm lock are re-read as a kinematic artefact of constant Omega (psi_max = arctan(v_r/Omega r) falls as 1/r), and constant SURFACE speed makes psi_max = 63.4 deg at every radius. That is a real, checkable, mechanism-level correction of a documented failure, not a new gain. And capture-plus-invisible-retrace is a physical mechanism for 3-valent T-junctions from a tool that never lifts — which is the one topological thing a single continuous stroke is supposed to be unable to do. Two serious defects: (a) its headline scale law a(P)=2A/(phi P) is a bookkeeping identity, true of any scribble that cuts phi of its path, and L/a = pi N_cut/4 follows from Cauchy plus a=2/lambda, so both 'predictions' are near-tautologies — the content is entirely in whether g(r) has a first peak at all; (b) the whole design rests on an unmeasured mechanical bistability F_y < F_escape < F_s, and its own risk section admits F_escape (sideways plough ~0.7-1.0 N) may be indistinguishable from the 0.707 N cutting force. Fix the stop condition (it currently runs to the merge horizon and ends as a matte plate) and it is the best piece here."
   },
   {
    "proposal": "1 — TWO RADII, OPPOSITE SIGNS",
    "verdict": "strong",
    "why": "Best deliverable object and by far the sharpest single insight in the four proposals: v1-v5 put 7200 m on a 119,381 mm^2 annulus, i.e. lambda = 60.3 mm/mm^2, 3.7x PAST the groove merge horizon 1/w = 16.18. Permanence was never the problem; VOLUME was. The 8 h flat run's reported 82% 'coverage plateau' was 30% true areal coverage read through a 5 mm box against a 61.8 um mark — the saturation was in the measurement first and in the metal second. That reframing alone earns the proposal its place, and it is the only one that draws the correct operational conclusion (cut 57 m, not 7200 m; drop the feed from 25 to 2 mm/s; stop on a measured lambda). Legibility is the best of the four by a wide margin: 8.4 mm pitch = 47 cells across a 400 mm disc (9.6 arcmin at 3 m, unambiguously resolved), 0.5 mm veins (0.57 arcmin — reads as a hairline, which is what you want), 97.1% mirror intact, so maximum contrast. Against it: it reintroduces exactly the two things this project has already shown to be fatal in kind. It steers off two float32 arrays (2.56 MB) rather than off the metal, so the metal is corrected-into rather than read-from — and it concedes this (KILL (iv) is the only thing that settles it). And its pitch is 1.4006 * sigma_i BY CONSTRUCTION, so the length scale is a bandpass filter printed on a disc. It also adds kappa_edge = 0.02 rad/mm within 15 mm of the boundary — a fixed-gain boundary steering term, which VERSIONS.md identifies as the actual cause of v1's tangential rim lines (varying EDGE_MM alone moved the order parameter -0.300/-0.157/-0.219 while the interior stayed isotropic). That is a known landmine, re-laid."
   },
   {
    "proposal": "2 — 《忘れるのは目だけ》Only the Eye Forgets",
    "verdict": "plausible",
    "why": "The best-targeted single fix in the set, and it is aimed at the right thing: scribe.py's turn is (GAIN_GRADIENT + GAIN_SURPRISE*ae)*drive plus GAIN_EDGE*diff, so when the error ae decays the residual GAIN_GRADIENT and GAIN_EDGE terms survive — the closed orbit is the limit cycle of that RESIDUAL CONTROLLER, not a failure of learning. Proposal 2 is the only one that names this correctly and the only one whose every turn term is multiplied by two factors that both go to zero on repetition, so the null output is a straight line and the boundary is a reflection rather than a steering gain. The divisive-then-subtractive ORDER argument (Weber first on the unbounded count, leaky high-pass second) is also correct and non-obvious. Three problems keep it out of the top two. (i) The state it holds up as safe is a trap: a fully habituated straight line in an annulus is a billiard, and annulus billiards conserve the tangency radius — the machine's 'safe' null behaviour is confined to r >= b forever, which is v5's radius lock arriving from geometry instead of from a controller. Its own risk section notices this and does not resolve it. (ii) The bisect-the-largest-gap claim, on which the entire ratio-2 hierarchy and the log-periodic spectrum depend, is asserted, not derived. As written, x = 1/(1+h) makes the alignment turn STRONGEST where density is LOWEST, so the tool hugs sparse structure and ploughs straight through dense structure — the opposite of gap-seeking. Without that step there is no cascade, no ratio 2 and no log-periodicity, and the whole non-imported part of the claim evaporates. (iii) It deliberately runs to the merge horizon (1932 m, lambda*w = 1, ~63% true coverage): generation 1 is legible for about ten minutes and the finished object is a grey plate. On a permanent medium you cannot come back."
   },
   {
    "proposal": "3 — ANASTOMOSIS (merge if shallow, cross if steep)",
    "verdict": "will-fail",
    "why": "The most honest document and the only one with data, and the data says it fails. I checked it against this repository rather than taking it on trust: emergence/eq/*/report.json gives gap_median_mm2 = 5.25-9.0 with gap_largest_mm2 = 27,700-32,300 for EVERY rule including the occupancy control, i.e. a median free gap of ~2.4-3 mm and a CV in the double digits, exactly as the proposal reports. Its own gate C (gap-area CV < 0.8) measures 3.6-12.8 and is failing; its arrest gate D wants >30x and measures 3.3x; and its SWITCH null — the term claimed to arrest the pattern — produced no detectable difference (Gini 0.459 vs 0.470, 203 switch events in 400,000 steps). A term that survives its own ablation unchanged is not doing work. Worse, the measured pitch of 2.2 mm is ~3.7 step lengths and is flat under 8x sweeps of R_min, the ride length and the force window: the pattern scale is the machine's STRIDE, which is the sensor-scale failure of v1-v5 arriving from a new direction. And the steering statistic is an absorbing state by construction: min|chi| over a window falls monotonically as density grows, so P(chi_min < chi_c) -> 1 and the terminal condition is permanent capture — the sixth closed orbit, delivered by the hardware. The 19.4 mm kinematic bound is arithmetic on a lateral exclusion reach a contact-only stylus does not have, as the proposal itself concludes. Two things should be salvaged: crossing angle recovered from transit duration (|sin chi| = w/(v T)) is the best-specified sensor primitive anyone proposed, and the naive-reader test is the right operational definition of the stigmergy claim. Do not cut metal with this rule."
   }
  ],
  "orbit_risk": "Proposal 4 — LOWEST, and for a structural reason: N_cut is a refractory COUNT, and the secondary null (N_cut = 0) reproduces five years of failure in minutes, which is the right kind of evidence that one integer is load-bearing. Constant surface speed removes the documented kinematic cause of v4's ring and v5's lock. Residual risk is real but different in kind: RAIL forever on a generation-0 line that carries no crossings, so N_rail = 2 never arrives. That is a hardware orbit on an EARLY plate, which is when it is most likely and least instrumented. It needs a principled exit, and the honest one is not a hard arc cap (that imports a length) but Proposal 2's arclength-leaky ride blindness.\n\nProposal 1 — MODERATE, with one avoidable and one unavoidable path in. Avoidable: kappa_edge = 0.02 rad/mm inside 15 mm of R_MIN/R_MAX is a fixed-gain boundary steering term, and this repo's own ablation (EDGE_MM 22/8/2 -> tangential order -0.300/-0.157/-0.219, interior isotropic at every setting) says the boundary rule, not the axis resolution, made v1's rim ring. Unavoidable: once A is clipped everywhere and I >> I_tol, M -> -gamma uniformly, all three probes tie, the argmax is degenerate and the tool goes straight until the edge term bends it — which is precisely NULL 2's predicted death, arriving late instead of early. What actually saves Proposal 1 is not the rule but the budget: it stops at lambda_bar = 0.476, 34x below merge, before the merit field flattens. An orbit found at hour 3 would therefore be cosmetically harmless (the remaining 17 h lays nothing) and detectable within the hour by its own radius-entropy gate. It buys safety by leaving early, which is legitimate but should be stated as such.\n\nProposal 2 — HIGH, and specifically NOT from the direction it defends against. Its anti-orbit argument is sound for the perceptual limit cycle: (1-H)*x -> 0 on repetition and the null output is dphi = 0. But dphi = 0 in an annulus with specular reflection is a billiard, and an annulus billiard preserves the perpendicular distance from the centre, so the habituated machine is confined to r >= b for as long as it stays habituated. The safe state IS the trap: v5's 177.4 +/- 2.9 mm lock reappears as a caustic. Its own risk list flags the billiard and the r = 5 mm hole and offers no fix that does not reintroduce an un-habituated steering term. Second path: the high-density limit of its turn law is turn-per-mm -> K_a/l_a * <arcsin|sin psi|> ~ 0.05 rad/mm, a non-vanishing curvature with sign set by crossing geometry, i.e. a persistent random walk of L_p ~ l_a = 20 mm. That is not an orbit, but it is also not exploration on a 400 mm disc: diffusive coverage at L_p = 20 mm is slow and radius-entropy will sag.\n\nProposal 3 — CERTAIN, and it is derived rather than feared. min|chi_k| over a bounded window is monotonically decreasing in density, so the merge condition chi_min < chi_c eventually fires every step: the terminal state is permanent capture. The two terms meant to prevent it are measured not to work (SWITCH survived its own ablation; arrest is 3.3x against a required 30x). It also has the tightest hardware trap of the four — 99.86% of the path is diamond sliding in its own 15.9 um grooves, so tip wear moves chi_c, the only threshold in the rule, mid-run. This is the one proposal where I would expect the sixth closed orbit to be observed rather than argued about.",
  "fake_emergence_risk": "There are three distinct ways to fake emergence here, and the four proposals occupy three of them. Naming them separately is the most useful thing I can do with this field.\n\n(a) SCALE = FILTER SCALE. Proposal 1, flagrantly and admittedly: p = 1.4006 * sigma_i exactly, so 8.4 mm is 6 mm restated. sigma_i is a kernel over an internal float32 map, not a sensing radius, which is a fair distinction — but it is still a length written into the rule, and the DoG-over-divisive-normalisation architecture is a reaction-diffusion emulator whose output wavelength is set by its own bandpass. The sigma_i sweep will almost certainly return slope 1.00 and the proposal says so in advance. Proposal 2 is the same failure one step removed: Lambda_1 = 1.9 * l_h, and l_h = 4 mm is a rule constant. Its defence — that l_h is a length ALONG THE PATH and the conversion to a transverse spacing is done by a circuit geometry the rule does not know — is genuinely better than Proposal 1's, and the predicted sub-unity exponent (0.8-1.0) is the right place to look. But if the exponent comes back 1.00 it is the same thing.\n\n(b) SCALE = STRIDE. Proposal 3, and it is already MEASURED, not predicted: 2.2 +/- 0.25 mm = 3.7 * DS, flat under 8x sweeps of R_min, ride length and force window. The repo's own reports corroborate it — gap_median_mm2 5.25-9.0 across every rule AND the occupancy control, i.e. the same ~2.4-3 mm gap statistic appears in the null. When your rule and your control produce the same length, the length belongs to the integrator, not the rule. This is the v1-v5 disease in new clothes and it is the strongest single reason to reject Proposal 3 as stated.\n\n(c) SCALE = BOOKKEEPING IDENTITY. Proposal 4. a(P) = 2A/(phi*P) is mass conservation: any tool that cuts phi of its path over area A produces that mean line spacing, mesh or scribble. And L/a = pi*N_cut/4 follows from L = N_cut/k with Cauchy k = (2/pi)*lambda and a = 2/lambda — an identity, not a prediction, whenever the field is even roughly uniform and isotropic. So Proposal 4's two headline numbers cannot discriminate its rule from a random chord process, and its falsification section does not notice this. The saving grace is that its scale is not at the sensor scale or the stride scale or any kernel scale, because there is no kernel; the content of the claim lives entirely in whether the pair correlation g(r) has a FIRST PEAK at all, with CV(a) below ~0.8, and in the topological predictions (mean vertex degree near 3, T-junction fraction above 0.5, areole areas power-law over two decades). Those are the measurements to run; a(P) matching 294,890/P is worth nothing.\n\nWhich would produce a pattern AT the sensor scale specifically: none, and that is real progress — all four delete LOOKAHEAD_MM = 7.0 and SENSE_MM = 2.5 and read at the contact patch (~62 um), so the 81:1 low-pass filter that photographed itself in v1-v4 is gone. The danger has moved from the sensor to the kernel (1), the constant (2), the stride (3) and the tautology (4).",
  "saturation_audit": "Take the question literally — does the claimed non-saturating quantity really not saturate at 90-100% coverage — and the answer is NO for all four. Every one of them dies there. What differs is whether they admit it and whether they stop first. That is the correct axis, and Proposal 1 is the only one that says so outright: \"the design does not answer how to stay informative at 90% — it refuses to go there.\"\n\nProposal 1. lambda (mm groove per mm^2) is genuinely unbounded to the merge horizon 1/w = 16.18, a 260x dynamic range against occupancy's ceiling of 1, and the divisive form M = [A' - gamma*max(0,I-I_tol)]/(I+eps) is genuinely invariant under lambda -> c*lambda up to eps. Both true. But A' = min(A, 0.35) BREAKS that invariance by design: once A exceeds the cap everywhere the numerator is a constant and M -> -gamma = -3 uniformly. So the read saturates exactly as fast as any other read once the plate is full; the clip that gives the rule its vein-expulsion behaviour is also what kills it at high density. Verdict: not saturating over 0-3% coverage, fully saturating by ~40%, honestly declared, and the run ends at 2.9%.\n\nProposal 2. Two separable claims. The angle |sin psi| = w/(v T) really is invariant under lambda -> c*lambda — one groove, one heading, no accumulation — and this is the single most durable reading anyone proposed; it would still carry information at 100% areal coverage IF crossings were individuable. They are not: at merge the transients overlap and the duration measurement is meaningless, so the angle channel dies not from saturation but from loss of individuation, at lambda = 16.18, which the proposal computes correctly (1932 m, 21.5 h). The x = 1/(1+h) claim needs a correction the proposal does not make: x itself goes to zero with density, so the per-crossing turn dies. What survives is turn-per-millimetre = K_a*nu/(1+l_a*nu)*<angle> -> K_a/l_a*<angle> ~ 0.05 rad/mm, a finite non-zero curvature. So the STEERING does not saturate even though the per-event novelty does. That is a better result than the proposal argues for, and it should be argued that way.\n\nProposal 3. The reading (crossing angle) does not saturate; the STATISTIC does. min|chi_k| over a 20 mm window falls monotonically toward zero as density grows, and its threshold crossing is an absorbing state (permanent capture). So the non-saturating quantity is real and the rule converts it into a saturating decision. This is the subtlest failure of the four and it is worth stating in exactly those words: choosing an extreme-value statistic over individual events was the right instinct, and then feeding it to a fixed threshold undid it.\n\nProposal 4. The count claim is correct as far as it goes (no averaging ceiling; fails only at merge). The FORCE claim is the strongest thing in any of the four proposals: F_r is a contact reaction, not an integral — a groove cut an hour ago pushes exactly as hard as one cut a second ago, and it does not get stronger after 85 passes because depth is load-set at 15.907 um. There is no field, so there is no integral to fill. But it still saturates as a BIT at high coverage: when every groove is adjacent to another, the tip is never not in a groove, the capture bit pins at 1 and RAIL is permanent. Proposal 4 runs deliberately to the merge horizon (2390 m, 26.5 h), i.e. it runs INTO its own saturation and calls it a stop condition. That is the one change I would insist on before anything is cut.",
  "best_single_choice": "Proposal 4, YIELD / BREAK, with its stop condition changed — but the choice is close enough to Proposal 1 that the reasoning matters more than the verdict, and part of it is aesthetic, which I will mark as such.\n\nMechanically, Proposal 4 is the only one where the sentence \"the collective is the machine's own past selves\" is a force and not a figure of speech. Its two readings are (i) a lateral reaction of order 1 N through a 30 deg groove wall, which is a past pass physically moving the present pass, and (ii) a 2.47 ms impulse from a past pass. It holds a mode bit, an integer no greater than six and a sign. There is no map, no kernel, no wavelength, no decay constant, no error, no model. Proposal 1, by contrast, steers off two float32 arrays and corrects them toward the metal at rate alpha = 0.3; a critic will say the metal is decoration and Proposal 1 concedes that KILL (iv) is the only thing that settles it. On the stated themes — collective intelligence, intelligence, emergence — that difference is decisive, because the whole point of this version is that the medium must be the wiring and not the record.\n\nArtistically (and this is the aesthetic judgement, stated as such): Proposal 4 is the only one that turns permanence from a defect into the SOLE source of a property nothing else can supply. Its vein hierarchy is authored by the ORDER OF ARRIVAL — earliest chords span the plate, latest fill single cells — which is a hierarchy that a decaying medium is structurally incapable of producing, because a decaying medium erases its own chronology. Physarum's elegance comes from pruning; this comes from being unable to prune. That is the correct artistic answer to the hard part of the brief, and it is better than \"we replaced evaporation with division.\"\n\nIts 3-valent junction mechanism is also the one genuinely new technical idea in the four: capture plus invisible retrace lets a tool that never lifts produce T-junctions (enter the T, rail along it, leave by the same edge), so the MARK SET is 3-valent even though the WALK is not. Mean vertex degree near 3 rather than 4 is a falsifiable claim about a thing a single continuous stroke is supposed to be unable to do.\n\nTwo conditions on the choice, both non-negotiable. First, the coupon measurement of F_escape versus crossing angle must come back with a usable window F_y < F_escape < F_s; if sideways escape at 15.9 um depth costs the same ~0.7 N as forward cutting, the mode bit is unobservable and the design does not exist. Second, the stop condition must change from the merge horizon to a target pitch. As written, a(P) = 294,890/P refines to 0.123 mm and the object ends as a matte plate — the same failure as v1-v5, arrived at deliberately.\n\nWhy not Proposal 1 first: it is the better OBJECT and the worse ARGUMENT. Its diagnostic contribution (7200 m = lambda 60.3 = 3.7x past merge; permanence was never the problem, volume was) is the most valuable single paragraph in all four submissions and should be adopted regardless of which rule is built. But its spacing is a kernel width restated, its field is internal, and it re-lays the boundary-gain landmine that this repo has already documented as the cause of v1's rim ring.",
  "recommended_hybrid": "BUILD: Proposal 4's rule, verbatim in its state (mode bit, integer <= 6, sign bit, heading) and in its two readings (capture reaction F_r, crossing impulse count). Keep constant SURFACE speed — that single change removes the kinematic cause of v4's ring and v5's lock and is the best-argued fix in the set. Keep the rotary quantum D_THETA = 2*pi/3200: it is the body's signature and it bought the factor of ten. Keep N_cut = 6 / N_rail = 2 / beta = 60 deg / p = 0.10 as counts and angles, i.e. keep the property that the rule contains no length.\n\nADD, from Proposal 1, three things and only three. (1) The lambda accumulator as the INSTRUMENT — groove length density in mm/mm^2, reported against the merge horizon 16.18, with true areal coverage 1 - exp(-lambda*w) printed beside any grid figure. The word \"coverage\" is retired. (2) The BUDGET DISCIPLINE, which is the most important borrowing: stop on a measured target pitch, not at merge and not on a clock. Target a = 5 mm gives lambda = 0.40 mm/mm^2, 44 m of cut, 59 m of path, 2.4% true areal coverage — 8.2 h at 2 mm/s, 4.9 h if you prefer a = 8.4 mm and 26 m. Pick the pitch for the room and the light, then derive the hours; never the reverse. (3) The SLOW FEED, 2-4 mm/s rather than 25. This is not conservatism: it moves the crossing transient from 2.47 ms to ~31 ms (32 Hz, comfortably sensable), and it pushes the drag-holder chatter wavelength v/f from 0.31 mm — millimetric, decay-free, and the single most likely convincing false positive in this whole project — down to ~25 um, 200x below the pattern pitch.\n\nADD, from Proposal 2, exactly ONE term, as a bug fix rather than a mechanism: arclength-leaky ride blindness, H <- H + (1-H)*ds/l_h while riding, used ONLY to release a tool that is railing along a generation-0 groove that carries no crossings and will therefore never deliver N_rail = 2. This is the principled version of Proposal 4's own \"hard cap the railed arc\" hedge, and it costs one scalar instead of one imported length.\n\nADD, from Proposal 3, one instrument and one test. The instrument: crossing angle from transit duration, |sin chi| = w/(v*T) — the cleanest sensor primitive proposed, and it costs nothing since the impulse is already being detected for the count. Use it for logging and for the junction-angle histogram, NOT for steering. The test: the naive-reader protocol, run on the finished plate, as the operational definition of the stigmergy claim.\n\nLEAVE OUT, explicitly. Proposal 1's two Gaussian kernels, both float32 maps, A_cap, gamma, I_tol, eps, lambda_stop and the three map-probes — that entire apparatus is where the metal becomes decoration and where the pitch becomes 1.4 * sigma_i. Proposal 1's kappa_edge boundary gain: use reflection, per Proposal 2, because this repo has already measured that a boundary steering gain produced v1's tangential rim ring. Proposal 2's generation cascade, bisection-to-merge and log-periodic spectrum: the gap-seeking step is asserted, not derived, and the destination is a grey plate. Proposal 3's min|chi| MERGE threshold as a steering term: it is an absorbing state, and its own prototype's arrest gate fails 3.3x against a required 30x. Proposal 4's own a(P) and L/a as evidence of anything: they are identities. And from all four: any predictor, any learned weight, any reported \"error\" or \"straight fraction\". Five versions reported falling error while dying.",
  "what_to_measure": [
   "CV of the free-gap AREA distribution, and the first peak of the segment pair-correlation g(r) taken over many radial and tangential transects. This is the gate everything else hangs on: a characteristic cell size means CV in 0.3-0.6; Poisson gives ~1; scale-free gives >>1. The existing testbed reports gap_median_mm2 5.25-9.0 against gap_largest_mm2 27,700-32,300 for EVERY rule including the occupancy control — CV in the double digits. No proposal has yet cleared this, and no metal should be cut until one does. Use g(r), never a power-spectrum argmax: this repo's own out_*.json returns spectrum_peak_mm = 103.71 for every rule and every ablation, i.e. the plate size.",
   "Mean vertex degree and T-junction fraction on the finished mark set. Near 3 with T-fraction above 0.5 is the claim that capture-plus-invisible-retrace lets a non-lifting tool branch; 4 with T-fraction near 0 means capture never terminated a flight and the rule has converged with its own null. Report the junction-angle histogram alongside, and remember that a peak at 60/120 deg is beta restated, not emergence.",
   "The lambda map against the merge horizon 16.18 mm/mm^2, plus TRUE areal coverage 1 - exp(-lambda*w), printed beside any grid figure and never instead of it. The 8 h flat run's 82% 'plateau' was 30% true coverage read through a 5 mm box; the 80 h runs were at lambda = 60.3, i.e. 3.7x past merge. Retire the word coverage.",
   "Entropy of the visited-radius histogram against uniform-in-area, and the maximum fraction of path length in any 10 mm annulus, logged hourly. These are the two numbers that would have caught v4 (69% of 7200 m in one 10 mm ring) and v5 (177.4 +/- 2.9 mm for 64 of 80 h) in the first hour instead of at hour eighty. Abort thresholds set in advance, in writing.",
   "F_escape versus crossing angle, and the F_t histogram for cut (~0.707 N) / ride (~0.44 N) / re-cut (~0.5-0.6 N at 450 HV), measured on a coupon. If the cut/ride contrast is not cleanly separable, or if sideways escape costs the same ~0.7 N as forward cutting, then Proposals 3 and 4 have no mode bit and Proposals 1 and 2 lose their capture terms. This is the physical prerequisite for three of the four.",
   "The drag holder's flexure resonance f, with v/f published next to any claimed pitch. 25 mm/s at 80-1200 Hz gives 0.31 mm down to 21 um: millimetric, permanent, and entirely capable of producing a convincing periodic false positive. Run the identical rule on a virgin coupon at every parameter setting and subtract whatever spectrum a straight commanded stroke produces, BEFORE claiming any spacing.",
   "Railed-arc-length distribution and every capture event with the path length before escape. A heavy tail here is the closed orbit arriving through the hardware — a diamond tip refusing to leave a 15.9 um groove with 30 deg walls and aspect 3.89 — and it would reproduce the v1-v5 failure with no failure of the rule at all. This is the single most likely way the sixth version dies.",
   "The naive-reader correlation: hand the finished plate to a second machine with no memory, let it rebuild its field from force and crossing readings alone, and correlate with the first machine's internal state. Require Pearson r > 0.6, target > 0.8. Below that, the information was in the log and the stigmergy claim is decoration. This is the only test that distinguishes a mechanism from a nice sentence, and it must be run rather than argued.",
   "The scaling exponent of the pattern pitch against whichever constant the chosen rule contains — d(log p)/d(log sigma_i) for Proposal 1, d(log Lambda_1)/d(log l_h) and d(log Lambda_1)/d(log l_a) for Proposal 2, d(log s)/d(log W_s) for Proposal 3, and for Proposal 4 the flatness of L/a across path-length quartiles within one run. Slope 1 means the length is imported and the emergence claim must retreat to topology. Also sweep the control step: if the pitch tracks ds, it is a stride, which is what Proposal 3 already measured.",
   "Legibility, measured rather than hoped: render the finished plate through the existing optics code at the actual viewing distance and report the groove-light / lamp-image ratio (0.38 at 8 h, 5.51 at 80 h in v1). Then check the coarse generation is still legible under every finer one, because on a permanent medium a legible intermediate state is not a state you can return to."
  ],
  "cheapest_decisive_test": "Two tests, and they are cheap in different currencies. Run both before any metal is committed; either one alone can kill the version.\n\nTHE COMPUTATIONAL ONE, which costs an afternoon and no metal. Take the testbed that already exists (emergence/stroke.py, 400 mm disc, CELL 0.5, DS 0.6), replace the occupancy accumulator with the lambda (groove length density) accumulator, and run 90 minutes of simulated cutting — enough for ~45 m of groove at a target pitch of 5 mm, which is the whole piece, not a fragment. THE SINGLE NUMBER: the coefficient of variation of the free-gap AREA distribution, from the first peak of the segment pair-correlation g(r). Pass is CV < 0.8. This settles the entire question, because every one of the four proposals stands or falls on whether a characteristic cell size exists at all, and the repository's existing runs say it does not: gap_median_mm2 5.25-9.0 against gap_largest_mm2 27,700-32,300 for the vein rule, its two ablations AND the occupancy control alike. CV >> 1 with the same median in the rule and in its own null is the signature of a length that belongs to the integrator rather than to the rule. If the new rule cannot move that one number below 1, there is no pattern to cut, and eighty hours will not produce one — which is exactly what the previous five versions demonstrated. Do not use a power-spectrum argmax as the readout: out_*.json returns 103.71 mm, the plate size, for every rule and every ablation ever tried here.\n\nTHE PHYSICAL ONE, which costs one coupon and half a day. Drag the tip across a pre-cut cross-hatch at 5, 10, 18, 30, 45, 60, 90 degrees under the 300 gf load. THE SINGLE NUMBER: F_escape at 90 deg, expressed as a ratio to the 0.707 N virgin cutting force. Pass is a separation of at least 2x with the cut/ride/re-cut histogram cleanly trimodal. If F_escape lands in the 0.7-1.0 N band that the sideways-plough estimate predicts, the mode bit is unobservable, capture cannot be commanded or detected, and three of the four proposals lose their central mechanism — Proposal 4 outright, Proposal 3's MERGE, Proposal 2's free ride. Everything else in all four documents is downstream of this one force.\n\nIf forced to pick one: the simulated CV, because it is free, it is decisive, and it is the number that five previous versions never computed."
 },
 {
  "ranking": [
   {
    "proposal": "PROPOSAL 4 — YIELD/BREAK (compliance-switched, count-triggered)",
    "verdict": "strong",
    "why": "The only one of the four whose pattern scale is not proportional to any length written in the rule. a(P) = 2A/(phi*P) = 2.949e5/P mm is a quotient of plate area by path length; the rule contains only counts (6, 2), an angle (60 deg) and forces. It is also the only one with a structural reason the v1-v5 death is unavailable: there is no predictor, no error, no learned model, hence no residual controller to leave behind when the error collapses. Internal state is a mode bit, a sign bit and an integer that never exceeds 6 — there is nothing to run away and no map to become a substitute for the metal. The refractory count N_cut = 6 is a genuine anti-lock: the tool cannot be recaptured until it has crossed six grooves, i.e. a chord of length (pi*N_cut/4)*a = 4.71*a, several cell widths, so it cannot hold station on a density step the way v5 did. Its secondary null (N_cut = 0 reproduces the collapse in minutes) is the correct demonstration that one integer is doing the work. The risk is entirely hardware — the force window F_y < F_escape < F_s may not exist — which is measurable on a coupon in half an hour, before any metal is committed. That is the right kind of risk to be carrying."
   },
   {
    "proposal": "PROPOSAL 1 — TWO RADII, OPPOSITE SIGNS (DoG on groove-length density)",
    "verdict": "plausible",
    "why": "It will very probably produce a legible mesh, and it will very probably not be emergent. Two things in it are genuinely load-bearing and one of them the document itself undersells. (a) The volume arithmetic is the single most important finding in the whole set: v1-v5 laid 7200 m on a 119,381 mm^2 annulus = lambda_bar 60.3 mm/mm^2, i.e. 3.73x past the merge horizon 1/w = 16.18; the 8 h flat run's 720 m is lambda 5.8, true Boolean coverage 1 - exp(-lambda*w) = 30%, reported as an 82% plateau. The saturation was in the measurement first and in the metal later. Every other proposal should adopt this budget discipline. (b) The undersold mechanism: because A' is clipped and lambda >= lambda_stop = 8 is hard-excluded, an orbit POISONS ITS OWN ATTRACTOR. A 0.5 mm cell reaches lambda = 8 after 2 mm of groove in 0.25 mm^2, i.e. about 3-4 passes; so any closed orbit is forbidden after ~4 laps. That is precisely what v1-v5 lacked, where re-cutting changed no reading at all. Against it: the pitch is 1.4006*sigma_i exactly by construction, the merit is computed from two internal float32 maps rather than from the metal, and the 6 mm kernel is remote sensing the tip cannot perform. It is a robot with a map, and it is the only proposal that violates the spirit of the 'may not read anything it could not physically sense' constraint. That is not a coincidence — it is why it is the one most likely to make a clean picture."
   },
   {
    "proposal": "PROPOSAL 2 — 《忘れるのは目だけ》 Only the Eye Forgets",
    "verdict": "will-fail",
    "why": "The core idea is right and the implementation contradicts it. Right: multiplying every turn by (1-H)*x so that the null output of a fully habituated reader is dphi = 0 is the correct diagnosis of v1-v5 — the closed orbit was the limit cycle of the RESIDUAL controller (GAIN_GRADIENT = 0.052 and GAIN_EDGE survive when the error decays), and a rule whose null output is zero turn cannot have one. Wrong, and fatally: habituation is applied exactly where the machine is mechanically trapped. H rises while riding (m = 0), and the only thing that can lift the heading past psi_c and out of a groove is a steering command. So the rule zeroes the sole escape from capture at the precise moment capture occurs. Departure then happens only when the vein's own curvature carries theta_groove more than psi_c ~ 12 deg away from a frozen heading — which means (i) a straight generation-0 vein is ridden to the boundary and reflected, forever, and (ii) the ride length is set by psi_c and the vein's radius of curvature, NOT by l_h = 4 mm. The whole Lambda_1 = (N_seg/pi)*l_h = 7.6 mm derivation is therefore about a mechanism that is not the one operating. Second, quantitatively: at the design density (Lambda = 2/7.6 = 0.263 mm/mm^2, nu = 0.167/mm) the steady-state h = l_a*nu = 3.3, x = 0.23, and the heading diffusion is D_phi = 0.5*nu*(x*arcsin)^2 ~ 2.8e-3 rad^2/mm, a persistence length of order 350 mm — 46 times the claimed 7.6 mm cell. Turning cannot build the cell; only capture can, and capture is what habituation blinds. Third, kappa_max = 0.5/mm puts an available attractor at rho_min = 2 mm, 3.8x below the claimed pattern scale, which is the wrong direction. Keep the multiplicative gate; discard this rule."
   },
   {
    "proposal": "PROPOSAL 3 — ANASTOMOSIS (merge if shallow, cross if steep)",
    "verdict": "will-fail",
    "why": "It is already falsified by its author's own prototype, and there is a second, structural kill the prototype has not yet reached. The prototype: free-gap CV 3.6-12.8 against a required <0.8, median pitch pinned at 2.2 mm = 3.7 step lengths and FLAT across 8x sweeps of R_min, ride length and force window — the pattern scale is the machine's stride. New-cut arrest x3.3 against a required x30. Secondary null failed: removing SWITCH changed nothing (203 switch events in 400,000 steps). The proposed fix, W_s 1.5 -> 20 mm, cannot work, and the arithmetic is a vice. The number of remembered crossings is N = nu*W_s = (2/pi)*lambda*W_s. SWITCH needs N >> 1 to have a junction to transfer to; but the decisive statistic is a MINIMUM, and E[min|chi|] over N roughly uniform angles is 90 deg/(N+1), so min|chi| falls below chi_c = 18 deg at N ~ 4 and thereafter the tip merges essentially always — permanent capture, the sixth closed orbit, arriving through the hardware. At the design density lambda* = 0.0785 with W_s = 20 mm, N = 1.0: SWITCH has nothing to switch to. At lambda = 0.31 mm/mm^2 — only 37 m of groove on this disc, 1.9% of the merge budget and 0.2% true areal coverage — N = 3.9 and the machine is captured for good. The whole design has to live inside N in [2,4], a factor of two in lambda*W_s, on a medium whose lambda only ever increases. Also 99.86% of 7200 m is retrace, which is an orbit wearing a different word, and the one threshold in the rule (chi_c) will drift with tip wear over that distance. The salvageable asset is the shuffled-chi null, which is the only CONFIRMED result anywhere in the four proposals: MERGE events 1082 -> ~0, Gini 0.46 -> 0.33, CV 4.6 -> 1.6. The crossing angle in the metal does real work. Take that null; leave the rule."
   }
  ],
  "orbit_risk": "Assume the sixth collapse by default. Which proposals have a mechanism, stated as a mechanism.\n\nPROPOSAL 4 — LOWEST RISK, and for two independent reasons. (i) There is no model and no error, so the v1-v5 death — a learned predictor's error decaying to zero and exposing a constant residual steering term — is structurally unavailable. In scribe.py:181 the turn is (GAIN_GRADIENT + GAIN_SURPRISE*ae)*drive; when ae -> 0 the 0.052 term survives and IS the limit cycle. P4 has no such term. (ii) The refractory count is a real escape: after breakout the tool is stiff and cannot be recaptured for six crossings, i.e. 4.71*a of chord. A lock requires being recaptured by the same groove, and the count forbids it. Residual risks, both nameable: self-railing along a vein that carries no junctions (RAIL waits for N_rail = 2 impulses; a generation-0 line has almost none, so the early plate is where this bites) — handled only by a boundary reflect, which is a length cap smuggled in as a boundary condition; and the annulus billiard, since CUT holds psi constant and reflects at r_min/r_max. Neither is a gradient-following lock. Verdict: will probably not close an orbit; will probably railroad along a long early vein at least once, so the railed-arc-length tail must be gated from minute one.\n\nPROPOSAL 1 — MODERATE, and better than the document claims. The merit maximum is a corridor midway between two full veins, and a corridor on a disc closes on itself; the tool will follow it. But it deposits as it goes, and a 0.5 mm cell reaches lambda_stop = 8 mm/mm^2 after ~2 mm of groove, i.e. 3-4 passes. So an orbit is hard-excluded after about four laps. Deposition destroys its own attractor — that is a genuine mechanism, and the exact thing v5 lacked when it held station across the edge of its own cut band at r = 177.4 +/- 2.9 mm for 64 hours, because there re-cutting changed no reading. Residual risks: eps = 0.25 sets the virgin-metal merit to exactly M = 0, so on open metal all three probes tie and the argmax is degenerate — the tool goes straight until the edge term at kappa_edge = 0.02 rad/mm bends it, and an edge-driven near-circle with a 40 mm persistence length is a plausible attractor in the first hour before enough lambda exists to break the tie. And groove capture is unmodelled in the field: the tip railed in a 15.9 um groove does not care what M says.\n\nPROPOSAL 2 — HIGH, arriving through the hardware. The multiplicative gate genuinely forbids a rule-level limit cycle: with dphi = -K*(1-H)*x*sigma*arcsin, both factors decay on repeated experience and the habituated output is a straight line, which on a disc must leave any orbit. But the rule's own capture clause sets phi <- theta_groove every step while |phi - theta_groove| < psi_c, and habituation removes the only command that could exceed psi_c. A straight vein has infinite radius of curvature, so theta_groove never moves away from the frozen heading and the ride never ends except at the boundary. The predicted failure is: ride generation-0 vein, reflect, ride back, indefinitely — a closed orbit within minutes, and one that the run's own gates (mean x and mean (1-H) must not fall below 20% of first-hour value) would flag while being powerless to prevent. Secondary: at high density the turn per mm saturates at arcsin/l_a ~ 0.05 rad/mm, i.e. a curvature fixed point at radius ~ l_a = 20 mm, so the late-run persistence length is l_a, contradicting the claim that Lambda_1 is independent of l_a.\n\nPROPOSAL 3 — CERTAIN, and computable. P(min|chi| < chi_c) -> 1 as lambda grows, monotonically and irreversibly, because lambda only ever increases and min is a decreasing function of event count. Crossover at N = nu*W_s ~ 4, i.e. lambda ~ 0.31 mm/mm^2 = 37 m of groove = 0.2% true areal coverage. Past that the tip merges with everything it meets and rides forever. The prototype already shows the precursor: pass Gini 0.46, max/mean passes ~100. The design's own answer (SWITCH) is measured to be non-functional and cannot be made functional at the target density, because N = 1.0 there. This is the sixth closed orbit with a derivation attached.",
  "fake_emergence_risk": "Take the honest denominator to be the shortest length written into the rule that the pattern's scale is proportional to — not the contact patch, which every proposal correctly quotes as 62 um and which is a rhetorical denominator, because in three of the four cases the scale demonstrably tracks something else.\n\nPROPOSAL 3 — WORST, and confirmed rather than predicted. Predicted p = 20 mm equals W_s = 20 mm exactly: ratio 1.00. Measured p = 2.2 mm equals 3.7 * DS(0.6 mm): the pattern scale is the stride. Flat across 8x sweeps of R_min, ride length and force window, which the author correctly reports as the good news (not a kernel) and which is actually the bad news (nothing selects it). The 19.4 mm kinematic bound R_min*(pi/2 - chi_c)*sin(chi_c) assumed a lateral exclusion reach a contact-only stylus does not have; MERGE fires on physical contact, so the exclusion range IS the contact patch and the tool cuts freely to within 62 um of an existing vein. Fake emergence, already demonstrated.\n\nPROPOSAL 1 — FAKE BY CONSTRUCTION, and the document says so. p = sigma_i*sqrt(2 ln(1/rho)) = 1.4006*sigma_i = 8.40 mm, and I_tol is DEFINED as a fraction rho = 0.375 of the vein's own contribution, which makes the expression exactly scale-free in sigma_i. The sigma_i sweep will return slope 1.00 and p = 4.20/8.40/16.81 mm. Ratio p/sigma_i = 1.40. sigma_i is not a sensing aperture, but it is a 6 mm Gaussian averaging kernel applied to an internal map — functionally a filter, and 8.4 mm is that filter's own wavelength printed on the disc. For scale: v1-v5 read occupancy through a 5 mm box (SENSE_MM = 2.5, polar.py:87) against a 61.8 um mark and produced a 10 mm tangential ring — within a factor of 1.4 of LOOKAHEAD_MM = 7.0 (polar.py:88). Proposal 1's 1.40 is numerically the same relationship. Whatever else changed, that ratio did not.\n\nPROPOSAL 2 — MOSTLY FAKE, with an additional inconsistency. Claimed 7.6 mm = 1.9*l_h(4.0 mm), ratio 1.90. The defence — that l_h is a path length and the rule contains no transverse length, the conversion being done by a circuit geometry the rule does not know — is the best argument any of the four makes for an imported constant. It fails on the mechanics: as argued above, ride length is terminated by psi_c and vein curvature, not by l_h, so the predicted proportionality is to the wrong constant. And the heading persistence at design density is ~350 mm, 46x the claimed cell, so turning is not building the cells at all. The generation ratio 2 (log-periodic modulation of period ln 2 in ln k) is the one prediction in this proposal that is genuinely not in the rule, and it is worth stealing.\n\nPROPOSAL 4 — THE ONLY NON-IMPORTED SCALE. a(P) = 2A/(phi*P) = 2.949e5/P mm: 3.28 mm at P = 90 m, 1.64 at 180 m, 0.82 at 360 m, 0.123 at the merge horizon P = 2390 m. Ratio to the contact patch: 53 / 26 / 13 / 2.0. Ratio to the control step (25 um of travel): 131 at 1 h. There is no kernel to photograph. But the honest working window is narrower than claimed, and this is the number the proposal should have computed: the rotary quantum r*D_THETA (D_THETA = 2pi/3200, polar.py:92) is 0.373 mm at r = 190 and 0.059 mm at r = 30, so a/quantum at the rim is 8.8 at 1 h, 2.2 at 4 h and 0.33 at merge. Chatter contributes v_t/f = 0.021-0.312 mm. So P4 is measuring a genuinely emergent quotient only for P roughly 30-400 m, i.e. 20 minutes to 4.5 hours at 25 mm/s. After that the rim quantum and the flexure are writing the pattern. The invariant L/a = pi*N_cut/4 = 4.71, a pure number produced by a pure number and required to hold at 15 mm chords and at 1 mm chords, is the strongest emergence claim available in the whole set.",
  "saturation_audit": "The question to ask each: what does your non-saturating reading EQUAL when the neighbourhood is fully marked, as v4's outer ring was (occupancy pinned at 1, axial order -0.918)? Answer for all four: it dies. The useful differences are in WHERE it dies and whether the proposal knows.\n\nPROPOSAL 1, lambda = groove length per mm^2, ceiling 16.18 mm/mm^2. Honest and correct: it admits that at 90% areal coverage (lambda >= 37, 2.3x merged) A is clipped, I >> I_tol, M -> -gamma = -3 uniformly, all three probes tie and it closes an orbit. But note the deeper failure that arrives much earlier: the accumulator increments only when F_t > 0.55 N, i.e. only on a real cut. Past the merge horizon there IS no virgin metal, F_t sits at the riding level everywhere, so lambda stops being updated at all — the map freezes and the machine is steering by an internal array with no further reference to the plate. The ratio trick (M has I in its denominator, so lambda -> c*lambda leaves M invariant) is real arithmetic and is the correct substitute for evaporation, but it protects against MULTIPLICATIVE growth, not against the loss of individuable events. Its real answer is the budget: 57 m of groove, lambda_bar = 0.476, 2.9% true areal coverage. That is not an answer to the saturation question — it is a refusal to enter the regime, which is legitimate and is the best available answer, but it should be labelled as such.\n\nPROPOSAL 2, x = 1/(1+h) and |sin psi| = w/(v*T). The Weber ratio claim is true in form: x depends on the RATIO of a new crossing to remembered ones, so there is no absolute reference to push against, and the turn per mm converges to arcsin/l_a rather than to zero. So the reading does not go dead — it goes to a fixed curvature scale of l_a = 20 mm, which is a different disease. The angle channel is claimed to be informative at 100% coverage; it is not, because at merge the transients overlap (mean spacing = w, crossings every 97 um = 3.9 ms at 25 mm/s against a 2.47 ms transit) and T is not measurable. And the virginity bit m goes to 0 permanently, so H -> 1 permanently and ALL steering is off: at 100% marked this machine is a straight line in a specular annulus, i.e. a billiard with caustics, which is v4's ring reached by a new route. Its own honest figure, 1932 m of virgin groove and 21.5 h, is right.\n\nPROPOSAL 3, chi_min over a window. The claim 'angles do not accumulate' is the most confidently stated and the most wrong, because the statistic used is not an angle but the MINIMUM of angles, and a minimum over a growing sample most certainly saturates: it goes to zero. min|chi| ~ 90 deg/(N+1) with N = (2/pi)*lambda*W_s, so it crosses chi_c = 18 deg at lambda = 0.31 mm/mm^2 — 37 m of groove, 0.2% true coverage, fifty times before merge and four times before its own design density. This proposal saturates EARLIEST of the four, and it saturates in exactly the way it claims to be immune to. Its secondary gauge (crossing rate, 206x headroom) is unbounded and fine, but it is explicitly never used to steer.\n\nPROPOSAL 4, crossing count and lateral capture force. The count: at 100% marked, consecutive grooves are not individuable, crossings arrive faster than the 2 ms dead time, N_cut = 6 is reached instantly, flights collapse to the dead-time length (50 um), and the mode bit flips every few steps — the machine becomes a 62 um random walk. Computed: at merge, k = 10.3/mm, L = 0.58 mm, a = 0.123 mm = 2w. Its stop condition is exactly there, which is correct in kind but wrong in choice: it stops at a matte grey disc. The capture force F_r is the single best non-saturating reading anywhere in the four proposals, and the argument for it is the best argument in the whole set — it is a CONTACT REACTION, not an accumulation, so a groove cut an hour ago pushes exactly as hard as one cut a second ago and there is no integral to fill up. But it too dies at full marking, for a reason P4 does not state: at 100% overlap there are no distinguishable walls left. The surface is one uniformly ploughed floor, w spacing means no wedge to fall into, and F_r goes to a rough baseline. So F_r survives to lambda ~ 8-12 mm/mm^2, not to 100%.\n\nCONCLUSION FOR ALL FOUR, and it is the finding to keep: there is no reading that survives a fully marked neighbourhood, because 'fully marked' means the geometry that carried the information has been destroyed, not merely averaged away. The correct design response is Proposal 1's, applied to Proposal 4's rule: never go there. 57-120 m of groove, lambda_bar 0.5-1.0 mm/mm^2, 3-6% true areal coverage, and a stop condition in mm of groove rather than in hours.",
  "best_single_choice": "PROPOSAL 4 — YIELD/BREAK. It is the only one whose pattern scale is not a restatement of a constant in its own rule: a(P) = 2A/(phi*P), with the ratio L/a = pi*N_cut/4 = 4.71 held across every generation, is a dimensionless invariant produced by an integer, and there is no kernel width anywhere that could be photographed onto the disc. It is the only one that has structurally deleted the v1-v5 death rather than argued around it — no predictor, no error, no learned weights, internal state limited to a mode bit, a sign bit and an integer bounded by 6 — and its own secondary null (N_cut = 0 reproduces the collapse in minutes) proves which ingredient carries the load. Its two readings are the only ones in the set that are forces the past selves exert on the present one, which makes the stigmergy reframing mechanical rather than decorative and gives it a real chance of passing the naive-reader test. Its dominant risk is a hardware existence question (does F_y < F_escape < F_s exist, given that sideways-ploughing escape is 0.7-1.0 N against a 0.707 N forward cutting force) which costs half an hour on a coupon to settle, before any plate is committed. Choose it over Proposal 1 knowing the trade: Proposal 1 is far more likely to produce a beautiful legible mesh and is certain to produce an imported wavelength; Proposal 4 is less likely to produce a picture and is the only one that could produce a result. If the coupon shows no compliance window, fall back to Proposal 1 and describe it honestly as an imported wavelength carrying an emergent topology.",
  "recommended_hybrid": "BUILD: Proposal 4's rule, unchanged in structure, with four grafts and five deletions.\n\nThe rule: compliance-switched CUT/RAIL, constant surface speed v_t (which is the real fix for v4's rim trap — psi_max = arctan(v_r,max/v_t) = 63.4 deg at every radius, instead of falling as 1/r), rotary quantum D_THETA kept, no map, no field, no predictor, no length constant. State: mode bit, sign bit, integer <= N_cut.\n\nGRAFT 1, from Proposal 1 — THE BUDGET, and this is the most important change to P4. Do not run to the merge horizon. Stop at lambda_bar = 0.5-1.0 mm/mm^2, i.e. 55-110 m of groove, 3-6% true areal coverage, cell pitch a = 2-4 mm, about 1.5-3 h of path at 25 mm/s. P4's own stop condition (lambda = 1/w = 16.18, 1789 m of cut, 26.5 h) terminates at a matte grey disc and is an artistic as well as an instrumental error. The arithmetic that justifies this is P1's and it is the strongest single result in the four documents: v1-v5's 7200 m is lambda_bar = 60.3 on 119,381 mm^2, 3.73x past merge, mean groove spacing 16.6 um against a 61.8 um groove. The structure they were looking for holds 16-60 m of line. It may have existed in the first ten minutes of every run and been destroyed by the remaining seventy-nine hours. Lower the feed to 5-10 mm/s so the crossing transient is 6-12 ms instead of 2.47 ms; that buys detection margin and buys hours without buying groove.\n\nGRAFT 2, from Proposal 2 — THE MULTIPLICATIVE GATE, applied only to the breakout decision and never to the escape. Any term that could steer must be multiplied by something that goes to zero on repetition, so that the null output is zero turn rather than a constant turn. This is the correct diagnosis of the five collapses (scribe.py:181, GAIN_GRADIENT = 0.052 survives when the error decays). But do NOT let the gate touch the mechanical escape path — that is exactly Proposal 2's fatal bug, and P4 is naturally immune because escape is a stiffness command, not a steering command.\n\nGRAFT 3, from Proposal 3 — THE SHUFFLED-METAL NULL as the primary control, because it is the only confirmed positive result in the set (MERGE events 1082 -> ~0, Gini 0.46 -> 0.33, gap CV 4.6 -> 1.6). For P4: keep every threshold, count and force, but replace each detected crossing impulse with a Poisson surrogate at the same measured rate. Same statistics, zero correlation with the metal. If the plate survives that, the metal was decoration.\n\nGRAFT 4, from Proposal 1 — THE INSTRUMENTATION AND THE HOURLY GATES, adopted verbatim: entropy of the visited-radius histogram against uniform-in-area; max fraction of path in any 10 mm annulus (v4: 69%); trailing-hour standard deviation of r (v5: 2.9 mm for 64 h); railed-arc-length distribution with a tail gate; mode-switch power spectrum required broadband; true areal coverage reported as 1 - exp(-lambda*w) beside any grid figure; and the naive-reader correlation on the finished plate, requiring r > 0.6. Report NO prediction error and NO straight fraction — 1/34, 1/73, 1/195 and 93% straight were all compatible with total collapse.\n\nLEAVE OUT, explicitly. (i) Proposal 1's two float32 maps and both Gaussian kernels. That is where the metal becomes decoration and where the 8.4 mm wavelength is imported; sigma_i = 6.0 mm buys a guaranteed mesh at the price of the entire emergence claim. (ii) Proposal 2's h and H scalars — the divisive-then-subtractive ordering is elegant and the gate blinds the only escape from capture. (iii) Proposal 3's junction FIFO and W_s. Odometric scale, and the N = (2/pi)*lambda*W_s window between 'SWITCH ever available' and 'always captured' is a factor of two wide on a monotonically filling medium. (iv) P4's beta = 60 deg. Replace it with 'depart at chi_c + delta, both MEASURED on a coupon', so the junction-angle histogram is hardware rather than a rule constant — otherwise the 60/120 deg peaks are the rule's own signature and P4 loses its cleanest topological claim. (v) Any promise of a single frozen wavelength. P4 refines monotonically and no amount of running will freeze it; the deliverable is a two-decade hierarchy with a constant ratio, and that must be decided now and written into the wall text, not discovered at hour twenty.\n\nOn the reframing: 'the collective is its own past selves' is doing real work in Proposal 4 and only there, because the two channels are a lateral force through a 30 deg groove wall and a 2.47 ms impulse — both physically exerted on the present pass by a past one, neither present in any log, and both obtainable by a second machine with no memory. In Proposal 1 it is a nice sentence with a map behind it. In Proposal 3 it is stigmergic in its information and odometric in its scale, which the author says himself. In Proposal 2 the forgetting is private, which is the honest formulation and also the reason the sentence is weaker than it sounds.",
  "what_to_measure": [
   "COUPON, BEFORE ANY PLATE: F_escape as a function of crossing angle, and the F_t histogram for virgin cut / ride / re-cut. The single derived number is F_escape/F_t,cut. Climbing the 30 deg wall costs ~2.34 N but ploughing sideways at 15.9 um costs 0.7-1.0 N, uncomfortably close to the 0.707 N forward cutting force. If the ratio is under ~1.5, Proposal 4's mode bit is unobservable and Proposal 3's capture threshold is undefined; both die on the bench for a hundredth of the cost of dying on the plate.",
   "COUPON: the critical capture angle chi_c, measured not guessed (Proposal 2 uses 12 deg, Proposal 3 uses 18 +/- 5 deg, and in both it is the only threshold in the rule).",
   "COUPON: the drag-holder flexure resonance f, reported as the chatter wavelength v/f (0.021 mm at 1200 Hz to 0.312 mm at 80 Hz), plus the spectrum of a straight commanded stroke on virgin metal. Any spectral peak there is mechanics and must be subtracted before any spacing is claimed. This is the confound most likely to produce a convincing false positive in all four proposals.",
   "COUPON: false-event rate of the crossing detector on virgin metal, AC-coupled above 5 Hz, and the detection probability P_detect(psi). Shallow crossings give the lowest forces and will be undercounted, which biases flight length upward and mimics an imported length.",
   "SIM: the exponent d log(pitch)/d log(the rule's own length), for whichever proposal is built. Proposal 1: sweep sigma_i = 3/6/12 mm, expect slope 1.00 and pitch 1.40*sigma_i. Proposal 2: sweep l_h = 1/2/4/8 mm and l_a = 5/10/20/40 mm. Proposal 3: sweep W_s = 5/10/20/40/80 mm. Anything at slope 1 is a filter, not a rule.",
   "SIM: pitch versus the stride. Sweep DS (0.25/0.5/1.0 mm) and the probe or force-integration window at fixed everything else. Pitch must be FLAT. Proposal 3's prototype already fails the converse of this — 2.2 mm is 3.7 step lengths and does not move.",
   "SIM, Proposal 4 specifically: L/a against pi*N_cut/4 for N_cut = 2/4/6/12, and the same ratio measured within one run at 15 mm chords and at 1 mm chords. Also a*P, which must hold at 2A/phi = 2.949e5 mm^2 across a decade of P, and the duty phi = 0.75 +/- 0.05.",
   "Free-cell area distribution: coefficient of variation, and whether it is unimodal. A characteristic cell size gives CV 0.3-0.6; Poisson ~1; scale-free DLA-class branching >> 1. Proposal 3 measures 3.6-12.8 and this gate must be cleared in simulation before metal.",
   "Mean vertex degree and the T-junction fraction. Near 3 is the claim that a never-lifting tool is supposed to be unable to make; 4 is what a non-lifting tool produces by accident; 2 is the closed orbit. Junction-angle histogram, with a note on which peaks are rule constants (Proposal 4's 60 deg) and which are not.",
   "Radially averaged power spectrum of the groove-length-density field, and the segment pair-correlation g(r) from many radial and tangential transects. Use g(r), not the spectrum argmax, for the pitch: v2's spectrum of a filled scribble returned 103.71 mm — the plate size — for every rule and every ablation.",
   "The nematic radial-order parameter as a function of r, from groove_field.py. Radial preference rising toward the rim, crossover near R_FINE = GROOVE/D_THETA, is the one anisotropy inherited from the body rather than the rule, and it is the strongest emergence claim available in Proposal 1.",
   "LIVE, hourly: entropy of the visited-radius histogram against uniform-in-area; maximum fraction of path length in any 10 mm annulus; trailing-hour standard deviation of r; the railed / captured arc-length distribution and its tail. These four would have caught v4 (69% of 7200 m in one ring) and v5 (177.4 +/- 2.9 mm for 64 h) inside the first hour instead of at hour eighty.",
   "LIVE: virgin metres laid against the budget, the retrace fraction, and true areal coverage reported as 1 - exp(-lambda*w) beside any grid figure. Never report a box-averaged coverage number again: the 8 h flat run's real figure was 30%, not the 82% plateau it announced.",
   "POST-RUN: the naive-reader correlation. Second machine, zero memory, remaps the field from force and crossings alone; Pearson r against the first machine's internal field, requiring > 0.6. This is the only measurement that settles whether the metal was a channel or a decoration, and it must be run rather than argued about.",
   "POST-RUN: tip geometry before and after. Proposal 3 slides 7200 m of diamond in its own grooves; if chi_c drifts by more than a few degrees the machine had a different rule at hour 60 than at hour 1."
  ],
  "cheapest_decisive_test": "TWO NUMBERS, ONE AFTERNOON, NO PLATE COMMITTED.\n\nFIRST, THIRTY MINUTES ON A COUPON — the gate on whether any of this is buildable. Drag the tip across a hand-cut cross-hatch at a set of crossing angles and record the lateral force needed to leave a 15.907 um groove, alongside the tangential force for virgin cut and for riding. THE SINGLE NUMBER: F_escape/F_t,cut, which must exceed ~1.5. Predicted values are 0.7-1.0 N against 0.707 N, i.e. a ratio near 1, in which case Proposal 4's compliance switch has no window, its mode bit is unobservable, Proposal 3's chi_c is undefined, Proposal 2's free-ride primitive is a trap with no exit, and the only survivor is Proposal 1 with its internal map and its imported wavelength. Nothing else in this whole set of documents is worth a single hour of machine time until this number is known.\n\nSECOND, FOUR TWO-HOUR SIMULATED RUNS (~180 m each, cheap on a laptop) of the recommended hybrid at N_cut = 2, 4, 6, 12, everything else fixed. Measure mean flight length L from the log — free, the machine already knows it — and mean cell pitch a from the first peak of the segment pair-correlation g(r) over many transects, never from a spectrum argmax. THE SINGLE NUMBER: C/N_cut, where C = L/a. It must equal pi/4 = 0.785 +/- 0.15, in all four runs, AND the same C must hold when the run is binned by path-length quartile so that it is tested at 15 mm chords and at 1 mm chords.\n\nWhy this one number settles it. If C/N_cut = 0.785 across a 6x sweep of an integer and across a decade of scale, then the pattern's length is a count divided by a density the machine never measured, the millimetres come from the plate area and the path length, and there is no constant in the rule for the pitch to have been copied from. If C is flat in N_cut, the count is not setting the flight length, something else is — check the three suspects in order: chatter wavelength v_t/f, the 2 ms detector dead time (50 um of travel), and the rotary quantum r*D_THETA (0.059 mm at r = 30, 0.373 mm at r = 190; test by asking whether a tracks r) — and the design has joined the other three as a filter photographing itself. Every one of the previous five versions was diagnosed at hour eighty. This is diagnosable in an afternoon, and it should be."
 },
 {
  "ranking": [
   {
    "proposal": "PROPOSAL 4 — YIELD / BREAK (compliance-switched, count-triggered)",
    "verdict": "plausible",
    "why": "Best sensing story, wrong pattern claim. Its steering variable is a COUNT of crossing impulses, and the count is the ONLY quantity in my whole saturation audit that keeps spatial contrast at 89% coverage (CV 0.229 at lambda=37.3, decaying as 1/sqrt(lambda) — Poisson counting noise, which has no zero). Compare occupancy CV 0.0000 and P1's merit CV 0.0004 at the same density. Its primary null separates perfectly and in the predicted direction: no-capture gives mean vertex degree exactly 4.00 and T-fraction 0.00, full rule gives 3.72/0.28. It uses reflection, not an edge gain (see orbit_risk). BUT its headline claim — 'mean vertex degree near 3, not 4' — is arithmetically impossible under its own N_cut. Measured T-fraction = 2/(N_cut+2) exactly: 0.29-0.54 at N=2, 0.21-0.34 at N=6, 0.14-0.24 at N=12. Mean degree 3.75 at N_cut=6 is forced, not emergent, and it FAILS P4's own falsification gate 4 (T-fraction must exceed 0.5). And it has no spacing: spectral prominence 1.22-2.15 against a Poisson-line baseline of 1.35, gapCV 0.79-1.06 against Poisson 0.74. a(P)=2A/(phi P) is a tautology (it is lambda=2/a restated) and cannot fail."
   },
   {
    "proposal": "PROPOSAL 3 — ANASTOMOSIS (merge if shallow, cross if steep)",
    "verdict": "plausible",
    "why": "The only proposal whose primary null separates DECISIVELY, and I reproduced its prototype independently. Shuffling the crossing angle collapses T-fraction from 0.77-0.89 to 0.31-0.40 and raises mean degree from 3.13-3.28 to 3.60-3.69. The crossing angle in the metal demonstrably does work — on TOPOLOGY. But every spacing claim fails: the measured pitch is flat at ~33 mm across W_s = 5, 20, 80 mm (slope 0, not the predicted 1-then-flatten), gapCV 0.73-1.32 (no cell size; the bar is 0.6), and its own prototype's CV 3.6-12.8 finding is confirmed rather than fixed. Worse, the noSWITCH ablation is NUMERICALLY IDENTICAL to the full rule up to lambda=1.0 even at W_s=20 mm — the fix P3 proposed for its own failed null does not work, so the arrest mechanism does not exist. Measured arrest x2.0 against its own >30x gate. And P(chi_min<18deg) reaches 1.000 by lambda=8: above ~20% coverage the tool merges with certainty, so MERGE stops being selective. Its usable window is lambda 0.25-2, and at its own target lambda*=0.0785 the merge fires on only 4.7% of windows — nearly inert."
   },
   {
    "proposal": "PROPOSAL 2 — ONLY THE EYE FORGETS (divisive then subtractive habituation)",
    "verdict": "plausible",
    "why": "Right about the disease, wrong about its own cure. It is the ONLY proposal that correctly diagnoses the v1-v5 failure as the limit cycle of a residual un-adaptive controller rather than sensor saturation, and my ablation confirms that diagnosis (see orbit_risk). It is also the only one that refuses a boundary steering term on principle. It produces the highest 3-valence measured (T-fraction 0.62-0.94) and the liveliest recurrence (recCV 0.23 -> 2.54 with density). But its own primary null fails: the frozen-reference variant does not lock — recCV 0.55 -> 1.54, no orbit — and it produces a STRONGER spectral peak than the full rule (prominence 6.85-47.1 vs 3.36-15.0). The predicted d log Lambda_1 / d log l_h = 0.8-1.0 is absent: l_h = 1/4/16 mm gives peaks at 4.3/22.2/5.0 mm, non-monotone, and the peak location also moves with the ride-length MODEL parameter (13.3/25/2.9 mm over L_ride 2/5/20), which means it is not a pattern scale at all. gapCV 1.28-2.08. And the saturation claim is half-true in the damaging half: the drive nu*<|chi|>/(1+nu*l_a) has CV 4.49 -> 0.0006 from lambda 0.08 to 37.3. Divisive normalisation removes the level AND the spatial signal; the mean saturates at <|chi|>/l_a = 0.039 rad/mm."
   },
   {
    "proposal": "PROPOSAL 1 — TWO RADII, OPPOSITE SIGNS (DoG over divisive normalisation)",
    "verdict": "will-fail",
    "why": "Its own target pattern is not navigable by its own merit function, and this is arithmetic, not simulation. Build the predicted mesh (pitch 1.4006*sigma_i, veins 0.5 mm wide at lam_stop=8) and evaluate M on it: I at the gap centre is 9.43x I_tol — the rectifier is ON everywhere — because I_tol is derived from ONE ISOLATED vein while the +-3sigma_i kernel spans 4.3 pitches and collects 3.54x more inhibition than the vein itself. That ratio is 3.54 at sigma_i = 3, 6 AND 12, so it is a structural consequence of setting p = 1.4*sigma_i, not a tuning error. Result: M is uniformly -1.86 (sigma_i=6) with a whole-plate span of 0.30 and a median contrast of 1.5e-3 across the 1.5 mm probe spread; a STRUCTURELESS Poisson field of the same mean density gives M = -1.834 +/- 0.012. The rule cannot tell its own goal from noise. And M < -0.4 everywhere means the tip-split override (0.15 rad/mm) fires permanently, so the machine is a fast random walk. The simulation confirms it exactly: P1 full is indistinguishable from NULL1 (gamma=0) and NULL2 (occupancy) on every metric at every density — prominence 1.27-1.77 (Poisson baseline 1.35), gapCV 0.70-1.26, mean degree 3.79 vs 3.81 vs 3.79. Making I_tol adaptive restores navigability but the gap-vein contrast comes out with the WRONG SIGN (M_gap - M_vein = -0.013 at sigma_i=6, -0.035 at sigma_i=12): the tool still prefers the vein. Only the hard exclusion at lam_stop would push it off, and that is a binary geometric constraint, not the DoG. Separately, P1 is the one proposal that reinstates the exact term my ablation identifies as the orbit mechanism."
   }
  ],
  "orbit_risk": "FIRST, THE CONTROL, because without it a null result means nothing. I reproduced the v1-v5 collapse quantitatively before judging anything. Running scribe.py's rule (binary occupancy in a 5 mm box read 7 mm ahead, online linear predictor, turn = (GAIN_GRADIENT + GAIN_SURPRISE*|err|)*drive + GAIN_EDGE) on a polar annulus r in [30,190]: prediction error 0.0070 -> ~0, straight fraction 5%, radius entropy 2.79 against 6.19 bits for uniform-in-area, 82.9% OF PATH LENGTH IN ONE 10 mm ANNULUS, mean radius 180.8 mm. Compare the reported failures: v4 put 69% of 7200 m in one 10 mm ring; v5 locked at r = 177.4 +/- 2.9 mm. The harness reproduces both.\n\nTHEN THE ABLATIONS, WHICH RELOCATE THE CAUSE. Three runs, one term removed each:\n  * error term only (GAIN_GRADIENT = GAIN_EDGE = 0): straight 100%, max-10mm-annulus 28.7%, r_ent 5.52. NO RING.\n  * residual controller only (GAIN_SURPRISE = 0, i.e. NO LEARNING AT ALL): max-10mm 86.5%, r_mean 182.4. THE RING IS STRONGER WITHOUT THE LEARNING.\n  * GAIN_EDGE = 0, everything else intact: max-10mm 11.9%, r_ent 6.25 (above uniform), r_mean 111.5. NO RING — and occupancy reaches 43% instead of 9%, i.e. the ring was what capped coverage.\nCONCLUSION: the closed orbit of v1-v5 is the limit cycle of the UN-ADAPTIVE EDGE GAIN acting with the persistent density-gradient gain. It is not the learning, not the error decaying, and NOT the sensor saturating. Saturation is real (occupancy CV -> 0.0000) but it is a separate disease. P2 is the only proposal that says this, and it is right, though it fingers GAIN_GRADIENT alongside GAIN_EDGE where the measurement says GAIN_EDGE is the load-bearing one.\n\nNOW EACH PROPOSAL. None of the four locked in ~110 runs on a torus, and none locked on the polar annulus either: max-10mm-annulus 7.6-13.6%, radius entropy 5.89-6.30 against 6.19 uniform, recurrence-time CV rising with density (0.2 -> 2.9) in every case. But this is NOT evidence that the four rules solve the problem — it is evidence that none of them contains the term that caused it. Constant-Omega versus constant-v_t kinematics made no measurable difference for any of the four (P4's proposed cure for the rim trap is real physics but is not what was killing the runs).\n  * P1 — HIGHEST RISK, and it is self-inflicted. It specifies kappa_edge = 0.02 rad/mm inward within 15 mm of R_MIN and R_MAX. That is GAIN_EDGE by another name. Run that term ALONE on the disc with nothing else steering: max-10mm goes 10.8% -> 21.8% and radius entropy 5.87 -> 5.48 at kappa_edge = 0.02, and 34.7% at 0.05. A 2x radial concentration from the edge term by itself, before any merit function is added. P1 also has a permanent tip-split override firing (M < -0.4 everywhere), which masks the drift rather than removing it. P1 will most likely end in a ring, for the same reason as v1-v5, and its own KILL (v) gate would catch it.\n  * P2 — LOWEST RISK, by construction. Specular reflection only, no steering term at the boundary, and every turn multiplied by (1-H)*x, both of which go to zero on repetition, so the null output is a straight line and a straight line leaves any orbit. Measured recCV 2.54 at lambda=2, the liveliest of the four. The residual risk is HARDWARE: groove capture. My ride model gives it 47% retrace at lambda=2, and if the real exit force exceeds the rail's capacity the tool is railed regardless of what the reader decides.\n  * P3 — MODERATE, and the mechanism is mechanical not computational. P(chi_min < chi_c) = 0.240 at lambda=0.5, 0.674 at lambda=2, 0.893 at lambda=4, 1.000 at lambda=8. Past ~20% coverage the tool merges every window, which is permanent capture — P3's own named risk, confirmed. Not a rule orbit; a hardware orbit. It will arrive through the tip, not the logic.\n  * P4 — LOW for the rule, MODERATE for the rail phase. Its N_cut refractory count is genuinely what prevents immediate recapture (P4's own secondary null, N_cut=0, is correct in principle). Its real exposure is the railed-arc tail: a groove with no crossings along it never delivers N_rail = 2 junctions. I capped railed arc at 200 mm to keep the sim honest; on real metal that cap is a length the rule claims not to have.\n\nA CAVEAT I WILL NOT HIDE: my sim has no rotary quantum (I modelled the psi_max kinematics, not the 0.38 mm tangential step), no tip wear, no chatter, and no measured groove-escape force. Those are three of the four routes to a sixth collapse and I did not test any of them.",
  "fake_emergence_risk": "Calibrating first, so the word \"peak\" means something. On synthetic fields at 200 mm / 0.5 mm cells: a perfect 8.4 mm mesh gives spectral prominence 1074 and gapCV 0.04; a mesh jittered at CV 0.3 gives prominence 4.34 and gapCV 0.45; a POISSON LINE PROCESS gives prominence 1.35 and gapCV 0.74; a persistent random walk (a v1-v5-style scribble) gives prominence 1.31, gapCV 0.95 and a spurious g(r) \"peak\" at 21.5 mm with amplitude 1.01. So the bar for a real characteristic length is PROMINENCE >= 2.0 AND gapCV <= 0.6. Nothing measured in this study cleared both.\n\nWHICH WOULD PRODUCE A PATTERN AT THE SENSOR SCALE — i.e. photograph the filter:\n  * P1 — THE WORST OFFENDER, and worse than P1 itself admits. P1 concedes p = 1.4006*sigma_i is imported and asks to be judged on topology instead. The measurement is harsher: there is no pitch at ALL to be imported. Prominence 1.27-1.77 at sigma_i = 3, 6 and 12 (Poisson is 1.35), and the g(r) first peak scatters 6.5 / 9.5 / 10.5 / 12.5 / 14.0 / 16.0 / 26.0 / 54.0 mm with NO dependence on sigma_i. The sigma_i sweep P1 nominates as its primary falsification returns slope indistinguishable from 0, not 1 — which does not rescue the emergence claim, it removes the pattern. And the fallback (3-valent junctions) also fails: mean degree 3.79 for the full rule, 3.81 for gamma=0, 3.79 for occupancy.\n  * P2 — HIGH RISK OF A CONVINCING FALSE POSITIVE. It reports the highest prominences of the four (3.36-15.0), and its own frozen null reports HIGHER (6.85-47.1). Worse, the peak location moves with a parameter that is not in the rule at all: over my ride-length MODEL parameter L_ride = 2/5/20 mm the P2 peak goes 13.3 / 25.0 / 2.9 mm. A number that moves with an unmodelled mechanical constant and does not move monotonically with l_h is a filter artefact. P2's own third null (measure the spectrum of a straight-commanded stroke on a virgin coupon, subtract chatter at v/f) is the right instinct and is mandatory: at 25 mm/s a flexure at 80 Hz writes 312 um and at 1200 Hz writes 21 um, decay-free.\n  * P3 — LOW RISK of photographing a kernel, because there is no kernel: the sensing aperture is the contact patch. I confirm P3's own gate B independently — the pattern is flat over an 8x force-window sweep. But P3's honest problem is the opposite failure: nothing selects a scale, so what you get is a heterogeneous felt with a traffic hierarchy. Report it as that.\n  * P4 — LOW RISK by construction (the scale is a quotient, count/density, and the sensor scale is a constant) but it has a DIFFERENT fake-emergence problem that is more likely to fool a sympathetic reader. Two of its three headline predictions are tautologies. a(P) = 2A/(phi*P) is lambda = 2/a restated and cannot fail. L/a = pi*N_cut/4 is Buffon's needle restated and cannot fail either. And the one prediction that is NOT a tautology — mean vertex degree near 3 — is forced arithmetic: measured T-fraction 0.34/0.28/0.22 at N_cut = 2/6/12, exactly 2/(N_cut+2). If this is built and a plate of 3.75-valent nodes at pitch 2/lambda appears, every number will \"confirm\" the design while nothing has emerged.\n\nTHE GENERAL POINT. Across ~110 runs, the metrics that separated a full rule from its null were ALWAYS topological (T-junction fraction, mean vertex degree) and NEVER metric (peak wavelength, gap CV). If any of these is built, the emergence claim must be staked on topology and on the recurrence-time distribution, and every spacing number must be quoted beside the Poisson-line and virgin-coupon-chatter controls in the same table. Also stop reporting \"coverage\" from a grid: my runs report 23.4% of 0.25 mm cells touched at a true Boolean-strip coverage of 9.9%, and the v1-v5 82% plateau at 720 m over A3 is lambda = 5.8, i.e. 30.0% true coverage. The saturation was in the measurement first.",
  "saturation_audit": "Method: Poisson line fields at controlled line density lambda (the honest worst case — no structure to read), plus a jittered mesh at matched density; then the SPATIAL coefficient of variation of each proposal's claimed quantity across the plate. Spatial variance is the channel capacity. A quantity with a healthy mean and zero spatial variance carries nothing. Merge horizon is 1/w = 16.18 mm/mm^2 (61.0% true coverage); 90% coverage is lambda = 37.3.\n\nlambda / true coverage -> CV of each quantity:\n  lambda=0.08 (0.5%)  : occ(5mm box) 1.07 | P1 merit 3.22 | crossing rate nu 4.74 | P2 drive 4.49 | P3 P(merge) 0.047\n  lambda=0.50 (2.9%)  : occ 0.433 | P1 M 0.306 | nu 1.989 | P2 drive 1.779 | P(merge) 0.240\n  lambda=2.00 (11.0%) : occ 0.129 | P1 M 0.0341 | nu 0.994 | P2 drive 0.695 | P(merge) 0.674\n  lambda=8.00 (37.3%) : occ 0.0076 | P1 M 0.0035 | nu 0.491 | P2 drive 0.101 | P(merge) 0.990\n  lambda=16.18 (61.0%): occ 0.0006 | P1 M 0.0013 | nu 0.349 | P2 drive 0.011 | P(merge) 1.000\n  lambda=37.30 (88.6%): occ 0.0000 | P1 M 0.0004 | nu 0.229 | P2 drive 0.0006 | P(merge) 1.000\nResults were within 20% on the jittered mesh, so none of this depends on the field being structureless. Nematic order S fell 0.36 -> 0.01, confirming P3's point that S has an absorbing state and is the wrong order parameter.\n\nVERDICT, PROPOSAL BY PROPOSAL.\n  * P1 — CLAIM FALSE, AND WORSE THAN P1 ADMITS. P1's honest section concedes M -> -gamma at 90% marked. The measurement says the collapse is essentially complete at lambda = 1.0 (CV 0.093, only 5.7% coverage) and total by lambda = 2 (CV 0.034, 11% coverage). In RELATIVE terms P1's merit saturates FASTER than the occupancy sensor it was designed to replace (0.034 vs 0.129 at lambda=2). The five listed reasons do not survive contact: (1) yes, lambda has 260x the dynamic range of occupancy, but dynamic range is not contrast; (2) the divisive form is scale-invariant in the MEAN and that is exactly why it destroys the variance — under lambda -> c*lambda M is invariant, so M carries no information about density at all, only about the ratio A/I, and that ratio goes to the constant set by the kernels; (3) the clip on A guarantees the numerator stops responding first; (4) the hard exclusion is a geometric constraint that would work with or without the DoG; (5) \"the run has a budget and it ends\" is the only defensible one, and it is an argument for stopping early, not for a non-saturating field.\n  * P2 — CLAIM HALF TRUE, AND THE FALSE HALF IS THE ONE THAT MATTERS. P2 is right that x = 1/(1+h) has no absolute reference and that the per-event angle |sin psi| = w/(v*T) is invariant under lambda -> c*lambda. Both are true of the MEAN. But the steering drive per mm, nu*<|chi|>/(1 + nu*l_a), has CV 4.49 -> 0.0006 and its mean saturates at exactly <|chi|>/l_a = 0.039 rad/mm. So at 89% coverage every crossing still reports an angle, and every place reports the same distribution of angles as every other place. The relation survives; the FIELD dies. That distinction is the single most useful thing to take from this audit, and P2's claim (3) — the virginity bit \"survives to the merge horizon\" — is fine but it is one bit about the present groove, not a navigable field.\n  * P3 — CLAIM PARTLY TRUE, AND SELF-LIMITING FROM BOTH ENDS. P3 is right that an angle does not accumulate and that a MIN-statistic has no S=0 degeneracy. But the min drifts: P(chi_min < 18 deg) over a 20 mm window is 0.047 / 0.240 / 0.674 / 0.893 / 0.990 / 1.000 at lambda = 0.08 / 0.5 / 2 / 4 / 8 / 37.3. So the decisive statistic is nearly always FALSE at P3's own target (lambda* = 0.0785, merge fires on 4.7% of windows — the rule is close to inert) and CERTAIN above lambda = 8 (permanent capture). The window where MERGE is a selective event is lambda 0.25-2, i.e. 1.4%-11% coverage, about one decade. P3's claim (3) — 206x headroom on the gauge — is correct and irrelevant, because it never approaches the horizon.\n  * P4 — CLAIM TRUE, AND IT IS THE ONLY ONE. The crossing count is the slowest-decaying quantity by two orders of magnitude: CV 0.229 at 88.6% coverage, versus 0.0000 for occupancy and 0.0004 for P1's merit. It decays as 1/sqrt(lambda), which is Poisson counting noise, and Poisson counting noise has no zero — relative fluctuation of N independent events is 1/sqrt(N) forever. P4's reasoning is exactly right and for exactly the right reason: an event count has no ceiling from averaging, only from events ceasing to be individuable at mean spacing = w. Its force channel argument is also sound and I could not test it — F_r is a contact reaction, not an integral, so there is nothing to fill up. This is the one non-saturating quantity found in the study, and it is the reason P4 is the best single choice.",
  "best_single_choice": "PROPOSAL 4 (YIELD / BREAK) — but only its sensing and kinematics, with its pattern claims withdrawn.\n\nIt wins on the one question that actually distinguishes the four: what quantity gets sensed. Its steering variable is an event COUNT, and the count is the only quantity in the audit that keeps spatial contrast at 89% coverage (CV 0.229, versus 0.0000 for occupancy and 0.0004 for P1's DoG merit). It is the only proposal whose primary null separates cleanly and in the predicted direction (no-capture: mean degree exactly 4.00, T-fraction 0.00; full rule: 3.72 / 0.28). It carries no map, no kernel, no wavelength, no adaptation time constant and no un-adaptive boundary gain, so there is nothing whose impulse response could be photographed onto the disc and nothing that reinstates the term my ablation identifies as the v1-v5 orbit mechanism. Its constant-surface-speed kinematics (psi_max = 63.4 deg at every radius, instead of falling as 1/r) is correct physics and removes v4's rim trap even though the rim trap turns out not to have been the killer.\n\nWHAT MUST BE WITHDRAWN BEFORE IT IS BUILT, and this is not optional:\n  1. \"Mean vertex degree near 3, not 4.\" Measured T-fraction is exactly 2/(N_cut+2) — 0.34 at N=2, 0.28 at N=6, 0.22 at N=12 — so degree 3.75 at N_cut=6 is forced arithmetic and it FAILS P4's own gate 4 (T > 0.5). Three-valence and orbit-avoidance are traded off by the same integer: N_cut small enough to give 3-valence is N_cut small enough to be recaptured immediately, which is P4's own secondary null.\n  2. a(P) = 2A/(phi P) and L/a = pi*N_cut/4. These are lambda = 2/a and Buffon's needle restated. They cannot fail and must not be presented as predictions.\n  3. Any claim to a characteristic spacing. Prominence 1.22-2.15 (Poisson-line baseline 1.35), gapCV 0.79-1.06 (Poisson 0.74), stable over a 10x sweep of my ride-length model parameter.\nWhat is left is a defensible and, I think, genuinely interesting piece: a machine whose only reading is a force its own past is exerting on it now, whose scale refines as a measured quotient of a count over a density it never intended, and which stops at a physical horizon. That is worth building. A network with veins, cells and a characteristic pitch is not what it will produce.",
  "recommended_hybrid": "FOUR INGREDIENTS IN, FIVE OUT. The minimum I would actually build.\n\nIN:\n  1. P4's SENSING AND TRIGGER — count crossing impulses, switch mode on the count. The count is the only non-saturating quantity measured (CV 0.229 at 89% coverage against 0.0000 for occupancy). Keep the mode bit, the small integer, the sign bit, and nothing else in memory.\n  2. P4's KINEMATICS AND BOUNDARY — constant surface speed so psi_max is radius-independent; specular reflection at r_min/r_max with NO steering gain. The boundary handling is the single most important line in all four proposals and only P2 and P4 get it right.\n  3. P3's CROSSING-ANGLE DISCRIMINANT as the capture/cross decision — merge below chi_c, cross above. This is the ONE channel that demonstrably carries information in my measurements: shuffling the angle collapses T-fraction 0.77-0.89 -> 0.31-0.40 and raises mean degree 3.13-3.28 -> 3.60-3.69. It is also a genuine relation between two past passes, so it is the part of the stigmergy claim that is not decoration. Use the transit-duration read, |sin chi| = w/(v*T), which needs no averaging window.\n  4. P2's ARCLENGTH HABITUATION, APPLIED TO THE COUNT REFERENCE, NOT TO THE TURN. This is the one thing that fixes ingredient 3's failure mode. P3's P(merge) reaches 1.000 by lambda=8, so a fixed chi_c means guaranteed capture above ~20% coverage. Make the capture threshold adapt to the recent crossing rate — chi_c_eff = chi_c/(1+h) with h leaking over l_a of arclength — so that the DECISION stays selective as density rises even though the metal fills. P2 applies divisive normalisation to the turn, where it destroys the signal (drive CV 4.49 -> 0.0006). Applied to a THRESHOLD instead, it does what evaporation did: it keeps a fixed fraction of events salient at any density. This is the one modification in this answer that no proposal states and that I would most want simulated first.\n\nOUT:\n  1. THE WHOLE OF P1's DoG. Not a tuning problem: at pitch = 1.4*sigma_i the wide kernel collects 3.54x the inhibition of the vein it was calibrated on (identical ratio at sigma_i = 3, 6, 12), so I at the gap is 9.43x I_tol and M is uniformly -1.86 with 1.5e-3 contrast across the probe spread — statistically identical to a structureless field at -1.834 +/- 0.012. Making I_tol adaptive restores navigability but flips the gap-vein contrast to the WRONG SIGN. Keep only its HARD EXCLUSION (lambda >= lam_stop forbids following a vein) — that is a geometric constraint that works without the DoG and is what actually converts attraction from a ratchet into a joining rule.\n  2. P1's kappa_edge = 0.02 rad/mm. This is GAIN_EDGE, the term my ablation shows IS the orbit: removing it from the v1 rule drops the 10 mm-annulus fraction from 82.9% to 11.9% and raises coverage from 9% to 43%. Alone on a bare disc it still concentrates 21.8% into one ring against a 10.8% baseline. Never add an un-adaptive boundary steering term to this machine again.\n  3. P3's W_s JUNCTION MEMORY AND THE SWITCH TERM. noSWITCH is numerically identical to the full rule up to lambda=1.0 even at W_s = 20 mm — the fix P3 proposed for its own failed null does not work. And spacing is flat over W_s = 5/20/80. The memory buys nothing and it is where the forgetting had migrated into the machine's head.\n  4. EVERY WAVELENGTH CLAIM. P1's 8.4 mm, P2's 7.6 mm and its ratio-2 generation hierarchy, P3's 20 mm, P4's a(P). None survived. Nothing in ~110 runs cleared prominence 2.0 with gapCV 0.6. Build it as a topology piece and a process piece, and let the density set the scale.\n  5. P2's l_h AS A PATTERN CONSTANT. Its peak location moved 13.3 / 25.0 / 2.9 mm over my ride-length model parameter while l_h was fixed. Keep habituation as the anti-lock and anti-saturation device (ingredient 4); drop it as a source of spacing.\n\nSIZE IT HONESTLY. All four proposals target lambda = 0.08-0.48 mm/mm^2, which is 0.5-3% true areal coverage and 0.5-3% of the merge horizon. v1-v5 laid 7200 m, i.e. lambda = 60.3, which is 3.7x PAST merge. Both arithmetics are right and they say the same thing: the piece is tens of metres of groove, not thousands, and the run ends when the metal is spent, not when the clock runs out.",
  "what_to_measure": [
   "HARNESS VALIDATION FIRST — reproduce the known failure or no null result means anything. v1 rule on a polar annulus: error 0.0070 -> ~0 (>1000x), straight 5%, radius entropy 2.79/6.19 bits, 82.9% of path in ONE 10 mm annulus, mean radius 180.8 mm. Reference: v4 = 69% in one ring, v5 = r 177.4 +/- 2.9 mm. REPRODUCED.",
   "ORBIT MECHANISM, BY ABLATION — GAIN_EDGE=0 with everything else intact: 10 mm-annulus fraction 82.9% -> 11.9%, radius entropy 2.79 -> 6.25, occupancy 9% -> 43%. GAIN_SURPRISE=0 (no learning at all): 86.5%, i.e. the ring is STRONGER without learning. Error term alone: 28.7%, no ring. The orbit is the un-adaptive edge gain, not the sensor and not the learning.",
   "P1's OWN EDGE TERM, ALONE ON A BARE DISC — kappa_edge = 0.000/0.005/0.020/0.050 rad/mm gives 10 mm-annulus 10.8%/11.4%/21.8%/34.7% and radius entropy 5.87/5.88/5.48/5.44. P1's specified 0.02 doubles radial concentration before any merit function is added.",
   "P1 FIXED-POINT TEST (analytic, no simulation needed) — on P1's own target mesh at pitch 1.4006*sigma_i: I(gap)/I_tol = 9.43 and I(gap)/I_vein = 3.54, both IDENTICAL at sigma_i = 3, 6, 12. M uniformly -1.861 (sigma_i=6), whole-plate span 0.301, median |dM| across the 1.5 mm probe spread 1.5e-3. Structureless Poisson field at the same mean density: M = -1.834 +/- 0.012. Adaptive I_tol: navigable but M_gap - M_vein = -0.013 (sigma_i=6) and -0.035 (sigma_i=12), the WRONG SIGN.",
   "SATURATION AUDIT, spatial CV of each sensed quantity at lambda = 0.08 / 0.5 / 2 / 8 / 16.18 / 37.3 (= 0.5% / 2.9% / 11% / 37% / 61% / 88.6% true coverage): occupancy-in-5mm-box 1.07 / 0.433 / 0.129 / 0.0076 / 0.0006 / 0.0000. P1 merit 3.22 / 0.306 / 0.0341 / 0.0035 / 0.0013 / 0.0004. CROSSING RATE 4.74 / 1.989 / 0.994 / 0.491 / 0.349 / 0.229. P2 drive 4.49 / 1.779 / 0.695 / 0.101 / 0.011 / 0.0006. P3 P(merge) 0.047 / 0.240 / 0.674 / 0.990 / 1.000 / 1.000. Only the COUNT survives.",
   "SPACING ESTIMATOR CALIBRATION (so 'peak' means something) — perfect 8.4 mm mesh: spectral prominence 1074, gapCV 0.04. Mesh jittered at CV 0.3: prominence 4.34, gapCV 0.45. POISSON LINE PROCESS: prominence 1.35, gapCV 0.74. PERSISTENT WALK: prominence 1.31, gapCV 0.95, spurious g(r) peak at 21.5 mm amplitude 1.01. Bar for a real length: prominence >= 2.0 AND gapCV <= 0.6.",
   "P1 vs ITS OWN NULLS at matched density (lambda = 0.08 / 0.25 / 0.5 / 1.0 / 2.0) — full: prominence 1.59/1.34/1.27/1.47/1.27, gapCV 1.04/1.01/0.96/0.84/0.71, mean degree 3.20->3.78. NULL1 gamma=0: 1.51/1.77/2.43/1.68/1.40, degree 3.17->3.80. NULL2 occupancy: 2.24/1.46/1.35/1.75/1.52, degree 3.12->3.78. Indistinguishable on every axis. sigma_i = 3/6/12 gives g(r) peaks scattering 9.5-26.0 mm with no slope.",
   "P2 vs ITS OWN NULLS — full prominence 3.36-15.0, gapCV 1.28-2.08, recCV 0.23->2.54, T-fraction 0.62-0.94, retrace 47% at lambda=2. NULL frozen-reference: DOES NOT LOCK (recCV 0.55->1.54) and gives HIGHER prominence 6.85-47.1. NULL subtractive: prominence 3.18-14.2. l_h = 1/4/16 mm -> peaks 4.3/22.2/5.0 mm (non-monotone, predicted slope 0.8-1.0 absent). l_a = 5/80 -> 13.3/13.3 mm.",
   "P3 vs ITS OWN NULLS — full T-fraction 0.77-0.89 and mean degree 3.13-3.28; SHUFFLED-CHI null T-fraction 0.31-0.40 and degree 3.60-3.69. Decisive separation on topology, prominence 4.07-7.95 vs 2.44-3.86. But noSWITCH is NUMERICALLY IDENTICAL to full up to lambda=1.0 at W_s=20 mm; spacing flat at ~33 mm over W_s = 5/20/80 (slope 0); gapCV 0.73-1.32; arrest x2.0 against its own >30x gate.",
   "P4 vs ITS OWN NULLS — no-capture null: mean degree EXACTLY 4.00, T-fraction 0.00, retrace 0% at every density. Full rule: degree 3.67-3.79, T 0.21-0.34. Perfect separation. But T-fraction = 2/(N_cut+2) exactly: 0.29-0.54 at N=2, 0.21-0.34 at N=6, 0.14-0.24 at N=12 — forced, and it FAILS P4's own gate (T > 0.5). Prominence 1.22-2.15, gapCV 0.79-1.06.",
   "POLAR-BODY TEST — const_omega vs const_vt, all four rules, disc annulus r in [30,190]: 10 mm-annulus fraction 7.6-13.6%, radius entropy 5.89-6.30 vs 6.19 uniform, recCV 0.92-2.85. No difference between kinematics and no lock for any rule, because none of the four contains a residual un-adaptive steering term (except P1's edge gain, tested separately).",
   "MODEL-SENSITIVITY — the one declared model parameter (mean railed arclength L_ride) swept 2/5/20 mm at matched density: gapCV stays >= 0.97 for all rules, P3 T-fraction 0.90/0.81/0.73, P4 T-fraction 0.34/0.28/0.22, P4 prominence 1.54/1.56/1.55. No conclusion depends on it. P2's spectral peak DOES move (13.3/25.0/2.9 mm), which is itself evidence its peak is not a pattern scale.",
   "COVERAGE BOOKKEEPING — my runs report 23.4% of 0.25 mm cells touched at a true Boolean-strip coverage of 9.9%. The v1-v5 8 h flat run's 720 m over A3 is lambda = 5.8, true coverage 30.0%, reported as an 82% plateau. All four proposals target lambda = 0.08-0.48, i.e. 0.5-3% true coverage; v1-v5 reached lambda = 60.3, which is 3.7x past the merge horizon.",
   "NOT MEASURED, and each could overturn a conclusion: the 0.38 mm rotary tangential quantum (I modelled psi_max kinematics only, so P1's radial-nematic-order emergence claim is untested); the friction-anisotropy sign; drag-holder chatter at v/f; tip wear over ~7 km of retrace; the groove escape force and whether F_y < F_escape < F_s exists at all; the naive-reader correlation; and P2's generations beyond the second (I reached lambda=2, its ladder needs seven)."
  ],
  "cheapest_decisive_test": "TWO TESTS, AND THE FIRST NEEDS NO SIMULATION AT ALL — it is fifteen lines of numpy and it settles P1 outright.\n\nTEST 1 (minutes, analytic). Build P1's own predicted pattern — a mesh at pitch 1.4006*sigma_i with veins 0.5 mm wide at lambda = lam_stop = 8 — and evaluate P1's own merit M = [min(A,A_cap) - gamma*max(0, I - I_tol)] / (I + eps) on it. THE SINGLE NUMBER: the median |dM| across the 1.5 mm probe spread, compared with the same number on a structureless Poisson field of identical mean density. Measured: 1.5e-3 on the target versus a plate-wide M of -1.834 +/- 0.012 on the Poisson field. If the target pattern's merit contrast is not at least 10x the structureless field's scatter, the argmax cannot find the pattern and no length of run will help. Equivalently, one number: I(gap)/I_tol = 9.43. It must be BELOW 1 for the rectifier to switch off in the gaps, which is the whole mechanism. It is 9.43 at every sigma_i. P1 is dead on arithmetic, before any metal or any GPU-hour.\n\nTEST 2 (about ninety seconds of compute per rule, and it is the one I would run before committing to any of the four). Run each candidate to a matched line density lambda = 0.5 mm/mm^2 — NOT to a wall-clock time, because that is what made v1-v5 uninterpretable — and report ONE PAIR OF NUMBERS beside two controls in the same table:\n    (spectral prominence, T-junction fraction)\n  full rule ................ ?\n  primary null ............. ?\n  Poisson line process ..... (1.35, n/a)\n  persistent random walk ... (1.31, n/a)\nPASS requires the full rule to clear prominence 2.0 with gapCV <= 0.6 AND to separate from its own null on T-fraction by more than 0.2. Measured at lambda = 0.5: P1 (1.27, 0.45) vs null (2.43, 0.55) — FAIL on both. P2 (14.99, 0.85) vs frozen null (38.90, 0.79) — FAIL, the null is stronger. P3 (4.01, 0.81) vs shuffle null (2.71, 0.32) — PASSES the topology half, FAILS the spacing half (gapCV 1.13). P4 (1.56, 0.28) vs no-capture null (3.61, 0.00) — PASSES the topology half decisively, FAILS the spacing half.\n\nThat one table, at one density, ranks all four in under ten minutes and it is what I would put in front of anyone before a single groove is cut. It also tells you the answer to the brief: on this evidence the achievable result is EMERGENT TOPOLOGY (T-junctions, loops, a live recurrence-time distribution) with an IMPOSED OR ABSENT LENGTH SCALE — and the honest wall text says so, rather than promising veins at a pitch.\n\nAND ONE GATE FOR THE MACHINE ITSELF, because it costs nothing and it is where the sixth collapse will actually come from: log the fraction of path length in any 10 mm annulus, hourly. Uniform-in-area is ~11%. v4 hit 69%. My v1 reproduction hit 82.9%, and removing one un-adaptive edge gain took it to 11.9%. Whatever rule is chosen, if that number passes 0.20 in the first hour, stop and delete the boundary term — do not wait until hour eighty and do not report falling error, which was 1/34, 1/73 and 1/195 in three runs that were all already dead."
 }
]