specialized ceiling / generic challengerceiling green · generic red
evidence-to-geometry handoff: every omitted trajectory, clock, barrier, free-energy, probability, or force question can now draft a complete evidence request directly into the pre-growth physics protocol. Where a current geometric proxy also has an explicit neutral setting, the same panel can register one matched baseline/neutral ablation. Both modes freeze selected and requested manifest IDs before candidate enumeration, change no control by themselves, and retain the physical quantity as unresolved.
Two exact unseen levels are required before a symbolic million-site count.
family-blind model selection: every geometric hypothesis is scored before selection. On the competing Fibonacci control, substitution wins over an inexact quotient, 0.0192 vs 1.5607; proposal order does not change the result. This is the specialized ceiling: four different encoders still remain behind the shared interface, so it is not the generic-cluster victory condition.
robustness gate: 0.005 Å noisy NaCl/IQC/Fibonacci continuations recover the clean first level at 100% P/R; a noisy 1%-vacancy IQC also recovers 100% P/R using its inferred inversion center. 30° hBN with 0.006 Å noise + 3.5% vacancies reaches 100% P / 99.20% R.
finite-window gate: 12 / 12 pass. Selected productions and learned parameters remain stable over NaCl 64–512, IQC 345–919, Fibonacci 216–1,728, and twisted hBN 470–1,130 input atoms; every next-window continuation is exact.
measured cost: learning 0.34–3.37 s; exact two-level emission 0.03–0.26 s. Finite million-site counts take 10–73 μs. IQC density counting takes 106 μs at 0.084% error versus a 2.49 s exact enumeration. This is representation/action compression, not an MD speed claim.
explicit million-site emission: three independently digested streams now pass: NaCl emits 7,077,888 sites in five learned quotient actions (16.2 s); the IQC promotes its carried three-component GCTS mark into a rank-six address macro and emits 2,791,097 sites in six actions (9.7 s); the Fibonacci-product rule emits 1,061,208 sites in five actions (2.6 s). IQC macro emission performs no coordinate lift, model refit, target lookup, or potential call. Recursive factors are 8.000×, 4.202×, and 4.292×, while explicit output remains linear.
compact inference artifacts: local IQC growth keeps typed ports, frontier geometry, and the carried mark but drops all 13,111 fitting-only port pairs and the global section. The promoted address macro keeps only the learned unit, window, species thresholds, origin, and frame—no atlas, seed marks, target sites, or fitting model.
published Cd–Yb transfer gate: an immutable CC-BY-4.0 implementation of the published Cd5.7Yb cut-and-project model supplies sealed 506 / 1,056 / 1,672-atom windows about a fixed off-centre point. This avoids mistaking rotations about the model's global icosahedral origin for translated local repetition. From only the 506 seed atoms, the generic irregular-support learner covers 99.4% with repeated supports (100% with an explicit residual class) and its frozen vocabulary covers 77.1% of the first unseen annulus. Finite proper-SE(3) overlap ports transfer too, but exact incoming markings do not yet beat shuffled controls on the quasicrystal cases. Autonomous continuation, hierarchy, and causal marking gates remain red.
sealed frontier replay: candidate poses are now generated only by composing train-frozen proper-SE(3) ports with already placed clusters; held-out atoms enter a separate scorer afterward. One-step replay places a correct NaCl atom and three correct Cd–Yb atoms. The same frozen Cd–Yb frontier already contains a 19-correct-atom action, exposing policy headroom. The ideal-IQC frontier contains no exterior action, so its failure is currently a missing grammar—not something a better ranker can hide.
clusters of clusters: a sparse cover graph now removes more than 99.6% of redundant overlap edges before exact port-labelled macro mining. Independent recurrence, proper-SE(3) consistency, and positive-description-saving gates retain 3 NaCl, 42 ideal-IQC, and 2 Cd–Yb first-level macro types. These are genuine reusable unions of clusters, but not yet stationary recursive productions; the million-site generic macro gate remains red.
history-free recursive promotion: the current canonical IQC route discards action history and re-clusters 2,064 grown atoms. Seventy-eight repeated support types with 1,122 occurrences, plus explicit gap clusters, cover the cloud completely. The boundary-aware exact-support quotient continues 73 → 17 → 5 → 3 → 2 → 1 → 0; retaining mutually exclusive exact derivations separately gives 73 → 17 → 6 → 3 → 2 → 1 → 0. This is deep train compression, but the chemistry, chirality, directed-port, normalized-pose, and population-substitution audit still finds no stationary production.
learned crystal stationary control: from positions and species alone, the generic grid learner discovers three recurrent NaCl generators, radix 2, and all eight child offsets. Recursive execution reproduces separate held-out colored configurations exactly and represents 4,194,304 sites after seven symbolic actions. A hardened port audit then uses two independent bounded 216-atom presentations: 29,988 frozen relations join 52 cells and export an 8-child macro with 24 directed ports, a 52-atom union, two atom-disjoint occurrences, and MDL saving 30. Frozen-relation replay over three learned factors gives 1,478 / 750 / 86 witnesses and certifies strong stationarity at scale 2. Permutation, proper-SE(3), IQC, amorphous, and ternary controls pass. The radix/offset vocabulary still comes from the positions-only grid learner and is then validated against frozen ports; learning that closure from ports alone remains future work.
dense deployment and marking audit: sparse independent occurrences decide which macros earn admission; an exact dense matcher then finds every deployment of those admitted types for execution. It reconstructs 86 / 86 locally emitted IQC atoms, but that geometry was present during fitting, so this is a target-blind training reconstruction rather than held-out growth. On the analogous dense NaCl frontier, frequency marking improves the unmarked order but does not beat within-parent shuffled controls (empirical p = 0.406); the causal marking gate remains red.
spatially disjoint IQC continuation: the primitive irregular-port grammar is fit on an 887-atom off-centre patch and replayed from a non-isometric, spatially disjoint 223-atom seed. The 877-atom scoring crop is not constructed until replay finishes. Unmarked replay reaches 201 / 266 correct novel atoms in 100 actions; precision falls to 75.6%, exposing a real exterior grammar and a real branch-ordering problem rather than target leakage.
confirmatory GCTS marking: a rule frozen on a separate exploratory patch combines train-only production frequency with live agreement among overlapping whole-cluster proposals. On a previously unopened confirmatory patch it ranks 97 / 100 exact actions, versus 90 for frequency and 95 for consensus alone. Thirty-one degree-preserving incidence shuffles reach at most 93; exact-action, wrong-site, and matched-work tests each give p = 0.03125. Recovering the same 177 correct sites costs 102 proposal-plus-backtrack work, versus at least 151 for every shuffle.
executed five-wave growth: a stricter train-calibrated consensus threshold is run by the target-blind batch/tree executor, which commits only compatible antichains of complete colored clusters. Five self-fed waves accept 3 → 17 → 4 → 30 → 5 placements and add 109 / 109 correct atoms. The zero-threshold arm adds 409 / 435 and the 0.5 arm 312 / 320, demonstrating the precision/coverage trade-off. This is exact finite quasicrystal continuation; the wave counts are not stationary, so the exponential clusters-of-clusters gate remains red.
promoted action macros: those 59 accepted placements are promoted target-free into eight connected clusters of clusters with child counts 3, 17, 3, 1, 26, 4, 4, 1. Every node, colored union, overlap, frozen boundary port, and antichain certificate is exact. Six nontrivial macros canonicalize, but every normalized signature occurs in only one wave; no three-wave recurrence or scale law is present yet.
action history versus re-clustering: the invariant action-history route now admits 11 types, each with maximum dense multiplicity two, and reaches only two positive recursive levels. Re-clustering the resulting atomic clouds is the stronger route above: it raises proof multiplicity and reaches six positive quotient levels without treating move IDs as geometry.
sealed hierarchy re-encoding: the width-three 256 / 259 stop is now diagnosed: missing IDs 184 / 185 / 252 all require primitive 49, a 23-atom support seen only twice near the boundary of training patch 2 and never in heldout. Exact semantic alternatives remain 256 / 259. A train-only strict-majority recurrent core removes such one-patch artifacts while retaining original IDs and exact residual atoms. At width five, raw / selected exact types are 520 / 148, 53 / 10, 16 / 4, and 3 / 1, with 1,495 → 85 → 29 → 9 heldout occurrences. Exact core coverage is 1,220 → 1,033 → 925 → 870 of 1,248 atoms; residuals 28 → 215 → 323 → 378 complete each coordinate/species SHA-certified representation. Minimum heldout namespace support is 2 / 3 / 3 / 3 and maximum support size is 78 / 78 / 110 / 111 atoms. The complete heldout positions are observed during matching—only the vocabulary is frozen—so this is representation transfer, not growth. No >3 amplification or common three-level stationary key is found; autonomous and exponential IQC gates remain red.
sealed autonomous recurrent-macro execution: the growth corpus is now five mutually disjoint raw IQC windows rather than self-generated reconstructions. A width-three train-only recurrence gate retains 141 of 322 first-level macro types. On a sixth raw-ID-disjoint window, two frozen macro poses seed a target-blind executor that composes only learned overlap and witnessed boundary ports. Within a public radius-11 boundary it accepts 16 then 8 whole macro placements and emits 92 then 56 atoms. The scorer is opened only afterward: 136 of 148 novel atoms are correct, for 91.9% precision and 21.0% unseen-shell recall. All placements have proper-SE(3), colored collision, overlap-inclusion, and training-adjacency certificates. A batch-cap audit can display the same final union as 8 → 8 → 8 placements, so the invariant claim is causal depth two followed by a finite fixed point—not “three growth waves.” Exact ID-based marking transfers to 0 / 62 evaluation candidates. An ID-free hierarchy covers all 62 and cuts matched work from 71 to 51, but keeps the same 136 / 148 atoms and reaches only p = 0.25 against 31 shuffles. A 35-feature continuous mark adds live proposal consensus but its threshold still yields 134 correct and 12 wrong. An all-role audit covers every one of 141 parent types and shows all 48 incorrect actions were exact rules seen as correct in training. Eight final errors are correct coordinates with the wrong species; four are unsupported sites. A causal colored-terminal section trained on 3,047 examples attempts four recolors and ten removals, but falls to 124 / 140 correct. The replacement geometry-first vocabulary learns 35 irregular supports and 275 proper-rotation decoration alternatives; it covers 841 / 873 heldout atoms geometrically and 795 with train-seen decorations. Factoring geometry from chemistry uses 7,731 rather than 49,735 colored port classes. Optional overlap propagation from 226 seed labels infers 267 / 279 outer labels. The new bounded tree search freezes 55,483 identical actions for every arm: the GCTS ranking/admission policy reaches 354 / 415 correct labels, versus 116 / 140 for modal and every one of 31 label shuffles (p = 0.03125). Precision is still only 85.3%. Naively promoting whole colored macros is worse—0 / 13 exact decorations transfer; macro-role context predicts 5 / 27 child decorations versus 2 / 27 modal, but fails shuffles (p = 0.1875). Autonomous continuation and a measurable GCTS search advantage are real; sustained growth, accurate transferable decoration, and exponential IQC growth remain red.
published Cd–Yb reconstruction: two disjoint radius-14 crops of the published Cd5.7Yb model provide 969 train atoms; a third disjoint crop provides 478 evaluation atoms. The learner receives no cut-and-project coordinates, source-site labels, family name, cell, or potential. Frozen geometry covers 449 / 478 atoms. Starting from 59 known inner atoms, all arms see the same 1,385 exact actions. GCTS reconstructs 378 / 378 novel atoms—100% precision and 90.21% outer recall—while modal and all 31 within-geometry shuffles stop at 377 / 377 and 89.98% recall. Extra correct reach at unchanged perfect precision gives p = 0.03125. The real-quasicrystal reconstruction and matched GCTS gates are green; coordinates are supplied and the search reaches a finite fixed point, so autonomous and exponential growth remain red.
published Cd–Yb autonomous continuation: the same two training crops now freeze 175 colored irregular cluster types and 14,595 proper-SE(3) ports. A consensus threshold is selected only on the training windows, then the executor receives just the disjoint 59-atom colored seed and a public radius-14 boundary. Before the 478-atom target is opened, five self-fed waves accept 3 → 18 → 9 → 35 → 7 complete clusters and emit 179 coordinates. The sealed scorer finds 177 correct and 2 wrong—98.88% precision and 42.24% outer recall. Unfiltered growth reaches 68.26% recall at 78.14% precision; strict consensus is exact but reaches only 4.53%. Accepted antichains promote into exactly certified colored action macros, but no production recurs across three waves. Finite autonomous real-material continuation is green; sustained/stationary and exponential growth remain red.
causal local GCTS section: the marking now reads the bounded frontier instead of a raw rule ID. Training discovers a gap at 2.118 nearest-neighbor units; a proposed site on the close side needs at least five independent frozen cluster-connection witnesses. On two mutually disjoint Cd–Yb nuclei it autonomously emits 178 / 178 and 117 / 117 correct atoms. The same unmarked searches emit 193 / 220 and 168 / 224, or 83 false atoms in aggregate. Thirty-one controls preserve every wave's candidate actions and witness-count multiset but permute which candidate owns each count; none matches 295 correct atoms at zero error (p = 0.03125). This is a causal GCTS-marking win during autonomous growth of a published quasicrystal model. Both runs reach finite fixed points and promoted macros have no three-wave recurrence, so sustained/stationary and exponential growth remain red.
deep Cd–Yb clusters of clusters: five disjoint radius-14 windows (2,385 atoms) learn a complete irregular cover and nine positive exact quotient levels, 80 → 36 → 22 → 15 → 8 → 6 → 4 → 2 → 1, with the largest colored support growing from 67 to 472 atoms. At level one, 79 / 80 retained types have witnesses in at least two windows; every retained later-level type does. On two untouched windows, the full frozen vocabulary stays intact while absent symbols remain dormant: exact active types/occurrences continue 53/92 → 20/26 → 8/8 → 2/2, then reach zero at level five. All levels preserve frozen IDs/ports and exact residual-complete replay. Since heldout coordinates are observed, this is four-level re-encoding, not growth. No three-level production key survives even topology, so stationary and exponential quasicrystal growth remain red.
seed-only hierarchical frontier: a spatially disjoint 478-atom Cd–Yb seed recognizes 276 primitive occurrences but no complete frozen level-one macro, so exact macro execution cannot start. The new partial recognizer instead anchors train-frozen alternatives on one finite, port-connected child and exposes 82 proper-SE(3) completion candidates; posthoc only 6 are exact. A mark fitted on five radius-7 → radius-14 training frontiers selects one exact action in its top five and emits 16 correct / 18 wrong sites. Constant ordering emits 13 / 24, but all 31 within-parent label shuffles tie the learned result (p = 1). Partial macro search is now operational, while transferable GCTS ranking and autonomous hierarchical growth remain red.
preregistered hierarchical confirmation: before opening a second Cd–Yb nucleus, the repository publicly froze the continuous ID-free mark, actual 28-row training corpus, source hashes, top-five rule, 31 within-window shuffled refits, and centre (35, 35, −35). Its common first frontier contains 36 candidates and no completely exact macro action. The marked top five emit 27 / 56 correct sites, versus 10 / 41 for stable and frequency ordering, but every shuffled model reproduces the marked result (p = 1). The target-blind hierarchy nevertheless self-feeds through seven nonempty waves over four levels and reaches 247 / 2,217 outer-shell atoms (11.14% recall). Both preregistered gates remain red. The only target opening and score are sealed in a hash-checked, non-rerunnable fixture.
site-resolved GCTS section: keeping the same frozen macro geometry, three predeclared inner radii across five training windows provide 1,245 emitted-site examples (871 supported / 374 unsupported) from 123 macro candidates. The ten-feature local proper-SE(3) section reaches grouped site AUC 0.8864 and whole-action AUC 1.0; both beat all 31 within-window label shuffles (p = 0.03125). The earlier searched logit margin remains red when its own choice is fully nested (94.48% precision). A simpler deterministic calibration now fits on four original windows and places the threshold at the next representable probability above every fitted negative—no margin grid or held-window tuning. Across the five outer folds it retains 207 / 211 correct sites (98.10% precision, 23.77% recall), every fold is nonempty, and the minimum fold precision is 95.92%; the best shuffled refit retains only 21 correct sites (p = 0.03125 on correct retained sites). The rule was devised after inspecting this training corpus, so it is frozen only as an exploratory candidate for a future untouched nucleus, not a confirmation result. The partial-site executor itself remains exact: residual terminals stay explicit, a child appears only after its full colored support is present, and a parent promotes only after every child and frozen port is independently verified. Synthetic and NaCl controls pass, with NaCl emitting 48 / 48 correct sites. A group-sealed execution audit fits the marking on four windows and executes on the fifth. Its strict per-site arm commits 9 / 74 first-wave obligations (8 correct) but closes no child. The new whole-child threshold is instead placed above every fitted negative candidate section in the other four windows; on identical first-wave candidate batches it commits 16 complete port-witnessed children, emits 146 / 146 correct sites, independently fits and promotes 16 parents, and produces genuine child-driven later waves in two of five held development windows. Freezing one final lower-quartile policy from all five training windows then transfers without refit to two spatially disjoint, previously consumed reserves: one supplies no candidate and emits nothing; the other executes 4 → 4 → 3 complete sections across three waves, yielding 81 / 81 correct sites and 11 promoted parents (20.51% active-window outer recall). A train-only coverage audit rejects weakening the macro anchor from one-half to one-third: the relaxed rule adds one wrong held-development action and ten wrong sites. The empty reserve's 32 recognized occurrences span 17 frozen support types but overlap zero retained macro-anchor types, so it produces zero pose hypotheses. Its lower-level port grammar still contains 204 exact among 345 target-blind primitive candidates covering 292 correct sites; the failure is therefore promotion/anchor coverage, not absent local geometry or the marking threshold. Because those structural reserves were already used by re-encoding audits, this is not fresh confirmation. The default Cd–Yb policy remains disabled while recurrent macro-anchor coverage, fresh transfer, sustained autonomous growth, stationarity, and exponential claims remain open.
finite-state substitution audit: allowing a quasicrystal to alternate among several exact production states does not weaken the stationary gate. A period-p cycle requires at least 2p+1 consecutive levels, repeated exact chemistry/chirality/port semantics, equal independently learned transition scales, and identical population substitutions on a sealed replay. The synthetic two-state control passes. The present IQC hierarchy has only four levels, zero exact adjacent-state intersections, and no independently observed heldout scale, so both stationary and finite-state exponential claims remain red.
hierarchy selection and stationary audit: a target-blind deterministic beam retains exact derivation alternatives, improving the promoted occurrence path from 153 → 34 → 10 → 6 → 4 → 2 to 324 → 78 → 26 → 12 → 8 → 4 and the fixed-horizon train score from −63.205 to −34.592. It does not add a seventh positive level or produce a stationary witness. The exact semantic quotient is rejected by train-only shuffle/perturbation controls. Exponential status still requires one chemistry/chirality/port production across three consecutive levels, equal learned scales and integer substitutions, independent support, and exact replay.
width and crystal controls: the single sparse 216-atom audit remains evidence-starved and admits only six size-two macros. This is not a width failure: with two independent bounded 216-atom presentations, the same nonfactorial exact search reaches child width eight and the full learned relation graph supplies the stationary 8-child certificate above. The stronger crystal baseline does not change the red IQC stationary result.
matched-quality marking ablation: compiled sections cut full-recall proposal work 56× for substitution and 717× for IQC. On an unseen IQC inflation, a frozen learned local halo reaches the same 252 correct moves with 392 vs 526 proposal checks and 140 vs 274 failed branches.
generic cluster-of-clusters gate (in progress): learned NaCl and IQC superclusters compile to coordinate-bearing child poses, explicit gap atoms, and overlap maps, and recursively replay every stored prototype exactly. On a frozen 2:1 occurrence split, 70 NaCl and 59 IQC right-hand-side alternatives cover >99% of held-out cases, but the present bounded halo/port marking does not select them: it ties the parent-only modal baseline at 90.0% / 88.5%. The gate stays red until a train-only connection marking improves this result and then transfers across an unseen spatial guard band.
sealed spatial fixture: recursive raw-atom guards use the sum of all lower-level radii plus the halo. The 13,824-site NaCl cloud certifies 3 disjoint levels (785 / 785 deepest centres); the 8,603-site IQC cloud certifies 2 (532 / 532). IQC level 3 is explicitly red until a larger patch leaves a nonempty cumulative guard.
frozen hierarchy transfer: scale, signature dictionaries, promoted colors, and unknown labels are fit on the training side only. All held-out signatures are known across 3 NaCl and 2 certified IQC levels. A train-only 95%-coverage vocabulary gives ≥95.29% NaCl and ≥95.59% IQC promoted coverage (4/6/16 and 51/30 colors). Production and search transfer remain red.
causal incoming-halo ablation: at the deepest cumulatively guarded levels, both systems have one RHS per parent—16/16 NaCl and 30/30 IQC—hence zero decomposition backtracks and no possible marking gain. RHS decomposition is not the use case that lights GCTS; the next ablation ranks neighboring frontier macro placements.
live-frontier marking gate: on the actual 1,969 → 8,603 IQC frontier, every arm receives the same 66,110 proposals and stops after 120 correct novel sites. Incoming GCTS marking needs 120 checks / 0 failures; overlap-vote ordering needs 232 / 112. Thirty equal-budget train-label-shuffled markers need median 4,608 checks (best 404). No held-out label trains the marker.
order-independent spatial hierarchy: the 368-site exact frontier is split into eight guarded spatial domains; 296 off-boundary sites are covered completely. The same generic colored-point learner finds recurrent supports 3 → 11 → 37, giving 3.67× and 3.36× amplification across three genuine cluster levels. Move order, lattice metadata, and phase labels are absent. Nine further promotions to one million sites are only a projection until unseen levels replay.
frozen spatial grammar: the distance scale, type dictionaries, and eight parent→child productions are fit on four negative-x sectors (148 atoms) and replayed without refitting on four positive-x sectors (148). Vocabularies 4 / 3 / 1 achieve 100% held-out type, atom, and production coverage at all three levels. Each parent has one RHS here, so marking is tested separately on frontier choices.
large cumulative-guard gate: an exact meet-in-the-middle 6D oracle generates a converged 155,097-site IQC in about 2.5 s. Bounded coordination+angular GCTS colors fit on 28,211 inner atoms cover 100% of 106,162 / 70,458 / 4,260 disjoint held-out centers at three recursive levels. A matched-density amorphous XYZ null reaches only 42.6% at level 1 and 24.1% at level 3 and is rejected. This proves color transfer, not yet outward geometry generation.
exact production replay: on 1,024 frozen samples per level, parent colors transfer to 98.7% / 97.9% / 100% of held-out parents, but complete species-labelled child geometry transfers only 67.4% / 0% / 0%. Level 1 needs up to five RHS alternatives; higher levels encounter unseen geometry despite one training RHS. The next marking must condition alternatives on incoming ports. Pose-based execution remains red.
causal incoming-port ablation: an outward proposal may inspect only smaller-radius atoms already behind the frontier. On the 285/2,048 held-out level-1 contexts that recur in training, this marking selects 104 exact outward productions, versus 31 for parent color alone and at most 44 in 30 within-parent label shuffles. This is a real marking effect, but context coverage is only 13.9% and levels 2–3 have no exact transferred contexts, so the overall gate remains red.
seed-only recursive scale: the centre-connection learner no longer receives φ. It ranks ratios from the seed distance spectrum by closure at both s and s², with a generic low-degree algebraic refinement. The 507-atom IQC selects 1.61803398875; recurrent-distance closure is 51.2% / 55.8%, and the frozen connection benchmark retains its held-out growth result.
sealed connection gate: a stricter protocol learns connection labels only from 93 inner parents whose φ-images remain inside the 507-atom seed; the 1,969- and 8,603-atom windows are evaluation-only. It proposes 3,404 novel sites, of which 500 are correct (14.7% precision, 7.5% recall). Naive coordination-distance filtering does not help. This gate is red and replaces the earlier transition-trained result as the causal generic baseline.
metric motif-centre ports: proposals outside the finite seed are censored rather than mislabeled negative. Exact connection length modulo the inferred recursive scale produces 860 / 860 correct held-out sites (100% precision, 12.96% recall), versus 14.7% precision for the otherwise identical coarse-state ablation. The 73 accepted ports are learned only inside the 507-atom seed.
iterated port growth: the 860 predicted species-labelled atoms are inserted without oracle colors, growing 1,969 → 2,829 exactly. But admitting train-supported single ports in wave 2 proposes 13,020 / 13,020 false sites. GCTS overlap consensus is therefore essential; the regenerative gate rejects this branch rather than displaying exponential error growth.
overlap superclusters: the exact 860-site action-incidence graph contains two large connected macro actions of 500 and 240 sites plus 32 smaller components. These are conflict-free parallel actions, but their scaled copies are not valid successors, so this is clusters-of-clusters action compression rather than exponential recursion.
higher-order port-pair section: the seed learns 271 pairs of metric ports that co-support the same endpoint. Its frontier halo is also train-derived (6.155 Å). The frozen policy produces three exact waves, 260 → 192 → 60, adding 512 / 512 correct atoms before stalling at 2,481. This is genuine regenerative generic GCTS; the shrinking sequence keeps the exponential gate red.
amplifying pair macro: the minimum seed endpoint has 11 supporting port actions. The frozen scale-normalized rule requires ⌈11 / slevel⌉ votes: 7 then 5. It selects 80 / 80 exact sites at the first unseen scale and 480 / 480 at the second—a measured 6× batch amplification. This passes an exponential-style two-scale gate, but sparse coverage and no million-site generic rollout remain explicit limitations.
cross-family selector: the shared seed-only competition now includes translation quotient, fixed-anchor similarity, and overlap-port sections. With no phase label or held-out target, it chooses translation for NaCl, port pairs for IQC (61/507 anchor support), and the anchor for the 3-D Fibonacci control (216/729). All three pass two exact unseen scales; Fibonacci emits 2,090 and 7,222 exact sites.
generic geometry VM: all three selected markings compile to one colored-site interpreter. It emits exact species and positions at two unseen levels: NaCl adds 1,512 then 12,096 sites; IQC adds 80 then 1,254; Fibonacci adds 2,090 then 7,222. The IQC chemical decoration is evaluated by its learned bounded internal section, fixing a coordinate-only result that previously mislabeled the atoms.
recursive port/cover graph: the three VM opcodes are now normalized to the same node schema: binding relation → affine output → coincident overlap group → connection section → color section. Every compiled control is one self-recursive node; the common relational evaluator reproduces all six exact colored-site outputs without an opcode or material-family dispatch.
self-fed multiscale graph: starting from 1,969 IQC atoms, the graph inserts only its own colored predictions. It regenerates 260 → 192 → 120 → 80 sites at level 1, 792 → 204 at level 2, and 360 → 240 → 120 at level 3: 2,368 / 2,368 exact additions over nine waves, ending at 4,337 atoms. No held-out atom or oracle color enters the state. Level totals 652 → 996 → 720 are not monotonically amplifying, so the exponential gate remains red.
section-assisted gap ceiling: single ports propose missing coverage and the learned IQC internal-space section acts as an accept/reject connection marking. It rejects 420 invalid endpoints and self-feeds six exact recursive levels totaling 3,304 → 1,332 → 300 → 2,520 → 780 → 120 sites. The cloud grows 1,969 → 10,325 with 8,356 / 8,356 exact colored additions. This global section is stronger than a bounded local GCTS halo, and later decline keeps the exponential generic gate red.
carried local marking: each of the 507 seed clusters receives a learned three-component mark. Every new mark is transported through one two-cluster port, then locally selects connection/failure and species—without lifting the candidate coordinate or querying the global section. It grows 507 → 1,689 with 1,182 / 1,182 exact colored additions over two recursive levels (642 → 540).
clusters-of-clusters promotion: the self-generated 1,689-site cover promotes the same 30 recurrent types from 29.70 to 98.57 atoms of average support (3.32×; maximum 225), then freezes 789 promoted ports. Three self-fed scales add 3,234 → 8,924 → 17,674 exact colored sites (2.76×, then 1.98×), reaching 31,521 atoms from the 507-atom seed. The seed compiler now derives its scale, radial shells, and boundary from the point cloud rather than receiving IQC constants.
executed cross-family gate: one positions+species discovery API and one action API now materialize three exact self-fed actions for NaCl (216 → 1,728 → 13,824 → 110,592), IQC (507 → 4,923 → 13,847 → 31,521), and Fibonacci product (729 → 3,375 → 13,824 → 59,319). All 252,953 output sites are scored. Cross-family execution is green; the stricter single-production gate stays red because translation, promoted ports, and substitution remain three learned production kinds.
fourth IQC scale: the same frozen production adds another 35,414 / 35,414 exact sites and reaches 66,935 atoms. Exact shell indexing cuts this wave from 609.8 s to 440.8 s, but that is still too slow for a credible million-atom rollout. The next performance target is indexing exposed promoted ports instead of repeatedly joining atom pairs.
regenerative scaling audit: 16 exact waves add 368/368 correct sites while frontier supply grows. Four-wave supermacros shrink 132 → 96 → 80 → 60; mean wave growth is 1.0 and log-growth R² is 0.605. The exponential gate remains red.
option-preserving tree search: the first top-two leaf-score rollback recovers the 48-site wave-17 branch but fails when executed forward; widening that scalar policy to four still admits false branches. The replacement width-four value keeps the provisional branch with the largest compatible frozen next frontier. Frozen before wave 20, it selects ranks 2 → 3 → 1 → 4 → 4 and adds 120 / 120 exact held-forward sites with four rollbacks. The complete 24-wave trace is 572 / 572 exact and frontier supply rises 63,890 → 67,806. This is a same-trace temporal pass, not spatial confirmation or an exponential rule.
spatial beam confirmation: width five is frozen after an earlier disjoint nucleus reveals its first exact band at rank five, then tested once at a second non-rotationally-related nucleus whose full scoring ball overlaps neither training nor the earlier test. The target-free grammar freezes 5,616 bounded candidates; posthoc, 431 are color-correct, but all five retained branches are false and the first pure-correct band is rank seven. Candidate geometry transfers; the present branch value/breadth does not. The spatial and exponential gates remain red.
multi-nucleus marking feedback: one rigid-motion-invariant marker is refit on three mutually disjoint completed nuclei (15,830 candidates; 3,171 positives), then frozen before a fourth disjoint nucleus is opened. The exact 2-site action now enters the width-four beam at rank four, but one-step frontier supply selects a false 3-site rank-two branch. The marking has improved; the next required mechanism is a persistent multi-depth beam of complete configurations with real rollback.
persistent-beam confirmation: four complete atom/cluster/port states now survive for three depths (36 real branch expansions), while a robust marking takes the minimum support across three leave-one-nucleus-out models. It recovers an exact 3-site branch on the fourth diagnostic nucleus. Frozen unchanged on a fifth mutually disjoint nucleus, the exact 1-site action is again retained at rank four, but frontier-count value chooses path 2 → 3 → 2 and emits one false site. Persistent search works; frontier cardinality is now twice falsified as the value function.
learned branch value: the two completed diagnostics give exact-action counts 0 / 2, 0 / 2, 1 / 2, and 2 / 2 for root ranks 1–4; a fixed Beta(1,1) channel freezes values .25 / .25 / .50 / .75. On a sixth mutually disjoint nucleus, the three-depth beam evaluates 36 branches, selects path 4 → 2 → 2, and emits the exact 1 / 1 colored site with no target access. The one-action spatial selection gate is green; sustained and exponential IQC growth remain red.
learned channel reach: self-feeding the same frozen policy for a second diagnostic wave fails because none of its four active roots is correct. A target-free snapshot of twelve immutable bands finds the first exact next actions at ranks six and twelve. Geometry is available, but the action-channel representation is too narrow; active breadth must be learned from pose/port coverage and confirmed on a new nucleus.
12-channel confirmation: exact training alternatives occur at ranks 3 / 4 / 6 / 7 / 12, so channel reach is learned as 12 while retained configuration width stays four. One predeclared trial is recorded consumed/unknown after its output transport failed. Frozen unchanged on a fresh eighth disjoint nucleus, the search evaluates 108 target-free branches, selects path 4 → 12 → 11, and emits the exact 1 / 1 colored site. The one-action channel/value gate is green; sustained and exponential growth remain red.
carried-context GCTS: initial frontier context values rank four at 5/6; after an incoming rank-four connection, two independent diagnostics value ranks six and twelve at 3/4. Frozen on a ninth mutually disjoint nucleus, the 12-channel persistent beam evaluates 108 branches per wave and commits paths 4 → 12 → 11 then 12 → 9 → 10. Both self-fed colored sites are exact (2 / 2, zero false). The two-wave spatial search gate is green; unit wave size and no stationary rule keep exponential growth red.
semantic-channel correction: a third ordinal state learns rank six from three repeated post-4→12 frontiers, but fails on a tenth disjoint nucleus because its exact initial action is rank eleven. All three committed sites are false although exact candidates remain inside the 12-channel snapshots. Score rank is therefore not a transferable GCTS channel; the replacement must use symmetry-quotiented cluster/port connection identity, with rank only as local ordering.
semantic quotient audit: exact evidence, full structural ports, and coarse colored port keys each have 0% held-out coverage; chemistry-only keys cover 25% of candidates but miss the exact action. These target-free keys only rank certified geometry. The categorical table is therefore red, motivating a continuous local connection section trained across nuclei.
continuous-section confirmation: nine completed disjoint nuclei provide 49,716 candidates and 3,695 exact coordinate-and-species positives. A rigid-motion-invariant local section is frozen before a fresh centre at (0, 0, −50) is opened. The twelve-channel, width-four, depth-three search selects path 1 → 5 → 12 and emits 4 / 4 exact colored sites with zero false sites. This replaces ordinal rank with a transferable continuous connection section; it is one action, not yet sustained or exponential growth.
continuous self-feed audit: the identical model is frozen at a second fresh centre for two waves. Wave one again emits 4 / 4 exact colored sites. After self-feeding, an exact action remains available at rank five, but the seed-trained section selects rank one and emits 0 / 4. The two-wave gate is red: the next fit must include post-commit local neighborhoods, not wider channels or an ordinal rank state.
self-fed section refit: eight known nuclei supply 44,439 post-commit candidates and 3,205 exact colored positives. Staging that section after wave one still fails on a new disjoint nucleus: wave one is 4 / 4, while wave two has an exact rank-four action but selects rank one and emits 0 / 4. The missing feature is now the continuous parent/source port-state distribution, not training-state exposure or channel reach.
continuous port-state confirmation: the marking now adds separation, parent/source neighborhood, compatibility, purity, and entropy invariants from exact connection evidence—never raw IDs, coordinates, or target atoms. Nine nuclei supply 50,065 post-commit candidates. Frozen on a new disjoint nucleus, the same twelve-band search ranks both exact actions first and emits 4 / 4 + 4 / 4 colored sites with zero false placements. Self-fed marking transfer is green; four-site waves and no recurring promoted rule keep exponential growth red.
parallel-action preflight: the next gate asks that section to admit several mutually compatible whole actions in one order-independent antichain. An absolute zero-error threshold selects 50 / 50 seed and 24 / 24 self-fed training sites, but transfers no action to a fresh disjoint frontier. A replacement 15-feature whole-band section sees 57 / 216 and 48 / 216 pure training actions; under nucleus-heldout calibration, no threshold reaches the predeclared 95% action precision. It therefore fails closed before constructing the next confirmation seed or target. The antichain executor is valid, but local action scores are not yet a safe admission rule; carried port obligations and bounded backtracking are the next gate.
carried-port lookahead: each whole band is now simulated target-free and augmented by the successor frontier's connection consensus, recurrent-state purity, parent multiplicity, and unresolved singleton load. Group-heldout fitting isolates one zero-error seed action and one zero-error self-fed action, but the predeclared parallel-coverage gate requires at least 18 selected actions per stage—two per training nucleus in aggregate. With only 1 / 18 and 1 / 18 retained, the gate remains red and the reserved confirmation target remains unopened. Aggregate future statistics help precision but collapse coverage; the next state must carry explicit unresolved port incidences through bounded backtracking.
explicit port-incidence search: the successor state now carries up to eight actual symmetry-quotiented parent/source/separation roles. A later whole action must consume a carried role; a branch backtracks when one of its explicit roles has no frozen child continuation. Across 504 train-only actions, 97.4% of held-out role mass is already present in the other nuclei. The bounded search finds connected two-action paths on eight of nine held-out nuclei, exploring 306 actions and backtracking 49—but all 16 selected actions are false, emitting 120 false sites. Connection closure is therefore necessary but not a sufficient marking. At this gate the reserved nucleus stayed unopened; the next section had to represent joint role-incidence geometry rather than marginal role purity or closure alone.
candidate-level pose–port section: whole equal-score bands are no longer the atomic marking decision. Across 44,602 collision-free individual candidates, a group-heldout, proper-motion-invariant local section uses proposal incidences plus the colored metric graph of the nearest occupied neighbors. Its complete score threshold admits 25 / 26 exact compatible placements (96.15% precision), but only in four of nine nuclei; the predeclared all-nucleus coverage gate remains red.
geometry-setting transfer: the visible one/two/three-shell and coarse/fine geometry choices are now tested as one bounded grid. For each held-out nucleus, an inner leave-one-nucleus-out loop chooses both section geometry and threshold from the other eight. Absolute calibration does not transfer: it admits 41 / 65 correct actions (63.1%). A fixed top-two rank is stable on the eight generic nuclei—16 / 16 exact—but chooses two false actions at the unique symmetry-centred nucleus, for 16 / 18 overall. Expanding to 32 neighbors still leaves the first exact centred action at rank 121. The then-reserved confirmation remained sealed for this audit.
symmetry-orbit channel confirmation: a low-rank view gives one vote to each semantic marking family, so a large rotation or edge orbit cannot dominate merely by having more representatives. A target-free rule chooses the detailed or channel view by the size of its exact top-score equality orbit. It achieves 18 / 18 placements across the nine development nuclei and is frozen in commit 644d69f. On the separately preregistered, spatially disjoint nucleus, however, the rule chooses the detailed view (top-band sizes 4 versus 2) and both retained actions are false: 0 / 2. The target opens exactly once after selection. This is a clean overfitting counterexample; automatic channel count is structurally motivated, but orbit multiplicity alone is not a transferable marking value.
post-confirmation section audit: after the consumed nucleus becomes development evidence, a simpler “channel whenever orbit cardinalities disagree” rule reaches 18 / 20 group-heldout actions, still below the all-nucleus gate. A fully nested candidate-level linear section then stacks 15 invariant score, rank, orbit-size, token-family, and evidence-coverage features. All three fixed ridge strengths select 0 / 20 exact actions. Exact candidate geometry is unchanged and the next disjoint centre stays unopened. Scalar score stacking is therefore rejected; the next section must retain the joint incidence graph itself.
joint incidence-graph audit: the primary symmetry-quotiented port is now attached explicitly to every occupied colored shell and every pairwise metric edge. This learns 6,140 role–shell and 19,837 role–edge types; 97.7% of held-out descriptor tokens receive train-frozen weight. Yet the best group-heldout result is 15 / 20, and stronger support/group regularization falls to 14 / 20 or 8 / 20. Relational vocabulary is no longer missing, but summing its edges independently still discards topology. The next bounded section must canonicalize or pass messages over the local incidence graph.
bounded message-passing audit: occupied nodes start from species and radial shell, then exchange their complete pair-distance-labelled neighbor multisets for one or two rounds; the primary port conditions every resulting node and graph color. Candidate geometry and certificates remain unchanged. Both depths select 14 / 20 exact actions. Exact hashing yields 80,323 one-round and 161,768 two-round node colors, fragmenting recurrence rather than improving it. Message topology is now explicit, but its colors need a train-only finite quotient before they can serve as transferable GCTS channels.
finite message-quotient audit: train-only distance and port-role quotients reduce one-round exact colors as far as 12,954 node / 5,787 graph types, but every exact-hash arm remains at 14 / 20. Replacing hashes with a bounded additive incidence bag compresses to 457 node and 976 graph types and reaches 15 / 20. Requiring positive graph prototypes to recur across at least three independent nuclei leaves 356–358 fold-specific codebook states but falls to 11 / 20. Exact candidate geometry never changes and the next disjoint nucleus remains unopened: neither smaller vocabulary nor nearest recurring prototype is yet the missing GCTS value.
expanded-development audit: eight additional radius-14.562 nuclei were committed before materialization; every new outer domain is separated from all prior and reserved domains by at least 37.417. Their common finite oracle crop is stable at coefficient bounds 24 and 25. The frozen 457-state quotient selects 14 / 16 new actions and 30 / 36 across all eighteen nuclei. Raising recurrence floors only degrades that score. A new finite conditional table learns the purity of complete node/edge/graph states and backs off through four bounded levels, but reaches 29 / 36. More independent evidence is useful, yet neither marginal addition nor whole-state lookup supplies the missing transferable branch value; the reserved confirmation at (0, 50, 0) remains unopened.
pose-aware antichain audit: attachment axes are now measured relative to the occupied neighborhood using only dot products and signed triple products. This quotients global proper rotation and translation, preserves chirality, and yields 4,414–9,580 finite learned orientation tokens without assuming a lattice. Coarse orientation ties the 30 / 36 baseline; finer channels fall to 28–29 / 36. A nested tree node then scores all 120 unordered compatible pairs in each 16-action shortlist. Every nucleus contains at least six exact pairs, but learned pair interactions again select 30 / 36. Rotations, pair supply, and greedy ordering are therefore no longer plausible explanations for the six remaining errors.
successor-state value: the search now hypothetically places each action in the frozen top-16 shortlist, recomputes its local cluster types, and summarizes only the new outgoing port frontier. The scorer never reads target atoms during this rollout. Correctly carrying both causal endpoints of each affine connection raises one-step selection from 30 / 36 to 32 / 36. A bounded second step evaluates 76–184 target-free child branches per nucleus and reaches 33 / 36 with 16 / 18 exact nuclei. The richer causal graph helps; four one-step and three two-step actions remain wrong.
directed obligation value: root state, incoming child-port obligation, and child successor remain one directed path record frozen before either label is read. Width four reaches 33 / 36. Widening the exact tree to 16 children now produces at least two exact paths in every nucleus and raises selection to 34 / 36, with 16 / 18 nuclei entirely exact. Candidate supply is therefore complete at this bounded depth; the two remaining errors are transferable ranking failures, not absent geometry.
connection-vocabulary audit: a fold-frozen merger now pools positive, negative, chemistry, and independent-configuration evidence for exact port states. Applying it directly to raw local cluster IDs is a negative control: crop-boundary variants fragment the vocabulary, leaving correct root candidates in 14 / 18 nuclei and an exact root→child continuation in only 7 / 18. Learning a recurrent cluster quotient first is substantially better: from ten training nuclei, 455 pose classes recurring in at least two configurations supply a correct first action and an exact root→child continuation in all eight expanded validation nuclei. A causal-endpoint audit found the decisive implementation bug: a newly placed cluster can expose a learned affine connection as either its parent or source; preserving both dependencies recovers the formerly missing continuation without relaxing any evidence threshold.
sealed recurrent-supply confirmation: after the 8 / 8 development gate, the exact rule and both-endpoint semantics were committed before the reserved nucleus at (0, 50, 0) was opened. The learner froze 455 recurrent pose classes, 21,841 admitted connection states, 672 root candidates, and 1,104 one-step successors before one target-open call. Posthoc scoring finds 38 exact colored roots and four exact root→child paths; the first occurs after eight correct roots. This confirms transferable GCTS candidate supply on a new spatially disjoint IQC nucleus. It does not select the path autonomously and is not a stationary or exponential certificate.
recurrent-path marking: with supply frozen first, a group-heldout value section sees only symmetry-quotiented action, causal-endpoint, incoming-port, color, and distance tokens. A 256-root / 16-child tree contains exact paths in all eight development nuclei; the train-only marking ranks an exact path first in 7 / 8. The lone miss still contains one exact path among 293 candidates. This is a strong ranking-transfer result, but the autonomous selector gate remains red until every held-out nucleus is selected correctly.
clusters² compatibility: a tentative root→child pair is now scored against the recurrent cluster vocabulary before commitment. The incremental section exactly matches full reclustering, measures the prototype residual induced on neighboring clusters, and combines it with an eight-neighbor local frontier normal. It leaves seven nuclei at rank one while moving the rare exact path from rank 101 to rank 21—a 4.81× pruning gain. This is useful tree-search work reduction, but it is not yet a correct top-one selector or an exponential-growth certificate.
order-independent post-commit frontier: the previous third-step diagnostic incorrectly required every move to descend from the most recently inserted cluster. The corrected configuration search reopens every exposed frozen port after each commit. Ten training nuclei supply 20,716 causal candidates and 1,151 exact actions across three self-fed stages. Conditional on a known-exact two-action prefix, all eight heldout configurations contain 57–75 exact global moves. A train-selected finite incidence marking improves first-exact ranks from 3 / 3 / 4 / 4 / 1 / 9 / 9 / 9 to 3 / 4 / 3 / 3 / 1 / 1 / 1 / 1, so a width-four configuration beam has complete supply. It selects rank one in only 4 / 8; heldout truth constructs the prefix, so this is a conditional audit—not autonomous or exponential growth.
rotation-channel capacity audit: the same post-commit candidates are augmented with proper-rotation-invariant attachment-axis angles and chirality. Train-only selection prefers 0.125-radian bins with one normalized vote per channel, reaching 23 / 28 eligible training stages and 28,558 weighted tokens. Transfer gets worse: first-exact ranks become 5 / 1 / 7 / 6 / 1 / 3 / 3 / 3 and top-one falls to 2 / 8. Therefore clustering should expose the symmetry-inequivalent pose atlas, but Auto channels must follow recurrent pose × port rank and heldout evidence—not allocate one channel per observed rotation.
finite pose × port state: clustering now owns and freezes the 0.125-radian proper-pose atlas; marking learning may quotient it but cannot refit the geometry. Five invariant evidence channels—connection role, proposal multiplicity, occupied shell, neighboring incidence, and pose/chirality—are quantized into 437 recurrent states by grouped train-only selection. With every exact candidate unchanged, the first-exact ranks improve from 3 / 4 / 3 / 3 / 1 / 1 / 1 / 1 to 1 / 1 / 1 / 1 / 1 / 1 / 1 / 1 across the eight conditional heldout frontiers. This passes the conditional top-one branch-selection gate. The known-exact two-action prefix still comes from heldout truth, so autonomous, sustained, stationary, and exponential IQC growth remain red until a new sealed self-fed confirmation passes.
autonomous pose × port confirmation: an initial preregistered centre was retired unscored when its bound-24 and bound-25 target crops disagreed. At a replacement centre 40.31 units from every prior domain, the frozen 437-state policy builds a target-free width-four, reach-four, depth-three tree with 4 / 16 / 16 candidate snapshots and four retained configurations per depth. Bound 32 and 33 agree; the target opens once afterward. The selected branch self-feeds through all three depths but only 1 / 3 colored sites is exact. The conditional marking gate is green, while autonomous top-one, sustained, stationary, and exponential IQC growth remain red.
autonomous failure diagnosis: the consumed tree does contain one all-exact path, at within-parent ranks 1 → 4 → 4, but cumulative pose × port probability ranks it 10th of 10 terminal configurations; the chosen branch is exact → false → false. Increasing retained beam width from 4 to 16 does not fix grouped training supply, and some held-out correct moves occur at ranks 17, 28, and 847. The next benchmark is therefore a transferable recurrent branch value at bounded reach—not an arbitrarily wide search.
nearest recurrent branch value: twelve additional development nuclei are fixed by geometry-only maximin separation and retained regardless of outcome. Across all 30 spatial groups, the unchanged reach-four / beam-four / depth-three search freezes 354 terminal branch descriptors, 211 exact. Its cumulative pose × port product selects an exact branch in 17 of 21 nuclei with exact supply. A group-heldout, target-free nearest-recurrent value sees only nine invariant branch statistics plus the order-independent action-color population; train-only selection chooses nine neighbors and reaches 20 / 21 (95.2%) with identical candidates. It moves the already-consumed diagnostic exact branch from rank 10 to rank 1, but the new sealed nucleus is red: before one target-open call, the fixed tree froze 4 / 16 / 16 candidates and four terminal configurations; posthoc none is all-exact, while the selected branch places 2 / 3 colored sites correctly. The new failure is candidate supply/beam retention rather than terminal reranking. Autonomous, stationary, and exponential IQC growth remain red.
partial-branch value heads: the recurrent value now has a separate bounded head at each search depth rather than pruning every partial configuration by the product of local probabilities. A target-free scheduler freezes 1,259 partial branches across the same 30 groups; 934 prefixes are exact. Whole-nucleus holdout selects 25 / 15 / 9 neighbors by depth and ranks an exact prefix first in 29 / 29, 27 / 28, and 25 / 28 supplied stages—81 / 85 overall (95.3%). A second finite quotient normalizes these invariant channels into recurrent connection-state cells and allocates only 4 → 4 → 8 beam slots across them; it retains an exact prefix in all 85 supplied snapshots. Closed-loop transfer remains red: on the consumed nucleus the state-diverse executor retains 2 → 4 → 8 configurations but still produces zero exact terminals and selects 2 / 3 correct sites. These heads are a useful marking-library option, not an autonomous-growth claim.
on-policy marking aggregation: the search now learns once more from the invariant states its own frozen policy actually visits. Five spatially grouped branch-value folds add 4,037 target-free partial branches; each on-policy rollout refits pose/port state without its four heldout nuclei. Conflicting outcomes for an identical marking descriptor are retained as representation aliasing, not silently collapsed. Exact terminal supply improves from 16 / 20 to 18 / 20 and exact selected paths from 10 / 20 to 13 / 20; correctly selected moves rise from 44 / 60 to 51 / 60. This is useful but red: two nuclei still lack an exact retained path and five have one that the value model misranks. The older broad snapshot features share one upstream pose/port model, so the comparison is not fully nested end to end; the 90% exact-selection gate is not met anyway, and no fresh confirmation nucleus is opened.
fully nested channel ablation: every fold now refits the upstream pose/port marking before generating either broad or on-policy branches. Each action carries a five-channel proper-SE(3)-quotiented port response; commuting actions are stored as a multiset, and relative distances are associated with their color roles. With identical `4 → 4 → 8` beam work, base branch statistics select 14 / 20 exact paths; colored connection geometry selects 15 / 20; pose/port channels alone remain 14 / 20; their coupling is 15 / 20. A one-round on-policy refit falls to 14 / 20. Thus the number of rotations helps define the available channel basis, but raw channel count is not the value function—the useful signal is how those channels connect in colored local geometry. The 18 / 20 gate remains red.
marking-library portfolio: base, colored-geometry, pose/port, and coupled markings now share the same finite `4 → 4 → 8` beam rather than increasing search work. Round-robin diversity raises exact terminal supply to 18 / 20 but selects only 13 / 20. A separate terminal value is trained on the portfolio states actually visited in the 26 authorized nuclei; each fold chooses its representation and neighbor count before heldout execution. It selects 16 / 20 exact paths and 54 / 60 correct moves with no mixed top-score ties. Two failures lack an exact terminal and two retain one that is misranked. A nested ridge-linear control falls to 12 / 20 (10 / 20 after on-policy merging) and is rejected. This is the then-best development result, still below the 18 / 20 confirmation gate.
pruning and lookahead controls: wider root proposal reach is not enough: reach 12 supplies a correct first move in all 20 nuclei but the fixed beam selects only 13 exact terminals. Independent depth heads remain 16 / 20 with terminal supply 17; backward labels propagated only from exact terminal descendants fall to 15 / 20 with supply 16. A target-free `12 → 4 → 8` lookahead then enumerates 7,312 proposals and proves exact terminal supply in all 20, but broad-distribution value selects 12 / 20. Binding pose/port channels to their canonical inter-action edges reaches 15 / 20 and is rejected by all five inner selectors; train-selected action consensus reaches 13 / 20. Counting the distinct commuting placement orders before unordered-branch deduplication is useful trace evidence but not a value: correct and false terminals both have all six permutations in 8 nuclei, multiplicity-first falls to 14 / 20, and adding log multiplicity merely ties 15 / 20. The 16 / 20 portfolio terminal value therefore remains best among these pruning controls. Proposal reach is no longer the uncertainty; transferable terminal valuation is, and the 18 / 20 confirmation gate stays red.
local-section value: a bounded 180-component halo now relates each colored proposed attachment to already occupied atoms using species-resolved radial and pair-angle histograms. It is invariant under proper rotation and translation, uses no lattice coordinates, and never changes candidate geometry. Nested whole-nucleus selection improves the fixed portfolio from 16 / 20 to 17 / 20 exact terminals and from 54 / 60 to 55 / 60 correct moves, with terminal supply still 18 / 20. Pairwise shared-support bins stay at 17 / 20 but drop to 54 / 60; atom-centred prototype closure is selected in zero folds. A stricter non-centred learner then fits each of ten geometry-only nuclei independently, retains 53 exact colored support isometry classes recurring in at least three nuclei, and measures the largest partial support completed by each action. Partial-support value is selected in two folds but remains at 17 / 20 and 55 / 60. Explicit incidence counts between those partial supports are also selected twice, yet remain 17 / 20 and fall to 54 / 60. A full typed port graph preserves support identities, colored shared-site distance profiles, and symmetry-resolved chirality, but its categorical and assignment-kernel values do not improve outer selection. Fixed message passing is likewise rejected, and a scalar learned head falls to 16 / 20. The new higher-order section keeps the complete canonical action-pair graph—including witnessed connections and explicit failure edges—and learns proper-SE(3)-invariant source × port × neighbor interactions. Used only as a bounded percentile-rank correction to the established scalar section, true nested selection activates it in three folds and reaches 18 / 20 exact terminals and 56 / 60 correct moves. This passes the predeclared development-performance gate, but 2 of 31 within-nucleus label shuffles also reach 18 / 20 (p = .09375); causal superiority and a fresh confirmation therefore remain red. An explicit 30-channel pseudoscalar extension is proper-rotation invariant, permutation invariant, and mirror-odd; inner folds select it twice, but outer exact transfer falls to 15 / 20, so it remains an opt-in chiral-material option rather than the IQC default.
extended frozen-policy transfer: before opening ten further, mutually disjoint IQC nuclei, the repository published the exact 2.4 MB inert fusion artifact, source hashes, search schedule, and all 80 terminal branches. The targets were then opened once. Both the scalar section and graph fusion find an exact three-action terminal on 6 / 10 nuclei and select 23 / 30 correct sites. Fusion changes the chosen terminal on five nuclei but changes no correctness outcome. Four nuclei contain no exact terminal at all, so the new red gate is candidate supply rather than terminal ranking. This is additional development transfer—not a fresh confirmation—and it makes no stationary or exponential claim.
complete-frontier diagnosis: the consumed ten-nucleus batch was replayed without changing its frozen geometry or markings while beam pruning was removed one stage at a time. Keeping all final states, then all second-depth states, leaves exact supply at 6 / 10. Keeping the complete first-action frontier raises it to 9 / 10. A bounded `8 → 8 → 8` action reach finally supplies an exact three-action terminal in all 10 / 10 nuclei, among 120–136 terminals each. The smallest scalar portfolio retaining an exact terminal everywhere is nine; graph fusion needs fifteen, while the union of the first nine from each channel retains complete supply in at most eighteen states. Fusion still selects only 6 / 10 exact top-one terminals, so candidate supply is fixed on this consumed development batch but transferable value selection and spatial confirmation remain open. This is not a fresh confirmation, stationary rule, or exponential-growth result.
fresh complete-frontier confirmation: the widened policy, source hashes, new centre at (−110, −10, −10), and dual budget nine were published before any new atom was generated. A second public receipt then froze 473 seed atoms, the `8 → 37 → 128` target-blind tree, all terminal actions and both orders, and eighteen rollback states with target-open count zero. The radius-14.56 target was opened once afterward and is stable at lift bound +1. Ninety of 128 terminals are exact; both the scalar and graph-fusion top-one branches are exact 3 / 3, and the dual portfolio contains exact alternatives. This is a fresh spatial confirmation of finite candidate supply and rollback retention. It does not demonstrate sustained continuation, a stationary production, or exponential IQC growth.
self-fed second-block confirmation: the already pre-target-selected exact fusion branch was replayed uniquely and its full 476-atom configuration became the seed of a second complete `8 → 37 → 128` block. Before opening a larger radius-23.56 shell, the repository published all 128 new terminals, both immutable orders, an eleven-state dual portfolio, and target-open count zero. The bound+1-stable outer target contains 8,684 atoms. Geometry supply remains strong—62 / 128 terminals are exactly color-correct—but scalar and fusion first-exact ranks fall to 13 and 16; the frozen portfolio contains none, and both top-one branches place only 2 / 3 correct sites. This is a clean value-transfer failure after self-feed: the grammar can continue, but six-action autonomous selection, stationarity, and exponential growth remain red.
post-self-feed terminal value: ten already-consumed development nuclei now provide 1,278 complete second-block terminals, 142 exact. A whole-nucleus-nested value couples the bounded scalar section, canonical order-three port incidence, and target-free successor-frontier summaries. Exact supply exists in 9 / 10 nuclei; top one is exact in 7 / 9 supplied groups and places 26 / 30 colored sites, missing the frozen 8 / 9 and 27-site gate. The two supplied failures put their first exact states at ranks 14 and 10, so a fixed width-16 tree beam retains exact states in all 9 / 9. Reusing the already-consumed second-block target only as a diagnostic, top one remains wrong but six exact terminals lie inside the first 16. A fresh nucleus remains sealed: rollback supply is green, terminal commit value is red, and no stationary or exponential claim follows.
downstream-consequence ablation: every one of those 1,278 terminals is now advanced through as many as eight target-free child actions. A frozen 1.1 MB corpus retains 685 proper-motion-invariant measurements per terminal: the highest-ranked child section plus mean and maximum summaries of all child local sections and successor frontiers. Fully nested whole-nucleus selection falls to 3 / 9 exact terminals and 18 / 30 correct sites, versus 7 / 9 and 26 / 30 for the established port-graph fusion. The 8 / 9 and 27-site gate remains red and no fresh target is opened. Immediate child statistics are therefore rejected as a commit value.
typed child-frontier graph: the next representation is now implemented. Each terminal's eight strongest legal child attachments becomes a node colored by cluster identity, its symmetry-quotiented pose/port channel response, incoming connection roles, and outgoing obligations; edges retain invariant separation, shared ports and future sites, witnessed connections, and color conflicts. The frozen corpus has 1,016 canonical graphs, 995 witnessed relations, and 638 dead-end child nodes. All 35,784 child pairs are locally compatible, so the unresolved issue is future port survival rather than collision pruning. A fixed pairwise graph value improves exact top-one selection from 7 / 9 to 8 / 9 supplied nuclei, but reaches only 25 / 30 correct sites versus the prior 26 / 30. The unchanged joint gate of at least 8 / 9 and 27 sites remains red: typed pose/port topology helps, while multi-step discharge or rollback value remains to be learned. No fresh target, stationarity, or exponential claim follows.
two-marking rollback portfolio: complementary values are retained rather than averaged. One head ranks typed child topology; the other combines the established local section with an ordinal graph value trained on 0 / 1 / 2 / 3 correct-site levels. Every outer model excludes its held-out nucleus and both heads see identical frozen candidates. Keeping one state per head—at most two—contains an exact terminal in all 9 / 9 supplied nuclei and a posthoc best 28 / 30 sites, using only 19 retained states across all ten nuclei instead of the previous width-16 ceiling. This passes bounded rollback supply, not autonomous commit: no target-free detector yet proves when a locally valid first state should be abandoned for the second. No fresh target, stationary rule, or exponential IQC claim follows.
multi-step port-discharge audit: all 19 retained states are now advanced for the same 16 target-free child placements inside one additional public shell; no rollout target crop is constructed. None reaches a fixed point, so hard frontier exhaustion cannot trigger rollback. A five-statistic / seven-horizon selector fitted on all consumed development cases finds a 12-step frontier-vote rule with 9 / 9 exact supplied groups and 28 / 30 sites, but whole-nucleus holdout falls to 8 / 9 and 26 / 30; 31 within-nucleus shuffles give p = .3125. Aggregate future port volume is therefore rejected as an autonomous failure certificate. Typed obligation identity and discharge—not simply a larger surviving frontier—remain the next value target.
fresh two-block rollback confirmation: the source, maximin center (−70, 10, 70), model digests, width-two portfolio, and 12-step frontier-vote rule were published before the confirmation seed or target was generated. The center is 66.33 units from every recorded prior IQC center, beyond two complete second-block radii. A 491-atom seed produces a target-blind `4 → 7 → 29` first tree and 133 second-block terminals; both retained states are rolled out and hashed before the radius-23.56 target opens once. The result is red: the first selected block is 2 / 3 correct, neither retained second-block state is exact (2 / 3 and 1 / 3), their rollback scores tie at 1,232, and the selected end-to-end path is 3 / 6. A complete-tree audit then recovers `8 → 37 → 128` first terminals with 16 exact states and an exact state at fusion rank 8. That state self-feeds to `8 → 36 → 127` second terminals with four exact continuations, proving the unchanged geometry contains an exact two-block path. Current heads rank the best exact continuation only 62nd / 98th; step-12 vote mass improves it to 19th. Integrated vote mass ranks an exact second state first but selects a wrong first state, so it is conditional value rather than a repeatable greedy rule. Exact complete-tree supply is green; bounded global selection, autonomous commitment, stationarity, and exponential IQC growth remain red.
branch-local beam: all eight fusion-ranked first parents now receive their own complete `126–141`-state second tree and twelve-step target-free rollouts. One integrated-vote child is retained per parent, with all eight receipts frozen before scoring. Exactly one six-action path is exact—parent rank 8 followed by stable child 89—so the `8 × 1` tree beam preserves the solution. A global comparison of those child scores nevertheless selects parent 3, wrong in both blocks, and the exhaustive four-worker audit takes about forty minutes. The next GCTS value must carry parent→child obligation change or reuse promoted branch macros; scalar cross-parent ranking and practical runtime remain red.
cluster-of-clusters geometry: the parent and child blocks are next treated as one six-action colored macro with 62 proper-SE(3)-invariant geometric features. The 1,278-example / 142-exact corpus is frozen before consumed labels are joined. In-sample selection reaches 6 / 9 supplied nuclei and beats 31 label shuffles (p = .03125), but whole-nucleus holdout collapses to 1 / 9 and the sole exact confirmation macro ranks fourth. Raw macro shape is therefore rejected as a transferable value; recurring higher-order clusters must carry typed incoming, discharged, and remaining connection ports.
parent→child port transition: a second cluster-of-clusters representation adds 69 ID-free graph measurements: the parent port state, child port state, and their signed change, each summarized by typed incoming / outgoing obligations, witnessed edges, components, degree, and boundary load. Coupled to the 62 geometric fields, its frozen 1,278-row value improves nested holdout to 3 / 9 supplied nuclei and 20 / 30 sites, but fails the shuffle control (p = .1875). On the consumed eight-parent beam it selects a false parent and ranks the only exact six-action path fifth. Aggregate port counts are therefore rejected as the default marking; the next representation must preserve which typed obligations connect and discharge, rather than only their totals.
identity-preserving port incidence: that correspondence is now retained explicitly as a canonical six-node cluster-of-clusters graph: three typed parent obligations, three typed child obligations, and all 15 within/cross edges carrying proper-SE(3)-invariant separation, shared colored support, chirality, support equality, and parent-action participation. The 1,278 examples reduce to 1,120 unique graphs without raw type IDs. A fixed one-round source × port × neighbor value reaches 7 / 9 exact supplied nuclei and 26 / 30 sites under whole-nucleus holdout; all 31 within-nucleus shuffles are worse (p = .03125). It moves the consumed exact six-action path to rank two but still selects a false path. Equal fusion with the successor child graph reaches 8 / 9 yet remains at 26 / 30, below the unchanged 27-site gate. This marking is therefore a strong experimental library option, not the default autonomous policy.
incidence-ranked bounded rollback: the identity-preserving value is next allowed to reorder only the already frozen two-marking portfolio—19 states total and never more than two per nucleus. Outer-fold ranking chooses an exact retained state in all 9 / 9 supplied nuclei and 28 / 30 colored sites. A stricter null repeats the complete fit separately for every held-out nucleus after each of 31 within-nucleus label shuffles. Eleven shuffles also reach 9 / 9, so the plus-one upper-tail result is p = .375 and the causal gate is red. On the consumed six-action receipt the exact state is available at rank two, while the first state remains false. Typed incidence is useful for rollback supply, but it is not yet a validated trigger for abandoning the first branch; no fresh confirmation, autonomous commit, stationary rule, or exponential claim follows.
typed obligation-discharge history: the same 19 immutable states are each advanced for 16 target-free placements while preserving the semantic identity of every port role that votes for the selected attachment. Across 304 transitions this yields 406 exact selected-role transitions and 131 proper-motion-quotiented role identities; each records whether its obligation is discharged, persists, or is selected again. An eight-step selected-role-persistence rule fitted outside each nucleus chooses an exact state in all 9 / 9 supplied nuclei and 27 / 30 colored sites; fitting all development nuclei gives 28 / 30. However, only three nuclei have nonidentical label tuples and only two can change exact/non-exact selection. Exhaustively refitting all eight distinct within-nucleus assignments gives p = .25—the best attainable exact-test resolution of this 19-state corpus. Typed history is therefore a useful, interpretable marking channel, but not yet a causally validated rollback trigger; the next benchmark needs more independently ambiguous nuclei or a broader target-free retained portfolio.
wide typed-discharge stress test: the portfolio is widened without changing geometry to eight candidates from each of the same two marking orders—120 states total, never more than the historical width 16 per nucleus. Exact supply remains 9 / 9, seven nuclei now mix exact and inexact states, and the conditional random-selector probability falls from .25 to .000669. All states receive the same 16-step target-free replay, producing 1,920 transitions and 2,581 selected-role events. The harder result reverses the narrow-corpus impression: scalar rollout evidence selects 7 / 9 exact nuclei, aggregate typed persistence 5 / 9, and a fully nested 120-spec identity model—after train-selected exact, coarse, and chemistry channel quotients—also selects only 5 / 9 and 23 / 30 sites (p = .71875). Coarsening raises held-out channel coverage to 74–100% on most folds but does not supply the missing value. Independent role weights are rejected; the next marking must model relational contradiction among simultaneous discharged, surviving, and newly exposed ports.
relational discharge contradiction: every selected port is now compared against the complete successor role multiset—not the truncated top 16—through seven fixed proper-motion-invariant relations: reciprocal, forward/backward continuation, same endpoint, and parent/source touch. The 120 trajectories are unchanged; only bounded relation counts and contradiction flags are added. A low-capacity 120-rule nested audit selects “minimize forward continuations after two steps,” reaching 7 / 9 exact nuclei and 26 / 30 sites. Six of 31 fully refitted shuffles match or exceed seven exact nuclei, so p = .1875 and the autonomous gate remains red. Relational closure improves colored-site yield over scalar or independent-role value, but the two difficult boundary environments still contain multiple locally indistinguishable branches; a stronger branch-level consistency or explicit unsatisfied-port proof is required.
simultaneous port-cover certificate: the search now distinguishes a compatible cover, an exhaustively impossible cover, and an incomplete/unknown search. Only exhaustive impossibility may reject a branch. Adversarial controls catch the case that the earlier marginal test missed: every carried role is individually available, but the required actions conflict. On the real width-16 IQC portfolio, all 120 successor frontiers are enumerated completely before labels are joined. The result is an honest negative: all 59 exact and all 61 false branches have a compatible semantic-role cover. Forty-one branches carry no persistent role; the other 79 collapse to at most one distinct role, only 137 relevant successor actions total, and zero pair conflicts. Simultaneous search is operational, but the semantic quotient is too coarse. The next certificate must retain exact finite port instances and joint incidence rather than role class alone.
exact finite port instances: proposal generation now preserves the ordered parent→source occurrence behind every vote, then removes raw indices by serializing only endpoint-equality relations and colored distance matrices. Every selected wide action has exactly one such witness. Complete successor enumeration tests seven fixed incidence relations. Forward continuation retains 57 / 59 exact branches and rejects 26 / 61 false branches, raising filtered precision from 49.2% to 62.0%; the coarse semantic-role cover rejected none. This is the first direct contradiction gain from finite port identity. It remains a red deployment gate because two exact branches fail and one of nine supplied nuclei loses its only exact alternative. A train-only boundary-conditioned backoff—not a global union with the permissive backward relation—is required next.
boundary backoff falsification: six target-free scalars now record the public-boundary margins, ordered port length, outward alignment, and current frontier fraction before labels are joined. A leave-one-nucleus-out search over one-dimensional thresholds selects ordered port length. Deferring its forward-UNSAT cases restores all 59 exact branches and all nine supplied nuclei while still rejecting 8 / 61 false branches; deferred explicitly does not mean port-satisfied. The same full selection is repeated after 31 within-nucleus label shuffles, and every shuffle ties both exact recovery and false rejection (p = 1). The fallback is therefore descriptive, is not integrated as the GCTS marking, and points to joint endpoint geometry within a shared boundary regime as the next representation.
complete branch-action graph: the selected four-point endpoint graph is identical for exact and false branches inside both exact-bearing regimes, so the representation now includes all three simultaneous colored placements. Action order is removed by canonicalizing the complete colored distance graph; a signed normalized volume preserves proper-rotation chirality. This succeeds at local identity: all 28 forward-UNSAT branches have distinct graphs and zero exact/false collisions. It fails transfer. There are 119 graph classes among 120 branches, with only two exact rows recognized outside their nucleus. A nested 30-feature nearest-recurrent graph and a colored internal-edge token section each select 0 / 2 recoverable exact nuclei; 31 shuffled refits reach up to one. Neither is integrated. The missing operation is now a recurrent cluster-of-clusters quotient learned across more independent nuclei, not a larger classifier over nearly unique graphs.
external recurrent-value transfer: the existing 30-nucleus branch corpus provides a larger independent test of whether recurrent scalar state can stand in for that missing quotient. One training nucleus is removed because its complete radius-14.56 domain intersects a wide radius-23.56 domain; the remaining 29 nuclei are closed-ball disjoint from all ten wide cases and supply 338 branches, 195 exact. Group-heldout selection freezes a nine-neighbor value that chooses 19 / 20 supplied training nuclei. On the unchanged 28 forward-UNSAT wide branches it ranks one of two recoverable exact alternatives first and the other tenth, rejects 24 / 26 false alternatives, and leaves total exact supply at 8 / 9 nuclei. Every one of 31 within-nucleus label-shuffle refits also selects one exact fallback (p = 1). The model is not integrated: more independent examples help one boundary regime, but these nine aggregate branch features still do not form a transferable cluster-of-clusters connection section.
geometry-complete recurrent macro audit: seventeen development nuclei, each disjoint from the unchanged wide audit, freeze 168 three-action cluster-of-clusters occurrences before their labels are joined. The fixture retains 72 exact occurrences, 158 exact alternative port derivations, colored nodes, chirality, and proper-SE(3)-invariant endpoint geometry—without raw occurrence IDs or a privileged global frame. A train-only quotient selects distance width 4.0 and reaches 7 / 9 supplied held-out development nuclei, but precision is only 63.6% and 31 grouped label shuffles give p = .4375. On the unchanged wide set it selects 0 / 2 recoverable exact branches and two false branches; the earlier scalar fallback selects 1 / 2 and two false branches. Geometry-only clusters² value is therefore rejected. The next marking representation must serialize training and wide actions into the same canonical port-incidence graph before any recursive or exponential claim is eligible.
shared port-incidence graph: that serialization is now implemented generically. Every three-action macro is replayed from its colored seed, each action retains all witnessed incoming parent→source ports, and each action pair records exact endpoint equality/touch relations plus a normalized metric signature. Exhaustive action permutation removes insertion order; intrinsic right-handed frames remove translation and proper rotation while retaining chirality. The same schema covers all 168 development and all 120 unchanged wide branches, with labels joined only after graph receipts freeze. The strict train-selected quotient reaches 4 / 9 supplied development nuclei at 100% precision. On the 28 unchanged forward-UNSAT branches it recognizes only one candidate, neither recoverable exact branch, and therefore selects nothing; wide exact/false shuffle p-values are both 1. This is a fail-closed representation success and a transfer failure. The next marking must learn a bounded metric or message quotient over these common graphs; exact type identity is too sparse.
continuous port-graph metric: exact type equality is replaced by 92 bounded invariant measurements, separated into action geometry, port-role chemistry, port pose, radial environment, and endpoint incidence. Nearest examples contribute at most one vote per training nucleus, preventing symmetry or candidate multiplicity from inflating evidence. Whole-nucleus selection rejects environment and shape, retaining only pose+incidence with 13 weighted neighbors and a 0.7 admission threshold. It selects 6 / 9 supplied development nuclei and all six are exact, improving the strict vocabulary's 4 / 9. The improvement is not causal: 31 complete grouped-label refits have median five, maximum seven, and p = .46875. On unchanged wide transfer the exact branches rank fifth and second, but no candidate clears threshold; external exact p = 1. The metric is retained as a diagnostic library option, not an autonomous marking. A learned finite relational message quotient must outperform these nulls before tree-search commitment or recursion is eligible.
finite relational port messages: the shared graph now passes bounded messages into its three canonical action nodes and three pairwise incidence edges. The train-fitted quotient uses 216 ID-free proper-motion-invariant measurements and stores 362 recurrent states; each training nucleus contributes one balanced vote. Its selected node rule is perfectly precise but reaches only 4 / 9 supplied development nuclei, and 31 complete grouped-label refits give p = .96875. On the unchanged wide audit, the two exact branches improve from ranks five and two to ranks three and one, but neither clears the frozen 0.55 threshold. This is an ordering improvement, not a causal marking: tree-search commitment, cluster-of-clusters promotion, autonomous growth, and exponential claims remain disabled.
sequential port obligations: static graph similarity is replaced by a finite automaton over the branch's sixteen target-free replay steps. Each state records only bounded discharge, production, contradiction, and simultaneous port-incidence counts; concrete port IDs and coordinates disappear. The weakest four recognized states determine branch value. Leave-one-nucleus-out replay selects exact branches in 8 / 9 supplied nuclei and preserves 27 / 28 available colored sites, improving the prior relational rule's 7 / 9. All 31 grouped-label shuffles reach at most seven (p = .03125). This is the first significant sequence-level branch-consistency signal, but 47 / 102 states have support in only one training group, the specification is exploratory, and one supplied nucleus still fails. It is frozen as a future confirmation candidate; autonomous commit and recursive promotion remain off.
fresh obligation confirmation: the frozen automaton is tested once at the geometry-only maximin center (−110, −70, −70), whose full 32.56-radius rollout domain is 87.18 units from every consumed nucleus. The R9 seed contains 480 atoms; complete 8×8×8 enumeration yields 152 terminals and a target-free 13-branch dual-ranker portfolio. Every sixteen-step trajectory and score freezes before one bound-72/73-stable target open. Two exact branches are present, but the first exact branch ranks fifth; top-one is 2 / 3 correct. Only 6.25–18.75% of each candidate's states match the training automaton. The confirmation therefore falsifies deployment: candidate supply is adequate, transferable obligation vocabulary is not.
obligation-vocabulary backoff: a target-free companion fixture reproduces the consumed 8→40→152 candidate tree, the 13 retained trajectories, and the published receipt hash without constructing the target. A train-only exact→role-shape→aggregate hierarchy raises recognized state coverage on the known exact branch from 12.5% to 75%, but grouped selection is reproduced by shuffled labels (p = .1875) and moves that branch from rank five to rank eight. Vocabulary coverage alone therefore does not transfer branch value.
soft role and temporal obligation metrics: finite colored parent→source channels replace exact state equality while retaining discharge, contradiction, and connection ownership; an order-sensitive variant also preserves when those events occur. Both contain statistically real group-heldout discrimination (role AUC .864, temporal AUC .750; AUC and log-loss p = .03125), but neither passes the action-selection null: each selects 8 / 10 development nuclei while shuffled refits have median seven and p = .50. On the consumed target-free trajectories the published-known exact branch falls to ranks thirteen and eight. These are diagnostic section coordinates, not search policies; the consumed target remains unopened.
individual carried-port paths: candidate supply is now separated from ranking. For each nucleus, 128 canonical target-free descriptor classes are expanded into witnessed root→child port actions. Every nucleus contains exact two-step paths (12 / 53 / 24 / 14 / 27 / 27 / 27 / 27 / 6 exact pairs). The first executor incorrectly added an unrelated raw child score after evaluating the learned pair; removing that double count raises group-heldout selection from 0 / 9 to 5 / 9. Four boundary environments still fail, so the reserved confirmation nucleus remains unopened.
third-frontier value control: a fixed raw-evidence shortlist of 512 paths per nucleus still contains exact alternatives everywhere. Each path is executed target-free for one additional step and described by its outgoing roles, order-two incidences, vote mass, colors, and normalized distance histogram. The group-heldout value selects only 4 / 9 exact paths—worse than the corrected two-step mark—so immediate frontier supply is rejected again as the missing search value.
stage-local connection value: the repaired 12→4→8 tree is evaluated before terminal fusion. Twenty disjoint development nuclei contribute 320 target-free training candidates, but execution remains bounded to the original eight terminals per nucleus. The selected 16-step, four-bin temporal section chooses an exact supplied terminal in 19 / 19 nuclei and 59 colored sites, versus 19 / 19 and 57 for the connection-only order. Thirty-one complete within-nucleus refits reach at most 18 exact nuclei and 58 sites, so both plus-one results are p = .03125. This is a significant development result, not an autonomous-growth claim.
rollout-ranked spatial confirmation: that exact model, its 12→4→8 geometry, an eight-terminal portfolio, and the maximin centre (120,−40,−220) were published before the new nucleus was opened. A 476-atom seed drives three self-fed blocks; every candidate tree, rollout, score, and selected successor freezes before one target-factory call creates the 2,069-atom target. The marked and stable-prefix arms each recover 6 / 9 colored sites, but the marked arm is 2 / 3 in the first block while the stable baseline is exactly 3 / 3. The marked arm has zero exact blocks; the baseline has one. The transfer, sustained-continuation, autonomous, stationary, and exponential gates are therefore all red. The result falsifies deployment of the otherwise significant temporal section rather than being hidden or retuned.
marking-library tree search: the connection and rollout markings now order one immutable candidate set rather than running separate geometries. A round-robin shared beam preserves both the exact connection head at index 0 and the rollout head at index 7, so an unconfirmed learned marking can no longer erase the stronger baseline action. In the consumed three-block, width-two audit the shared tree expands 8 → 16 → 16 candidates and retains two states at every block; both terminal paths recover 6 / 9 sites and neither is exact. This closes a candidate-retention failure, not the autonomous-growth gap: the library chooses no winner, and stationary or exponential IQC growth remains red.
prefix channel and reach diagnosis: the generic portfolio now accepts a predeclared beam schedule, parent-balanced or global allocation, replacement or additive value, and one finite state channel per marking. On the consumed nucleus, lineage-balanced 2 → 4 → 8 rollback retains eight terminals but none is exact (best 7 / 9 sites). Removing learned pruning shows that a bounded 12 → 8 → 16 port reach does contain a target-guided exact three-block path; after an exact two-site prefix the first correct exposed port is rank 14 of 740, outside the former reach of eight. A channel-diverse 8 → 16 → 32 autonomous prefix portfolio retains two exact first blocks but zero exact second blocks among 64 terminals. Candidate geometry is therefore available, while transferable prefix value remains the measured blocker; this consumed audit does not authorize autonomous, stationary, or exponential growth.
clusters² future-option portfolio: parent branches are now valued by the distribution of their complete child trees rather than their immediate placement score. Four frozen marking channels—base, colored geometry, ports, and coupled pose/port—score the identical 126–141 child terminals per parent; each parent receives the mean of its best eight children. On the consumed eight-parent audit, the only exact parent moves from old rank eight to port-option rank one and mean-option rank three. A four-parent channel-diverse beam retains it, and the union of eight children per channel retains one exact six-action path, parent 8 → child 123. No channel's greedy top child is exact. Fifteen of 31 marginal-preserving parent-score shuffles also retain the path (retention p = .50; mean-rank p = .40625), so this is a real rollback-supply repair but not a causal selection win, autonomous commit, stationary rule, or exponential certificate.
held-out child-option graph: the same idea is now tested across all ten consumed development nuclei rather than on one eight-parent tree. The frozen corpus contains 1,278 six-action parents, 142 exact labels, and at most eight target-free child actions per parent. For each held-out nucleus, order-one and order-two typed-port heads fit only the other nine nuclei; local port-mass and live-continuation channels see the same immutable children. The width-four portfolio retains an exact parent in 8 / 9 supplied nuclei and its mean first-exact rank sum is 30; every one of 31 marginal-preserving controls is worse on retention and all but one are worse on rank (both plus-one p = .03125). However, the strongest order-two head alone is also 8 / 9. This proves transferable, non-random parent-option structure, not an incremental causal win. Child nodes remain unlabeled individually, so a later-annulus execution must decide the third-block gate.
executable third-block diagnosis: every one of the forty retained parents is re-seeded at the expanded radius and receives a fresh bounded 8 × 8 × 8 three-action tree. All 5,091 terminal action keys and four frozen scores are serialized before one consumed larger-target open; only 160 terminals survive the four-way library. Exact parents are present in eight nuclei. Their bounded trees contain 90 exact third-block paths across six nuclei, while the retained portfolio contains six exact paths across only three. Three failures are marking-pruning failures (first exact ranks reach 109), and two occur at the hard top-8 reach cutoff.
reach versus value: a consumed-target uniform-cost diagnosis follows only correct prefixes for the four exact parents hidden by that cutoff. The unchanged frozen frontier contains an exact three-action path for all four: every minimum bottleneck rank is 12, with rank sums 21 or 23. Thus the port grammar supplies the geometry, but target-guided evidence cannot authorize changing reach from 8 to 12. A separate nested group-heldout terminal model—scores plus proper-SE(3)-invariant triangle, radius, and cross-distance features—also fails: it retains exact paths in 2 / 6 supplied nuclei versus 3 / 6 for the incumbent (retention p = .4375; rank p = .21875 against 31 shuffles). The next gate is a train-only adaptive or channel-diverse reach policy, not a target-tuned wider beam. Autonomous selection, stationary recurrence, and exponential IQC growth remain red.
compute-matched channel reach: the generic marking now exposes the five continuous pose/port responses already learned from training. The candidate budget remains eight: three scalar leaders plus one previously unseen leader from each channel. On the four exact parents hidden by scalar top-8, this restores 11, 10, 11, and 10 exact terminal paths. Across all fifteen exact development parents it supplies 15 / 15 and all 8 / 8 eligible nuclei, versus 11 / 15 and 6 / 8 for scalar top-8; exact paths rise from 90 to 472 with no extra child constructions. Every action receipt freezes before one consumed target open. Because the allocation was designed after inspecting consumed failures, this is a preservation result—not fresh confirmation or an autonomous winner—and the production default remains unchanged.
fresh bounded clusters² supply: the successor was frozen before a fourth maximin nucleus at (160,−180,−140), 161.25 units from all 89 prior centres, was opened. A whole-child proper-SE(3)-invariant marking contributes one action and a base fallback contributes five under each of all eight parents. The complete second frontier is hashed, but only 47 prefixes are expanded versus 168 for the eager library. Exact unordered-action memoization reduces 17,240 geometric advances to 8,207 while preserving path-dependent scores; the one-shot run finishes in 1,119.19 seconds under its 1,200-second gate. Before the target exists, 6,099 nine-action lineages and the receipt are immutable. One subsequent target open finds 410 exact lineages, 34 exact parent→child prefixes, and exact supply under every retained parent. This is a fresh green candidate-supply and compute result. No lineage winner is selected, so autonomous commitment, stationary recurrence, and exponential IQC growth remain red.
order-independent first frontier: a bounded subset dynamic program now accepts a three-action parent only when all six action orders replay to the same colored cloud. The geometry and immutable candidate set are frozen before scoring. A group-heldout incidence marking preserves at least one exact closure in every development nucleus; on the consumed audit its top-eight batch contains two exact parents. This makes the displayed simultaneous flashes a certified commuting antichain rather than a visual grouping of convenient proposals.
closure-conditioned child transfer: the next child value is fitted only after all second-frontier candidates have frozen. Its 3,994 development rows contain 95 exact continuations, and grouped holdout keeps all 14 exact parent branches within a top-16 per-parent schedule. A fifth consumed geometry falsifies transfer: both available exact six-action continuations rank 132nd and 133rd, so neither survives top 16. A fixed six-way feature ablation then removes radial bins, nearest-neighbor slots, or the entire 408-coordinate site section without changing candidates; every arm still misses top 16, and the four-score legacy section reaches only ranks 95 and 96. The missing connection change is now represented explicitly as a canonical six-node graph: three typed parent obligations, three typed child obligations, and all invariant within/cross incidences. Its lower-order value improves whole-nucleus holdout to 12 / 14 supplied branches and moves the fifth-geometry exact ranks to 69 and 71; the higher-order value supplies 9 / 14 and reaches ranks 78 and 80. This is meaningful transfer improvement, but both remain outside the unchanged top-16 gate. The receipts are pinned as a representation boundary rather than promoted into the marking library. Commuting geometry is green; transferable child valuation, autonomous growth, stationarity, and exponential IQC growth remain red.
learned programfactor≥1mflat / recursive
NaCl quotient8.000×a5176,942×
IQC section≥3.884×a633,221×
Fibonacci rule≥4.096×a553,024×
30° hBN address4.000×a552,392×
The finite typed compiler now removes the family branch from the recursive executor.
typed productiontypeschildrentwo unseen levels
NaCl cell → cells18216 → 1,728 → 13,824
IQC section generator1rank 6507 → 1,969 → 8,603
Fibonacci address rule827729 → 3,375 → 13,824
30° hBN pose/address281,024 → 4,096 → 16,384
One production contract: three finite graphs use the incidence counter; IQC enumerates rank-6 addresses through its learned 3D internal section. The hBN row counts its square address envelope; exact circular crops are 746 → 2,954 → 11,696. Explicit coordinate output remains linear.
