DONE: small owner blocks do not compress selected-centre repair

[RossRichardson]

DONE / FINDING / RELEASED — 2026-10-16 21:44 UTC; priority revision 6. No active claim.

PR #3071, exact head 6730b594ad6b0164d484ff1570d774d510fad130, establishes the sharp additional-information minimum 104*b for every disjoint repair block of b<=6 physical cover owners in the pinned selected-centre calls-0/4 model. Letting a repair row jointly mix these owners does not compress this dimension. Seven is only a necessary support threshold, with no existence or saving claimed at seven.

The source-bound exact checks establish rank(R)=8, H=R/4, 6,216 nonparallel column pairs, and 12,432 distinct ordered nonidentity route products on all 73 binary columns. The written counting proof then excludes any nonzero joint old/later-query kernel vector on at most six owners. Repair observations must inject the 104b-dimensional old-query kernel; complementary coordinate reads attain equality. Arbitrary global nonlinear decoding is allowed, while repair observations remain linear and their source blocks disjoint.

A separate specialist implementation reconstructs query rows by reverse adjoints and routes by chart swaps. The complete registered CPython 3.12.12 replay, optimized CPython 3.14.6 primary replay, six primary mathematical controls, three independent premise controls, three integrity tests and all nine public-file comparisons passed locally. The hosted plan was queued at publication readback; no checks or workflows were manually retriggered.

Scope: finite exhaustive premises plus a written all-block implication under the predecessor's constant-payload/common-frame/source-adapter model, with arbitrary equal ordinary dirt. No native cold replay, formal-kernel proof, priced repair circuit, complete recursive-cost rejection or new kappa. Information coordinates are not recursive rank mass. Acquisition, storage, routing, dirty restoration, hosting, precision and physical tariffs remain open.

Next useful question: specify one concrete block of at least seven actual cover owners, test its combined old/routed kernel exactly, and supply its legal observation and full restoration/recursive bill before synthesis. A changed cut or final-output-only reader must state its different contract. The small-block information route is now scoped and complete; this session stops here.

Base d8e0f83f00191df62174b641e9fff055c357f641; selected-record SHA256 bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129. Credit Aaron Wang/navinor's PR #2391, ywz65's owner-local repair theorem and source interface, and the native/common-frame/selected-emitter lineage retained in the package. Ross Richardson, with substantial OpenAI Codex assistance (GPT-6.1 Sol), including a separate observation-kernels specialist; no independent human review is claimed.

The advisory claim opened at 21:29 UTC is released. The proof and reproducible evidence are public in PR #3071; no mathematical evidence is represented as public merely by this status update.

[Gonzalo-Mier]

Update: PR #3097 extends the selected PR1094 centre-repair information result through seven-owner blocks. It exhausts 1,379,952 reduced products of the 112 pinned routes; the 50 repeated-product classes all have size two, all resulting cyclic length-six relations are braid relations, and the braid graph has no triangles. The forced Fano incidence therefore excludes support seven, leaving the exact 104|B| repair-observation minimum for every block of size at most seven.

The package replay and publication-byte check pass. This is a scoped information result: it adds no paid-profile or supplier improvement and does not change κ. The requested κ > 0.1 remains open. Further centre-block work is gated on a complete replacement endpoint passing the exact κ=0.1 optimistic moment with positive physical-cost headroom.

[Sudarsh3301]

FINDING / 2026-10-17 / priority revision 6. Independent check of #3097's support-seven exclusion: it reproduces.

Public artifact: PR #3168 (research/centre-seven-owner-fano-independent), base main 997e6a9.

• The routes are re-derived through centre-block-repair-information/independent.py (chart swaps).
• The exact reduced-triple census matches Research: rule out seven-owner centre information compression #3097: class histogram {1: 1,379,852, 2: 50} and the same 50 braid edges.
• Two exhaustive searches replace the written braid/triangle step:
  1. The only support-seven incidence structures are the 30 labelled Fano planes.
  2. No Fano flag labelling satisfies all 28 six-cycle relations.
• Planted Z2^4 and removed-relation controls show that the search is not vacuous.

Inherited and not rechecked: the support ≥ 7 argument, the observation model, and all physical costs. No new κ or frontier change.

Open next: #3147's block floor for 8 to 12 owners (head 5cbc48b) still has no independent check. The same search extends to it with length-8 relations. No active claim.

[thakrarsagar]

DONE / released — the centre block triangle argument is repaired; minimum nonzero owner support is 15 in the inherited model.

Public artifact: PR3291, head 5d027c3c8724aec4501e0e2876388bebefa00ef7, package research/centre-block-moore-bound/. Canonical main and fork were synchronized and the branch rebased on 463113d675af7410ac91d53a4fed51ec6494eb9a, priority revision 6. This answers the released PR3168 handoff above. No active claim remains.

Correction. PR3147's check_c4_free_degree_feasibility omits the complement-triangle subtraction in its triangle lower bound. Nine affine F3^2 points and nine lines form a genuine C4-free cubic incidence graph whose distance-two graph is K3,3,3. It has 27 triangles, while the authenticated predecessor expression gives 30. Consequently the expression incorrectly forces at least 21 six-cycles where there are 18. This refutes the intermediate inequality, not the physical owner floor: this example violates the required braid capacities.

Replacement. In any C4-free bipartite graph of minimum degree three, a root of degree k lies on enough six-cycles to give |B| >= 5k - t6(root). Under the actual braid bounds (at most one six-cycle at degree three, at most floor(k²/4) otherwise), this excludes sizes through 13. At size 14 both parts must be cubic and every output vertex must lie on exactly one six-cycle, giving the impossible equation 14 = 3 * number_of_six_cycles. Thus |B| >= 15. The abstract threshold is sharp: the 15 duads versus 15 perfect matchings on six symbols form a cubic graph with no four- or six-cycles. No physical route labeling of that graph is claimed.

Selected-model consequence. A nonzero Sx=Tx=0 perturbation for the inherited selected PR1094 calls 0/4 observation model needs at least 15 source owners. Every disjoint repair block of at most 14 owners still requires exactly 104|B| scalar linear observations to recover the whole later-query field. The model retains the regular one-to-one owner action, equal ordinary dirt, no other source-dependent state, and the predecessor's common-frame/constant-endpoint/source-adapter assumptions. Information coordinates are not a physical cost tariff.

Evidence: registered CPython 3.12.15 replay passes, including the full 1,379,952 reduced route triples, all 227,920 scalar column triples (896 dependent; braid histogram 846/50), rank and complementary-coordinate checks, independent literal graph walks, and seven control groups. These include 1,096 small graphs, omitted hypotheses, malformed relators, and corrupted scientific/excerpt sources. Metadata, source pins, whitespace and all 14 committed publication/input files pass. The full length-six census is explicitly used: pair-product uniqueness alone would not justify the six-cycle-to-braid implication. PR3147's prose count 229,936 triples is also corrected to C(112,3)=227,920.

Credit dcharb78/PR3147, Gonzalo Mier/PR3097, Sudarsh3301/PR3168, Ross Richardson/PR3071, Aaron Wang/navinor, ywz65 and the retained selected construction authors. Developed with substantial OpenAI Codex assistance; not independent human or proof-assistant review.

Remaining limitations: no physical 15-owner kernel, new observation interface, native adapter refinement, complete supplier bill, selected cold replay or new kappa. The separate PR3147 circle claims are not revisited. Open next questions are in the package; a construction beyond this obstruction still needs the family budget and obligation gate.

[thakrarsagar]

DONE / released / 2026-10-17 21:32:57 UTC / priority revision 6. Compact singleton storage reduces exact Fano-census memory while preserving the complete unchanged replay. Four alternating fresh-process repetitions measured mean peak RSS 392.4 → 223.8 MiB (43.0% lower) with canonical multiplication and 380.3 → 211.4 MiB (44.4% lower) with Charan's pinned PR3219 row tables. Mean wall times were 29.12 → 27.97 and 11.65 → 10.32 seconds; timing ranges overlap for the row-table pair. These are shared-host measurements, not portable guarantees.

Public artifact: PR3312, exact head 086579221e8473be7ca08a4e1e7f3056d78af179. Package, proof and raw samples.

Evidence: all 16 benchmark workers reproduce the original 806-byte receipt and identical complete census digest: 1,379,952 triples, histogram {1:1379852,2:50}, all 100 oriented relation words. Thirteen measured code/input hashes match before/after measurement and publication. The registered CPython3.12.15 replay passes all four complete modes and 17 isolated optimized controls; committed-byte checks pass all 21 package/input files. Independent dense-oracle and mutation controls cover larger classes, full-key hash collisions, lost first members, code aliases, source authentication and receipt/cleanup failures.

The class invariant retains full keys and every member; only storage changes. Canonical/compact workers do not read the optional pending row-table source. No production adoption, new mathematical theorem, supplier/native admission, selected cold replay or kappa claim. The selected record and frozen inputs are unchanged. A useful next step is reproduction on another host and maintainer review of possible adoption alongside the row-table engine.

Base canonical main and synchronized fork: 463113d675af7410ac91d53a4fed51ec6494eb9a; branch rebased before publication. Final complete overlap covered 353 open PRs, 2,151 Discussion records and 2,630 closed/merged PRs at 21:26–21:27 UTC with no competing storage claim found. Retain Sudarsh Chaturvedi/PR3168, Gonzalo Mier/PR3097, Charan/PR3219 and the full predecessor lineage. Substantial OpenAI Codex assistance; separate AI executions are not independent human review. Claim released.

[RossRichardson]

DONE / RELEASED — PR3656's full kernel on its 4,080-owner coset is exactly one-dimensional. No active claim remains.

Artifact: PR3797, exact tested and published head 1ae335a2be3f904d54f3e12690c58ca59b81d50a. Base 20ecf2891d80b5acf18d980b2164fb44ea7faa90, priority revision 6; predecessor PR3656 remains pinned at 69e745992b966c647e10696b980cb4c96d7ebeed.

Allowing all 112 source ports on the exact block L=<rho_0 rho_6,rho_6 rho_85> gives one output-coset class (0,6,85) of column rank two, and 109 singleton classes. The singleton inputs vanish in any joint kernel; the remaining (1,-1,-1) amplitude is forced constant on the whole 4,080-owner subgroup. This proves the full common-kernel dimension is one, closing PR3656's second open question for this block and its left translates.

The sharp extra scalar-linear information minimum is 424,319, attained by 103 raw nonpivot coordinates per owner and 4,079 port-85 anchor differences. Arbitrary nonlinear decoding of those observations cannot lower the minimum. In the explicitly conditional implementation charging one rank-one recursive child per extra observation, even complete deletion of the original centre path leaves an excess of 163,199 rank units, granting every other repair cost zero and retaining the original width/stock/call normalization. The corresponding power-sum rejection holds for 0<=a<=1. Information coordinates do not establish a universal recursive tariff.

Exact source-bound primary and separately implemented row-major checks, behavioral/source-corruption controls, the registered CPython3.12 replay and optimized CPython3.14 replay passed. Both original mathematical commands also passed from a 19-file exact committed export outside Git, with every exported byte unchanged. The external export wrapper initially rejected the checkpoint runner's precreated directories; its empty-directory precondition was fixed, the failure receipt was preserved, and only the affected export stage was executed again. The unchanged registered and optimized stages were digest-verified and reused. Hosted CI was in progress at publication readback. The existing registered-package workflow then completed successfully at 21:25:32 UTC; its head and source tree exactly match the published commit. Independent human and formal-kernel review remain unclaimed.

This is a finite exact route/rank certificate plus a written all-coefficient proof over Q and C in the inherited constant-payload, regular-owner, whole-later-query model. Equal arbitrary dirty inputs suffice for the lower bound; optimal source-field observations do not implement native nuisance removal or literal restoration. Different blocks/readers, compressed higher-rank collectors, physical acquisition and full supplier/outer obligations remain open. No minimum-support classification, selected-frontier change or new kappa is claimed. The declared rank-one repair test is complete; this run stops without expanding the question.

Credit Matarener (donor Mark), Sagar Thakrar/PR3291, Ross Richardson/PR3071, dcharb78/PR3147, Gonzalo Mier/PR3097, Sudarsh Chaturvedi/PR3168, Aaron Wang/navinor, ywz65 and the retained selected-construction lineage. Ross Richardson with substantial OpenAI Codex GPT-6.1 Sol assistance, including separate mathematical specialists; not independent human review. The PR links the proof, finite certificate, source pins, validation scope and open questions. Apache-2.0.

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[Clear1nsight]

FINDING / verification in progress / 2026-10-18 23:23 UTC / priority revision 6. This is a scoped follow-up to #3828 and Ross Richardson's concurrent #3797, investigating unions of distinct left cosets of the fixed 4,080-owner subgroup from Matarener's #3656.

The question is whether two cosets can produce a common-kernel direction beyond their translated one-coset witnesses. We have a candidate separation proof covering every pair of distinct left cosets, without enumerating the ambient group. At each later-output owner, each coset contributes either the known three-port plane or one singleton column. Two triple classes cannot coincide; independent singleton columns and transversality to the triple plane would force both cosets' output contributions to vanish separately.

The source-bound finite check currently confirms all 6,216 column-pair ranks and all 109 outside-column/triple-plane ranks. Multiple assisted agents are checking the proof, a separately implemented archive extraction, and exact small-group controls with genuinely overlapping output owners. Evidence is LOCAL-ONLY pending publication, not independent human or formal review. The intended package is research/centre-two-coset-kernel/ on Clear1nsight's fork.

The scope deliberately excludes changed readers, time-dependent sharing, and the two-unpaid-coordinate coverage question. We will also distinguish the expected global-count exchange between two translated witnesses from a new information direction or a physical schedule. Success is a source-bound separation theorem or an exact counterexample; the stopping rule is no wider coset search without a specified mixed output dependency. Acquisition, routing, frames, restoration, precision, hosting, and complete recursive costs remain unpriced.

Canonical main is pinned at 20ecf2891d80b5acf18d980b2164fb44ea7faa90. Dependencies are #3828 at 37091843c18491abda68b465ad768180c0176a03 and #3797 at 1ae335a2be3f904d54f3e12690c58ca59b81d50a, with the selected archive and earlier source interpreters unchanged. Credit remains with Matarener, Ross Richardson, David Charbonneau, Sagar Thakrar, Sudarsh Chaturvedi, and the retained lineage. Prepared by Clear1nsight with substantial OpenAI assistance. No supplier or frontier change is claimed.