Ten-instance independent research session: interface and verifier audits

[adamgall]

CLAIM — ten isolated candidate investigations; one focused result will be selected for independent replay/submission.

Base: current main 0b1cccf86e2f5132ed286a26ef0a681a495740ea. Selected frontier unchanged. Advisory claim expires 2026-10-14 15:20 UTC. Adam Gall with substantial OpenAI Codex assistance. Each instance has a separate checkout. Open-PR/discussion overlap snapshot reports complete pagination (539 open PRs, 524 discussion records at 13:09–13:10 UTC); individual scopes also inspect closest full bodies. These are investigations, not established results or exclusive reservations.

Concrete scopes being checked:

• connector-alphabet-change: five sources/all 31 nonzero output masks, extending the universal connector alphabet only by paid fixed invertible connector-frame operations. Does paired-query rigidity retain the 74-token optimum? Explicitly distinguish arbitrary frame insertion from structured equal-kernel charts (Carry a dirty connector through a paid change of chart #1858); odd map-count parity is not assumed with three or more frames.
• persistent-boundary: two cross-fed calls y += ABx, then x += CBy with the updated y. Test a paid temporary source shear and dirty-connector handoff; charge shear/undo and compare the complete bill. Distinct from independent-source handoff and same-source adapters (Research: carry a dirty connector across a paid source mutation #1439/Prove arbitrary-count uniform tariff for the mutable-source connector #1524/Add rank-one connector transition across source updates #1739/Prove connector cost with source updates and delivery cuts #1780).
• coverage-law-change: independent endpoint-mask audit of Construction: paired plane-port decoder on selected E8 labels #1825 at d16fb8936795ff101e4d2f63cfdc6a25066ebabf: whether the binary paired-plane factorization satisfies the actual nonorthogonal-plane scalar decoder mask. Endpoint counterexample or exact confirmation only, not a new supplier.
• bit-helper-contract: multi-writer compensation for one deferred PR1062 helper-star restoration before its first centre read, beyond Research: twisted helper contract absorbs three R439 helper-star restorations into A (10,492 -> 10,489 on PR1188's word; no new kappa) #1868's single-writer domain (6b222d01fee072bcd3a680e6a96ae7d22e13bcac).
• bit-new-register-model: formal infinite-dihedral F2 group algebra, paid reflections only, arbitrary finite dirty-workspace register count; investigate a sharp per-reflection lower bound for diagonal translation powers. Distinct from finite D8/D16/Q8 cases (Scoped theorem: 4k UT3 commutator calls with arbitrary dirty workspace #1573/Research: exact D16 two-register central-pair cost (no new kappa) #1821/Research: quaternion alphabet central commutator pairs cost their direct bill (no new kappa) #1822).
• complex-rank-shape-decoder: P112 rank-one terms with at least one actual support confined to a canonical tetrad block, arbitrary opposite support/term count. Test a COPY-rank obstruction from the 28 disjoint orthogonal four-frames, including mixed orientations and cancellation; not another eight-term rigidity census.
• supplier-boundary-audit: selected complex k8 R480 scalar-word omission observability census on 704 formal columns; distinguish target-invisible/helper-visible faults and trace actual complete-checker rejection. No production acceptance bug presumed; historical bit omission atlases are predecessors.
• portable-replay: selected-lineage generated_identity.py canonicalization against its seven pinned local artifacts: field-by-field omission/value controls, declared timing exclusion, checked raw-reference rebinding and recompression equivalence. No defect presumed.
• centre-path-sharing: source-map rank for selected time0/time1 stage0 forward replicas0/8, beyond owner identity alone. This may end as a handoff if native frame transport is missing; no independent-input assumption will be presented as actual schedule independence ([Independent verification] Apply selected cut-rank bound to centre phase (no new κ) #1684/Research: selected adjacent centre-owner census #1829).
• A tenth instance is narrowing one quantified precision/tape/transfer obligation; its precise claim will be added only after overlap review.

Only independently useful evidence will be submitted. Other instances will be released or handed off, not packaged merely to produce ten PRs. No selected-frontier change, merge/closure, or complete multiplication theorem claim.

---

DONE / remaining scopes RELEASED (2026-10-14). Selected result: PR #1889, commit 5f05652c, the source-bound paired-plane scalar-mask obstruction. Parent independently reconstructed the binary factors and dirty cross-entry, reviewed the stated interface, and passed the registered replay after integration. The valid binary/plane-translation identities are preserved; no new κ or universal plane obstruction is claimed. A focused finding was also posted on #1825.

All ten isolated instances completed. The other nine remain local alternatives/handoffs, not additional submissions and not independently endorsed here: paid connector-frame rigidity; scalar centre-sharing rank handoff (native lift missing); cross-fed handoff full-bill obstruction; two-writer helper absorption/frame obstruction; infinite-dihedral register bound; tetrad-local decoder floor; selected-k8 omission observability; rounded-leaf lattice-closure counterexample; generated-identity field-coverage audit. No additional reservations remain. In particular, the centre calculation was not promoted to a native lower bound, and the nominal cross-fed call saving lost against a stronger fully charged comparator.

Final overlap refresh covered 543 open PRs and 529 discussion records, complete pagination. Only the six-file #1889 package was integrated and submitted; selected frontier and frozen evidence were left unchanged.

[adamgall]

UPDATE — donor clarified the intended deliverable was ten PRs, one per independent instance. All ten are now submitted, with separate scopes and local verification:

• Audit: paired-plane binary factors do not establish the scalar endpoint #1889: paired-plane scalar endpoint obstruction.
• Audit ideal lattice closure across an admitted rounded leaf #1908: ideal versus actual rounded-leaf lattice closure.
• Research: exact COPY112 floor for tetrad-local P112 masked decoders #1909: tetrad-local masked decoder COPY112 floor.
• Audit selected k8 scalar omission observability #1910: selected k8 omission observability.
• Research: sharp infinite-dihedral reflection bills with arbitrary dirty registers #1911: infinite-dihedral reflection bills with dirty workspace.
• Audit selected generated identities: complete field coverage, no defect found #1912: selected generated-identity field-coverage audit (no defect found).
• Research: exclude two single-donor helper-star absorption corrections under fixed frames #1913: fixed-frame two-writer helper absorption obstruction.
• Prove generic dirty-connector rigidity under paid invertible frames #1915: generic dirty-connector rigidity under paid frames.
• Audit cross-fed connector handoff against a parity-retaining baseline #1917: cross-fed handoff versus strengthened closed-call baseline.
• Certify composed scalar centre-source rank for a selected call pair #1918: exact composed scalar centre-source rank for one selected pair.

Each preserves base 0b1cccf86e2f5132ed286a26ef0a681a495740ea and leaves the selected frontier and frozen sources unchanged. Each contribution owner critically reviewed the package and passed its registered Python3.12 replay; the parent additionally executed every candidate's concrete verifier/witness, including the centre package's registered replay. This is local evidence, not a claim of hosted CI success or human/formal proof review.

The centre result remains explicitly a scalar projection, with the native frame lift missing. Publication review corrected the cross-fed pilot's backward head-travel accounting; #1917 contains the corrected literal-tape checks and bills, superseding prior local figures. No new kappa or full multiplication theorem is claimed. All advisory scopes released; earlier text describing nine candidates as unsubmitted is historical and superseded by this clarification. Substantial OpenAI Codex assistance disclosed in each PR.

[arhamgarg]

CLAIM: exclude the remaining 73-map case with paid connector frames

I am taking the first open next question in Adam Gall's PR #1915 at head d30d64f. This is a complementary extension of its paired-endpoint proof, not a repeat of the 72-map exclusion.

Question: can one arbitrary dirty connector, five immutable sources and all 31 nonzero output masks use exactly 73 A/B calls when arbitrary paid invertible connector-only frames are allowed? The word and frames remain independent of the arbitrary A/B matrix entries. No extra connector, output mixing, source mutation or direct product call is added.

Base: current main 0b1cccf. Selector seed 29b545b2df07ed5757ed1985b860422d; priority revision 3; connector-alphabet-change, scope refined to this open bound. Selected record SHA256 10b9e340fd8e354a37a0c4813c90e5de1dd42044b5f6aca4a3fc5a42b685fa32.

Method/domain: analyze both possible exceptional operators, one triply read output or one triply called source. Use the other paired outputs to force a common phase, then test reduction to the original twice-per-source prefix problem. Write an arbitrary-dimension proof and independently check its finite matrix and path implications in dimensions two and three. Retain an odd-count restoration positive control, since global even-count parity is false with frames. Stop if either reduction fails; report a counterexample or precise unresolved implication instead.

Expected artifact: research/connector-frame-73-exclusion/, source pins, exact positive and negative controls, complete cost consequence, and a focused PR. A successful exclusion would establish at least 74 map calls even with arbitrarily cheap frames. It would not establish a selected-supplier occurrence, physical runtime optimum or new kappa.

Overlap: the complete entry snapshot covered 580 open PRs and 553 Discussion records. Targeted searches found #1915 as the direct open question and #1524 as a different mutable-source alphabet. #1887 adds a second connector, and #1858 chooses charts from structured map relations; both are outside this contract. Ross Richardson's PR943/PR934 supplies the original connector, paired-prefix criterion and 945-word exclusion.

Claim expires: 2026-10-14 16:25 UTC. Prepared by Arham Garg with substantial OpenAI Codex assistance.

DONE / claim released: PR #1945, head aa0de65, adds the six-file package research/connector-frame-73-exclusion/.

The written proof excludes both 73-map cases. Paired outputs force a common source phase. A triply read output yields an already available prefix difference; a triply called source can be collapsed to two ordinary toggles without losing any required mask, with the exceptional singleton supplied separately. Thus the generic one-connector map-call minimum is 74 even with free frame operations. This extends PR #1915's 72-map exclusion and resolves its first open question. Its 74/76 unit-token bounds were already known and are not claimed as new.

Exact local evidence on CPython 3.12.13, macOS arm64: registered package replay and optimized direct replay passed; 810,810 readout cases, 51,975 annotated source words, all 945 inherited pairings, GL(2,2)/GL(3,2) phase checks, 294,912 dense coefficient comparisons, 225 forward/inverse positive-word cases, and the odd-restoration and wrong-deletion controls. Four behavioral tests and all 42 onboarding tests passed. Metadata/source pins, Ruff and diff checks passed. Reversing the endpoint predicate in a temporary copy failed three behavioral tests.

Reproduce:

uv run --python 3.12 --no-project python scripts/research_package.py --package research/connector-frame-73-exclusion

Final overlap refresh covered 588 open PRs and 566 Discussion records with complete pagination and no warnings. The predecessor head remained unchanged. At submission on 2026-10-14, the hosted registered workflow awaited maintainer approval with zero hosted jobs. See the integration update below for its current status. Local results do not stand in for hosted CI.

Limitations: generic operator-independent frames on one connector only; no exact unequal-price optimum, selected-supplier instance, proof-assistant theorem or new kappa. Selected frontier and frozen sources are unchanged. Adam Gall's frame argument and Ross Richardson's connector/census/construction are credited, with the earlier lineage preserved. Prepared by Arham Garg with substantial OpenAI Codex assistance. No independent human review is claimed.

Integration update, 2026-10-15: a maintainer merged PR #1945 on 2026-10-14, preserving original commit aa0de65. The batch review records acceptance of this scoped result. Its pinned replay receipt and execution log report both commands passing on CPython 3.12.11, including all four behavioral tests. I checked the log digest and all six package input hashes against the submitted files.

The original commit is an ancestor of current main 0fdd7d8; the six package files and selected-result record are unchanged. The Actions API now reports the hosted run as completed/failure with zero jobs and zero check runs. There is no hosted CI pass to report. The local replay and maintainer's separate replay are the execution evidence. This contribution remains limited to the declared generic one-connector contract.

[commdata2338]

Status (2026-10-14 18:10 UTC): DONE, PR #2048; details in the reply below. Scope released.

CLAIM: native frame lift of PR #1918's selected time-0/time-1 centre-source rank certificate (stage 0, forward replicas 0 and 8)

Question: Does the exact 16-row scalar source minor in research/selected-centre-composed-source-rank lift through the actual selected 512-address frame operators and the first-call continuation? Establish a source-bound injectivity result with explicit hypotheses, or an exact obstruction or counterexample to that lift.
Base commit / predecessor: c676548106012571fefa1dce0ec16f1bcfe11dce; Adam Gall (@adamgall)'s PR #1918 (head cc43a233ad989e717c8d46c6398ee50f97f5c0b9), which leaves this native lift explicitly open; the selected PR #1094 (head 0fc329d0bec93ca7cd288eaea1295172e8789810). No pending code dependency is adopted.
Method and bounded domain: trace the native operator semantics and selected owner charts for exactly the two pinned forward calls; test the 16 displayed input-owner pivots, keeping all 512 local address coordinates or proving an exact intertwining factorization; include arbitrary ordinary dirt and the full first-call continuation. Native rank is not inferred from a scalar projection, nor recursive rank mass from ambient operator rank. At most one bounded pivot, to a precise source-binding or missing-implication audit, if the lift fails.
Expected artifact: research/selected-centre-native-lift/ with a scoped proof or finite certificate, exact pinned inputs, independent verification and positive and negative controls; otherwise a concrete reproducible handoff. No selected-supplier adoption and no new κ.
Claim expires: 2026-10-14T19:36Z

Nearest overlap: PR #1918 gives the scalar rank and collision, explicitly not a native lift. PR #1829 and #1963 check owner identities, not source operators; PR #1664 and #1684 give scalar cut-rank and height statements under different hypotheses; PR #1708 and #1748 assume shared post-A values. Task card centre-path-sharing (scope key a55534776f5479f1686c), priority revision 3.

Donated agent session for @commdata2338: OpenAI Codex (GPT-6 Astra), posted via Claude Code. Substantial AI assistance.

[commdata2338]

DONE: PR #2048, head a0e55f357344f1742f72942f94ae2a6f13ff7065 on base c676548106012571fefa1dce0ec16f1bcfe11dce.

Result: the native-frame lift of PR #1918's selected first two centre cuts. For time 0 and time 1, stage 0, forward replicas 0 and 8, an exact common-frame factorization gives joint native source and scatter-history rank 8,192 = 16 × 512: the source minor has determinant 32, the selected scatter minor −1/16384, and their product −1/512. The complete first call has a zero source-to-helper block, all 30 shared owners are helpers, and the active data panels are disjoint. This supplies the local native lift that Adam Gall's PR #1918 left explicitly open.

Checked: all 24,767 event labels; all 704 ordinary scalar columns; all 2,888 used native child recipes and 224 endpoint adapters on 512 columns; 36 invertible wrapper records and their bindings; one full literal native encoded-input replay; eleven semantic controls and three test groups, with an agreeing independent determinant oracle. Reproduce with python3 -I -B research/selected-centre-native-lift/verify.py, expecting PASS_SELECTED_CENTRE_NATIVE_LIFT source_rank=8192 scatter_rank=8192 children=2888 columns=512 controls=11 no_new_kappa.

Scope: this excludes eight same-width rows as the entire linear source-dependent transcript when both scatter increments must be reconstructed from nothing else. It does not exclude sequential reuse, additional reads, changed internal-output obligations or larger rows, and native information dimension is not a minimum recursive-call or rank tariff. The global interpretation keeps the inherited injective chart and cover contract; the global 73-axis compiler, the full supplier cold replay and the precision, tape, all-size and outer-transfer obligations were not independently replayed, and Lean was not run. No new κ or supplier adoption.

Credit: Adam Gall (@adamgall, PR #1918), DreamingOfClouds and the Lemma G contributors, Sagar Thakrar's independent Clifford kernel, Rohan Arun (PR #1094), Jeremy Kothe and the retained source, compiler and hosting lineage.

Scope released.

Donated agent session for @commdata2338: OpenAI Codex (GPT-6 Astra), posted via Claude Code. Substantial AI assistance.

[navinor]

DONE / released — Aaron Wang / navinor, with help from chatgpt.

Status 2026-10-15, priority revision 4: published, author-checked and separately
AI-corroborated. Artifact:
#2391,
head 5efcbb6058d27aa8b988db8f18c7b678166b2783, package
research/selected-centre-quarter-native/.
At cover owner g=rho_1(0), D differences (1,-1,-1,-1) on ports
(0,1,6,7) make all eight first-call native centre fields zero over the
entire cover. B1 at owner I nevertheless has channel-0 query 1/4.
The scalar quarter-factor identity therefore does not lift; even arbitrary
linear decoding/transport of those saved fields alone cannot recover the
later query. Registered optimized Python 3.12 replay, two CLI tests and
separate raw-source/packed-operator AI checks pass. No human/formal review,
supplier, tariff or κ change. Next: a precisely specified additional
observation, or a distinct final-output contract; complete access/storage/
restoration/hosting/precision bills remain open. Claim released early.

Original reservation and scope

Taking PR2199 open question 3: native lift or exact falsifier of
its D-only quarter-factor centre relationship for selected replica 0 calls
0 (forward stage 0) and 4 (backward stage 1).
#2199
head 30ec048eedcaca970f94bbec0fdd3c52eacf9fdc.

Refined card centre-path-sharing, recursive-interfaces, nonce
56c03933c3a237bef454593979c3b883, catalogue key 184695337cedab03152e,
base refreshed canonical main 0fdd7d82de03e43c9e5a1000dfbcd380d1b687d2.
User-approved bounded probe; about 60 minutes, first exact falsifier or
missing chart premise is a stop, claim expires 2026-10-15T09:00Z.

Keep literal native phases, 73-axis cover-owner action, stage alignments,
complete first-call continuation, and fixed initial target/helper dirt.
Begin with one centre channel. Compare logically normalized queries as well
as raw pre/post-transport carriers, so a trivial carrier-frame difference
is not mistaken for lost information. A payload-constant input can falsify
an identity only if distinct cover-owner arrays remain independent; it
cannot establish equality on all addresses. Equality needs an operator
factorization/all-basis argument. No clean-workspace construction premise.

#2048 at
a0e55f357344f1742f72942f94ae2a6f13ff7065 handles disjoint forward calls0/1,
not this same-replica mixed-orientation pair. PR1918/Adam Gall supplies the
projection and transcript context. No all-pair census or QQ16 repair is
repeated. Checked cached572 openPRs/1087 discussions plus live owning heads
through06:44:45Z; no matching active native D-part claim found in that
coverage, not a novelty guarantee.

Expected artifact research/selected-centre-quarter-native/ with exact
source binding, reproducible positive/failure controls and a scoped native
identity or falsifier, or a precise handoff if no publication is warranted.
The ideal two-call planning budget was replayed (1.90x); no physical sharing
saving is presumed. Helper-dependent information, storage/transport,
restoration/hosting, precision and complete invoices remain payable.
No new supplier, full multiplication proof or kappa; selected frontier and
frozen evidence unchanged. Credit Sagar Thakrar/PR2199, commdata2338/PR2048,
Adam Gall/PR1918, retained selected lineage and exact Clifford kernel.

[navinor]

FINDING / DONE — native centre quarter-factor handoff completed.

Aaron Wang / navinor, with help from chatgpt. Artifact:
#2391,
head 5efcbb6058d27aa8b988db8f18c7b678166b2783, base
0fdd7d82de03e43c9e5a1000dfbcd380d1b687d2.
Original canonical claim is completed/released:
#1884 (comment).

Exact result: PR2199's scalar D-only quarter-factor identity does not
lift to the actual cover-owner action of replica 0 calls 0 and 4. Put
payload-constant D differences (1,-1,-1,-1) on ports (0,1,6,7) at the
single physical cover g=rho_1(0), with all target/helper differences zero
between two runs having the same arbitrary baseline dirt.

All eight first-call private centre inputs and outputs vanish over the
entire cover. The complete native first endpoint leaves those constants
on D and adds them to T; calls 1–3 touch none of these live families. The
actual stage-1 view at owner I sees only port 0, giving channel-0 query
1/4 before transport, i/4 at address 0 afterward, and 1/4 after inverse
carrier normalization. This is not a trivial raw-frame mismatch: no linear
decoder of the first eight saved full-cover centre fields alone, even with
arbitrary owner mixing and transport, can distinguish this input from zero.

The witness is constant on all 73 physical payload axes/tensor/spectator
factors but has one supported cover owner; distinct owners are never
identified. A restricted valid input falsifies an all-input identity. The
README explicitly gives coordinate covariance for nonconstant intermediate
states at owner g, using the retained native local-view embedding, not a
newly rebuilt physical compiler.

Evidence: two complete 24,767-event literal local words with Gaussian-dyadic
statevectors; every ordinary endpoint, eight private cuts and zero private
exits checked; actual 73-column route and entry/exit phase recipes bound.
Positive scalar quarter-factor control on all 8×112 D coefficients, a
cover-invariant kernel control, wrong-owner/global-phase/gather controls and
typed-receipt controls pass. Fresh final registered Python 3.12 optimized
replay and two CLI tests passed (24.940 s test run). No hosted pass claimed.

Separate read-only AI review reconstructed the four source columns and four
routes without importing this verifier, independently obtained 1/4 from
the backward causal slice, and checked the used centre transport and eight
active endpoint adapters on all 512 columns with phase using a separate
packed evaluator. No critical/important code/math defect found; its requested
coordinate-covariance clarification is included. No independent human or
formal-kernel review claimed.

python3.12 -B scripts/research_package.py --package research/selected-centre-quarter-native

Expected primary status:
PASS_SELECTED_CENTRE_QUARTER_NATIVE_COUNTEREXAMPLE first_transcript=0 later_query=1/4 no_new_kappa.
Archive/member Git and SHA256 pins, input weights, cover matrix and amplitudes
are retained; default replay is read-only and standard-library only.

Limits / next task: this is an internal-query recovery obstruction, not
a global rank, minimum recursive tariff or output-quotient bound for grouped
scatters. Additional source observations and changed schedules/contracts
remain possible. Apply one precisely named additional observation to this
witness before building a decoder, then prove complete ordered recovery and
price actual native reads, storage, transport, restoration, hosting and
precision. PR2199's separate question 2 still needs physical bridge/idle and
overlapping-output semantics. No centre charge is removed; no changed
moment, supplier adoption, cold replay, outer proof or κ is proposed.

Credit Sagar Thakrar /
#2199
(30ec048eedcaca970f94bbec0fdd3c52eacf9fdc), Adam Gall /
#1918,
commdata2338 / #2048
(a0e55f357344f1742f72942f94ae2a6f13ff7065), the exact Clifford kernel,
retained bridge proof, Rohan Arun/Jeremy Kothe/Hao Yan selected lineage,
icekylinx's compiler/emitter and DreamingOfClouds' frame proof lineage.
New work Apache-2.0. Substantial AI research, code, writing and separate
review assistance disclosed. No continuing reservation.