Sharp eight-query temporal cut for the frozen P104 itinerary

[adamgall]

Result

This adds research/p104-temporal-query-cut/: a sharp temporal communication obstruction for the complete frozen P104 itinerary of PR1972/PR1991.

Even permitting arbitrary additional or replacement common-frame linear role mixing at every one of the 4,059 cuts, while retaining the original transports and private-storage lifetimes, the source-to-target transfer has rank at most eight arrays. The original dirty-restored G/2 channel attains that rank. Therefore no zero-new-transport correction in this domain can complete it to the 104-port identity.

This does not exclude the separately proposed terminal +208 H1 correction, new or retimed transports, new storage lifetimes, or non-common-chart native operations. It supplies no new supplier or kappa. The 96 missing array directions are not a 96-child native lower bound.

Method and proof-critical step

The checker authenticates the exact source witness, reconstructs frames by literal binary XOR closure, and saturates each equal-frame class at every cut. Thus it includes all permitted additional scalar edges, not just the original ADD list or equal-rank registers. It includes all 72 dirty helpers and eight owned-private-copy lifetimes.

At cut 2429, after events 0–2428 and before the first D-helper transport:

• the forward source cone is all 104 X registers, 32 G helpers and eight Q queries;
• the backward target cone is all 104 Y registers, 32 D helpers and eight Q queries;
• their intersection is precisely Q0,…,Q7.

Deleting those eight wire crossings disconnects every X input from every final Y output, including possible later full-frame-helper routes. For a finite address space of dimension d, every admitted linear X→Y block therefore factors through eight d-dimensional query values and has rank at most 8d. Identity completion requires rank 104d. A query's rank-eight frame is not eight arrays: wire dimension and native child rank are kept separate.

The written argument covers arbitrary finite linear programs in this fixed-itinerary model; it does not generalize a finite coefficient search.

Exact evidence

The reproducible certificate reports:

• 4,058 original events, all 4,059 cuts, 444 exact frame subspaces;
• 106,254,468 implicit directed common-frame edges with chronological multiplicity;
• both directional causal scans and a separate cut-deletion scan;
• all 280 arbitrary logical input columns, all 72 dirty helpers and sources restored by the attaining original word;
• an exact G/2 principal minor on ports [0,1,2,3,7,14,22,33] with determinant 1/256, proving rank-eight attainment;
• R^t R = 26 I, G² = 26G, and (I-G/2)^(-1) = I-G/24, showing the residual has rank 104;
• eleven semantic negative controls and one positive basis-invariance control.

The negative controls leave each query out of the separator in turn, introduce a prohibited cross-frame bypass, or remove initial dirty-query compensation / final query cleanup. The graph controls reopen genuine source-target paths; the scalar controls reject the arbitrary-input endpoint. Every mathematical field is regenerated and compared canonically with RESULT.json.

Complete favorable budget and limitations

The unchanged local profile is {1:1074,2:58,3:86,4:104,5:48,6:24,7:8,8:8}, with mass 2368 = 2312 boundary coverage + COPY56, 2,624 scalar additions and eight allocate/copy/discard lifetimes. The tested completion adds zero transports, copies or lifetimes, and generously treats additional scalar mixing, hosting, idle remainder and precision cost as free. It still fails the exact communication condition before a recursive moment comparison is meaningful.

No global owner assignment, native phase recompilation, all-size lifting, precision theorem, outer multiplication theorem or formal-kernel proof is claimed. Inherited PR1991 native identities are explicitly distinguished from the independently replayed logical/frame facts.

Provenance and relation to prior work

• Scientific base: 564148b82ae9df72163f22106f15e73efca8aff2, priority revision 4.
• Single independent selection seed: 5e89c7275a4bd70898735aea8ad1e35d, complex-mechanisms, refined p104-side-correction; complete selection preserved in SELECTION.json.
• Rohan Arun, PR1972 head fd82d172f46933fd253c2c6de4bd5eaff5429cfd: the entire scalar/frame G/2 channel and dirty cancellation. Witness SHA256 0f541bef7f19fdeffd67157684e9f03d785f42c89973632f508fc1a0452b580e.
• Chafik Boukhalfa, PR1991 head 6e222517e182e98499239bc9a4009f540e1c5520: native realization and retained source distribution.
• Adam Gall, PR1940 head a9b7dfe2809092a9a4c90784d12bb60061e995e8: 32-chain schedule; Josie Elliston / PR1071: P104 fixture; Ali Romman / PR1125: fixed-term carrier bound; retain the PR968/717/446/595/620 lineage.

The contribution is the whole-chronology sharp rank capacity under arbitrary added common-frame mixing, not a new geometry, schedule, tight-frame identity, generic cut lemma or terminal correction. Discussion2080 and discussion1167 comments 18931708 / 18931718 add 208 transports and are outside this theorem.

The submission checkpoint 0fdd7d82de03e43c9e5a1000dfbcd380d1b687d2 changed workflow guidance only; catalogue, selected record and scientific sources remained unchanged. Refreshed overlap covered 353 open PRs and 738 discussion/comment/reply records with complete pagination, supplemented by targeted live and local predecessor reads. Offline-cache warnings and coverage limits remain explicit; absence is not a novelty guarantee.

Exercised validation

uv run --python 3.12 --no-project python -B scripts/research_baseline.py
uv run --python 3.12 --no-project python scripts/research_package.py --package research/p104-temporal-query-cut

Observed: PASS_RESEARCH_BASELINE_BINDINGS_ONLY, PASS_P104_TEMPORAL_QUERY_CUT, and PASS_REGISTERED_RESEARCH_PACKAGE research/p104-temporal-query-cut outcome=negative-result. The registered command uses CPython3.12 with -I -O -B; the final registered run took 19.05 seconds locally. The baseline is a source-binding check, not the selected cold replay. Hosted CI is not claimed.

Open next questions

A successor should change the itinerary or the common-chart operation contract: exhibit and price a source-information route around this separator, then check native identities, restored frames, whole-call hosting and precision. The package explicitly leaves non-common-chart monomial-wrapped additions open; their logical operator must be proved, not inferred from equal frame ranks.

Prepared by Adam Gall with substantial OpenAI Codex assistance. Apache-2.0; predecessor attribution retained. No independent human review or formal verification is claimed.

[Tairitsu-Aya]

DONE / independent corroboration; claim released. Priority revision 4. The retiming investigation is complete and published at bb473eb4838c271112a95861833847faed55c579. The live submission check found Jeremy Diviney's concurrent #2113, head fa1a45f91c14bb4b372d19dd7d66e11fea480ef5, already proving arbitrary-frame-path interleaving. This branch is therefore offered as independent evidence and an explicit directed-type extension, with no competing PR. Two code-disjoint checkers recover the same eight-array obstruction and all 280 formal input columns. They also certify a 222/222 partition of the 444-chart directed atlas, so fresh storage and unlimited reuse of existing upward types still cannot help while crossing occurrences total eight. The next useful change is a new directed transport or intermediate chart with a jointly executable, fully priced word. No supplier or kappa is claimed.

The exact directed atlas has 740 types, 1,410 occurrences and the same eight rank-seven private descents identified by #2082. No original event order or role availability is retained in the quotient proof. The independent literal-span implementation uses 1,698 phases and gives disjoint 853/845 forward/backward cones; each restored drop reaches 52 targets. The original G/2 endpoint, 72 dirty helpers and 104 source restorations replay exactly. The general rank implication records the actual crossing messages, not a phase-vertex or edge-type count; with q crossings it gives rank at most q array dimensions.

Both checkers pass under optimized Windows CPython 3.12.9 and the registered Ubuntu 24.04 / CPython 3.12.3 replay (1.25 s, maximum RSS 35,744 KiB). The separate unchanged PR1991 native replay also passed (17.059 s, sampled peak RSS 36,466,688 bytes). Public reproduction and meaningful source, endpoint, rank, reverse-edge and missing-cut controls are in the linked package. No proof assistant, native regeneration, hosted CI or all-size admission is claimed.

Original claim: legal retimings preserving each register's local order, posted before computation at this comment. The experiment was broadened after finding the stronger chronology-free separator. PR2113 was discovered before publication and is credited explicitly; the shared retiming conclusion and cut set are not claimed as new relative to it. Prepared for Tairitsu-Aya with substantial OpenAI Codex assistance; both separate implementations are by this author/assistant, not independent human review.