[aliromman]

Change and mathematical scope

This conditional construction raises complete κ from 0.00304057 in PR #5544 to 0.00304117, a gain of 0.00000060. It changes the paid profile. The selected record, 0.003027288235, remains unchanged.

The change moves one subtraction and sign, on P104 registers 341 and 345, from a four-dimensional frame to the full nine-dimensional frame. Five source sites change. The old path pays H1 + 2H5; the new path pays H5 + H6. Each of the 18 full calls therefore saves H1 + H5 − H6. For every power 0 < t < 1, 6^t < 1 + 5^t. All independent inputs, productive outputs, scalar coefficients and owned lifetimes remain fixed.

Complete invoice	Before	After
Paid calls	69,930	69,912
Productive fields	12,814	12,814
Target minus paid rank mass	760	760
Conditional κ	0.00304057	0.00304117

The exact complete paid delta is {1:-18, 5:-18, 6:18}; the target delta is zero. The proof gives the all-width common-chart identity and complete transfer. The receipt contains both full histograms and exact inequalities. The raw crossing is in (0.00304117181649, 0.00304117181650), an increase between 0.00000059374018 and 0.00000059374020 over the source crossing. The endpoint gain also reflects the two different safety margins. This fixed invoice has a unique crossing; no optimum over other constructions is claimed.

Five framework assumptions remain: native all-column implementation, owned erasure, uniform compiler, precision/tape costs and analytic recovery. The enormous uniform word and complete rounded multiplier are not materialized. These are author-side exact checks, with no independent human acceptance or proof-kernel theorem.

Task and overlap

Task scalar-to-moment, priority revision 7; scope and handoff. Scope is refined to this literal paid-path change. The donor requires a κ improvement. The newly released PR5544 supplied a useful complete caller after earlier screens found no gain.

Research started from canonical main 32890bc5de034ab8fc93ac88ead7279a6a416d04, which remains current after the final fetch. Immediate predecessor: PR5544 at e2a6cce2f9db5a2c5f9714f4b9e5292dd3a10581. This PR retains that original commit as a dependency. The successor adds only research/p104-full-frame-contact/; the predecessor package is unchanged. Review only this contribution in the two-commit successor diff. Final head: 18968423711fd902aaee1099979497d55603e1dc.

The canonical claim records the scope changes. The final overlap refresh covered 403 open PRs and 4,828 Discussion records. The exact register/contact search found only this claim. Local package-note coverage was sparse and was supplemented with relevant Git-object reads; no exhaustive novelty claim is made. The existing shared-chart and dual-ADD packages supply the general retiming method. This contribution is the new source contact and its fully charged endpoint.

Validation

CPython 3.12.14, macOS, standard library. Both registered normal and optimized replays passed:

python3 -B scripts/research_package.py --package research/p104-full-frame-contact
python3 -B scripts/research_package.py --package research/p104-full-frame-contact --check-only
python3 -B scripts/check_research_commit.py --package research/p104-full-frame-contact

Expected marker: PASS_P104_CONTACT_COMPLETE_KAPPA_00304117.

Two exact endpoint interpreters check all 552,049 public/owned coefficients. Native checks cover 2,981 distinct paid/helper maps, 208 main adapters, all 1,054 normalizers for 527 helpers, 7,488 caller contacts, and every main/idle target phase. Two rational moment engines, completion tails, compiler threshold N=2^337848000000000, ordinary BIT stock, and all 54 strict plus four functional outer predicates pass. The shared signed-invoice comparator reports uniformly_better.

Controls reject a one-sided move, wrong sign, intervening source read, omitted paid charge, missing central translation, native phase error, old cutoff and insufficient BIT stock. The read-only, Git-free optimized export replay passed in 73 seconds with all 34 exported files unchanged. A changed-source control failed before imports. Committed bytes, metadata/pins and export integrity passed at the final head. Scientific code, receipts and inputs are byte-identical to the tested scientific commit bea205d91409506c794ababd81454ca42450d5d2; only proof and validation prose changed afterward.

The optional full-history preflight could not run because the checkout is shallow. Direct base/predecessor ancestry and all source-byte checks passed. See validation and source pins. Hosted CI is separate from these local results.

Credit

Ali Romman's PR5544 supplies the productive caller, source interpreters and pricing engine. Gareth Davidson (@bitplane), PR2305, composes David Arias's (@DavidAriasC) PR2152 and Cinna Davis's (@1337isnot1337) PR2219. The shared-chart and dual-ADD packages retain credit for two-operand transport. Jacob Alan Sussman, Cinna Davis, zxv, Cao Yifan and all earlier geometry, scalar, native, COPY, compiler and analytic authors retain the credit recorded in the predecessor proof and native notices.

New contact, proof and complete endpoint: Ali Romman with substantial OpenAI Codex assistance. No subagents. Apache-2.0.

Open next questions

Independent review should begin with the five-site constructor, its source-read intervals and all-width identity, then replay the native endpoint and complete price. Independent scientific review remains pending. Further scope.

[Clear1nsight]

FINDING / HANDOFF — focused contact audit and a ceiling on repeating only H1+H5→H6 (no new κ)

Research discussion / PR / artifact: This PR is the canonical public handoff. I found no gap in the reviewed five-site replacement or its complete invoice transfer under the inherited chart contract. The new repeated-edit ceiling below is deliberately narrower than P104. My separately written checker and receipts remain LOCAL-ONLY, not an authenticated public replay package; the numerical checks are provisional local evidence, while the model and analytic argument are stated here for inspection. No construction scope is reserved.

Exact commit: Reviewed 18968423711fd902aaee1099979497d55603e1dc, predecessor e2a6cce2f9db5a2c5f9714f4b9e5292dd3a10581, canonical main 32890bc5de034ab8fc93ac88ead7279a6a416d04. The captured predecessor input bytes used here match SOURCES.json. Predecessor WORD compressed SHA256: e5e955d7c9d5ea5dfea49c0e093037df577aa43813dcad5427ebca41a4ad35ec. No frozen predecessor was changed.

What is established:

• A separate interpreter checked the actual source/destination read windows, the five edited sites, strict nested frames and common scalar charts, owned INIT/COPY/CLEAR, all743 normalized endpoint rows (552,049 coefficients including zeros), and unchanged527 helper targets. Independent emission matches the complete successor WORD as decompressed JSON. The complete scalar/owned chronology is unchanged.
• Recounting18 full occurrences,15 query sites,15 idles and32 main banks reproduces both complete invoices and delta {-18 H1,-18 H5,+18 H6}, with zero target delta. Under the chart premise, the common-transport ADD/SCALE identity supplies the all-width algebraic implication, with coefficients outside tensor powers. It is a real recursive improvement.
• The reported raw crossing is independently bracketed, and the integer compiler threshold/grid-predecessor arithmetic checks. This is not full compiler or parent admission.

Scoped ceiling. Freeze this PR's targets and all other work; allow ONLY further H1+H5→H6 edits. Optimistically grant every remaining H5 a legal independent contact with no added work. There are107 per local word, hence1926 globally. At supplier C=.0033, H_r=r^(1−C):

Raw necessary screen	Moment, approximately
Current complete invoice	−64.234980048987475
One additional global edit's gain	+.008886830489500512
All1926 optimistic edits	−47.118944526209489

The deficit requires at least7229 global edits, or402 identical contact families repeated18 times; the inventory permits at most107. The all-edits relaxed raw crossing is in (.003106074473,.003106074474). Thus this fixed edit family cannot fund .0033; this is not a ceiling on P104, different retimings, changed targets or callers.

For a larger-C exclusion rather than a single failed test, put t=1−C and divide the all-edits moment by6^t. The signed coefficients at ranks1..9 become
(-43338,-10026,-7002,-1098,+648,-2232,+198,+2196,+5274).
Only the positive rank-five term has an adverse derivative below6. On0≤t≤1, the positive rank-one derivative is at least (43338/6)log6>7223; the adverse rank-five magnitude is at most 648log(6/5)<648/5. Other low terms increase. The retained high terms are416 copies of the normalized rank-r/r+1 differences for r=16,24,…,64,208 copies at r=72, and208 positive rank145 terms; all increase. The normalized moment is strictly increasing, with rank surplus760 at C=0 and count deficit−55172 at C=1. Its crossing is unique, and smaller numbers of edits have still smaller moments.

As a breadth control, discarding chronology and regrouping the fixed5894 local rank units into children1..9 minimizes concave paid cost at654H9+H8. With unchanged targets/nonlocal work, that unconstructed relaxation has raw moment about +470.055147407096 at C=.0033. It is not an available budget or a physical witness. It cautions against treating the narrow ceiling as a reason to retire broader P104 paid-path work.

What remains uncertain: I did not rebuild the archived PR2305 source generator or freshly rerun actual native/absolute-phase lowering, the265-axis physical caller, the full precision/tape contract or all58 compiler/outer obligations. The five framework assumptions remain. Hosted CI passed separately; no independent human/proof-kernel acceptance, selected promotion or new κ follows from this focused audit.

Smallest useful next task: independently check one actual native/caller/funding layer of the complete P104 interface, or propose one explicitly different chronological paid-path change with a complete feasibility budget. Check live claims first. Repeating only the frozen H5 edit cannot reach .0033. Our reassessment stopped after this result; no broader scan or full replay was launched.

Reproduction command and expected runtime: At this PR head the public registered reproduction remains python3 -B scripts/research_package.py --package research/p104-full-frame-contact; I did not rerun that full suite. My local focused checker ran normal/-O under a shared serial guard in8.854s, sampled peak64.38MiB, cap150s/512MiB, with complete output equality and no exclusions. Controls reject one-sided transport, wrong sign and an intervening source read. To reproduce the new ceiling, take complete_cost.paid/targets from this PR's RESULT.json, subtract1926 from paid ranks1 and5, add1926 to paid rank6, and enclose the resulting moment with the declared rational engine. The local result SHA256 is 3c4d8db5a9695924027f5801901b55cefe0cdc5ea07450aaf396de7e5887e608; reused interval code is not an independently implemented second algorithm.

Predecessor credit: Ali Romman/#5544/#5545; Gareth Davidson/#2305; David Arias/#2152; Cinna Davis/#2219/controller; Jacob Alan Sussman, zxv, Cao Yifan and shared-chart/dual-ADD/native/compiler/outer contributors. Focused audit and scoped ceiling prepared by Chris R/Clear1nsight with substantial OpenAI Codex assistance. Apache-2.0.

{
  "schema": "integer-mult-coordination/v1",
  "kind": "HANDOFF",
  "task": "scalar-to-moment",
  "scope": "Independent focused PR5545 contact/invoice audit and optimistic frozen-target H1+H5-to-H6 repetition ceiling; no new kappa; checker local-only",
  "base": "32890bc5de034ab8fc93ac88ead7279a6a416d04",
  "expiry": null,
  "artifact": "https://github.com/CrocSwap/integer-mult-bounds/pull/5545"
}

[Clear1nsight]

Public replay update: the previously local focused audit and scoped retiming ceiling are now inspectable in #5548, exact head b038f9d9b5cf0ce92184da909e57a3be476fc812.

The package also adds a separate dense exact interpreter checking every column of the three actual rank-1/5/6 lowered transports and the old/direct route composition, including absolute phase. The conditional positive-width replacement implication, full target retention and -18H1-18H5+18H6 invoice are explicit. Registered normal/-O and read-only Git-free export pass locally; no full parent native/caller/precision/compiler/outer admission or new κ is claimed.

Canonical seven-field handoff and remaining tasks. The complete parent construction and gain retain Ali Romman's and the predecessor authors' credit. This audit is stopped; no new search scope is reserved.

[Clear1nsight]

Public caller-validation follow-up: #5550, exact head 6125c07ae8ba4b8550e2a0a28a2c6be503153059, now makes the previously local 265-axis forward caller/target audit reproducible.

It checks the 7,488 contacts, literal free-Laurent caller, main input/output aliases, helper ownership and positive-query/whole-idle recipes, with the unchanged 69,912-paid / 12,814-productive invoice. Registered normal/-O and read-only Git-free replay passed. The complete-caller raw inverse transpose, untouched paid-native foundation, owned-erasure premise, precision/tape and full compiler/outer admission remain separate. No new κ is claimed.

Canonical seven-field handoff. This follows the contact/native/ceiling audit in #5548, whose package remains unchanged. The completed layer is stopped; no new construction scope is reserved.