Conditional κ = 0.00308189 (+7.6453e-8 raw over #5569)

research/p104-event-contact-step/CLAIM.md

@@ -0,0 +1,23 @@
+CLAIM — compose a further event-level P104 retime with the priced helper-706 handoff.
+
+Base: current canonical main `5e0052ca0aa3036a3afa8b0438927377c8d97d53`, priority revision 7. The exact construction input is [PR #5569](https://github.com/CrocSwap/integer-mult-bounds/pull/5569) at `af9f091ac6f30c6eaacb9c27777bfbe2d0e5ffdf`. I take its open joint-retime/handoff question and the released [free-stop handoff](https://github.com/CrocSwap/integer-mult-bounds/discussions/1166#discussioncomment-19181969).
+
+Question: does one additional legal event-frame change survive helper 706's changed endpoint and improve the complete paid profile beyond the raw .00308181851522-.00308181851523 crossing? Start with the exact event lattice from [PR #5568](https://github.com/CrocSwap/integer-mult-bounds/pull/5568), pinned at `47a347ff70044615e7be6581d275d12f5df38295`, with a 60-second single-worker solve; inspect and simplify any output to a small explicit edit. Event-order changes are a separate bounded fallback. This does not claim the predecessor retime or handoff as new work.
+
+Success requires an exact regenerated word, arbitrary-input forward/transpose and native replay, unchanged or explicitly repriced targets, the full physical caller, all ordinary costs, two rational moment engines and all compiler/outer predicates. A float/solver gain is not a kappa result. Retain the five framework assumptions and the helper-endpoint contract, pending independent scientific acceptance. No selected-frontier update.
+
+Overlap: 320 open PRs and 4,836 Discussion records were scanned with complete remote pagination at 20:03-20:04 UTC. Sparse local coverage is incomplete; the relevant P104 predecessor sources and live handoffs were read directly. The free-stop lead is released; toolkit construction and the existing native/caller audits remain credited and separate. The p19 headline in PR5440 has an explicit unresolved physical/compiler attachment and is not treated as a complete paid-caller baseline.
+
+Expected artifact: one source-pinned package, a short proof of its actual paid delta, complete replay and a focused conditional-kappa PR if the step survives. Ali Romman with substantial OpenAI Codex assistance. Apache-2.0.
+
+```json
+{
+  "schema": "integer-mult-coordination/v1",
+  "kind": "CLAIM",
+  "task": "scalar-to-moment",
+  "scope": "P104 event-frame retime after the PR5569 priced helper-706 handoff; complete paid-profile step",
+  "base": "5e0052ca0aa3036a3afa8b0438927377c8d97d53",
+  "expiry": "2026-10-25T22:05:17.733973+00:00",
+  "artifact": null
+}
+```

research/p104-event-contact-step/LITERAL-CHANGES.diff

@@ -0,0 +1,13 @@
+--- PR5569 pricing.py
++++ pricing.py
+@@ -14,2 +14,2 @@
+-KAPPA, TESTED = Q('.00308181'), Q('.0030818105')
+-PREVIOUS = Q('.00304117')
++KAPPA, TESTED = Q('.00308189'), Q('.0030818905')
++PREVIOUS = Q('.00308181')
+@@ -142 +142 @@
+-    return encode({'kappa':KAPPA,'kappa_decimal':'.00308181','previous_open_pr5545':PREVIOUS,'gain':KAPPA-PREVIOUS,
++    return encode({'kappa':KAPPA,'kappa_decimal':'.00308189','previous_open_pr5569':PREVIOUS,'gain':KAPPA-PREVIOUS,
+@@ -154 +154 @@
+-                                   'tensor_native_growth_bound':'Each rank-r Gaussian has row l1 norm at most 2^(rf); sum of local ranks is 5894.'},
++                                   'tensor_native_growth_bound':f'Each rank-r Gaussian has row l1 norm at most 2^(rf); sum of local ranks is {sum(r*n for r,n in local["paid"].items())}.'},

research/p104-event-contact-step/PROOF.md

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+# One contact changes the complete P104 paid profile
+
+## Source and statement
+
+The input is the exact PR5569 word at
+`af9f091ac6f30c6eaacb9c27777bfbe2d0e5ffdf`. See
+[SOURCES.json](SOURCES.json) for the source bytes and retained PR5545 engine.
+All event numbers below are zero-based source indices.
+
+The construction changes the chart of `ADD 451 += 228` at event 12658.
+It retains every scalar instruction, coefficient and position in the scalar
+sequence. It also retains all 735 public initial and final frames, 527 helper
+targets, eight owned lifetimes and the 104 literal ports.
+
+At each of the 18 forward local calls, the paid change is
+
+```text
+H2 - 2 H3 + H4.
+```
+
+The complete conditional claim is kappa = 0.00308189. This claim uses the
+five inherited framework assumptions and the source helper-endpoint contract.
+It does not change the selected record.
+
+## Exact contact identity
+
+Let O, A, B and C denote the following binary subspaces. Each list is an
+independent basis in the fixed nine-dimensional ambient space.
+
+| Frame | Name | Basis | Dimension |
+| --- | --- | --- | --- |
+| 3 | O | `[]` | 0 |
+| 262 | A | `[11,21,486]` | 3 |
+| 737 | B | `[11,21,33,455]` | 4 |
+| 520 | C | `[1,10,20,32,64,390]` | 6 |
+
+Their spans satisfy O < A < B < C. The replay checks these inclusions on
+the complete binary spans. Chart transport preserves the abstract row.
+Two transports through an intermediate chart compose to the direct transport.
+A common chart change commutes with addition of two rows.
+
+Register 228 stays at A after event 9575. Its next scalar use after the
+changed contact is event 12674 at C. Register 451 stays at O after event
+12591. Its next scalar use after the changed contact is event 14424 at B.
+The constructor checks every intervening register access, including reads.
+
+The old paths are 228: A to C, and 451: O to A to B. They meet at A for
+the addition. The new paths are 228: A to B to C, and 451: O to B. They
+meet at B for the same addition. Thus both abstract rows agree at their
+next unchanged use. Every other row is unchanged. This proves the local
+identity for arbitrary inputs, including arbitrary helper inputs.
+
+The old bill is H3 + H3 + H1. The new bill is H1 + H2 + H4. Their
+difference is H2 - 2 H3 + H4. Paid count and rank mass are unchanged.
+The only newly used ordered native frame pair is (3,737). The exact
+native replay checks this pair and all 2,921 distinct paid/target pairs,
+including their signed Pauli images, absolute phases and ranks.
+
+## Strict concave gain
+
+For 0 < k < 1, x raised to 1-k is strictly concave on positive x. Hence
+
+```text
+2^(1-k) + 4^(1-k) < 2 * 3^(1-k).
+```
+
+Let M(k) be target moment minus paid moment. The new complete moment is
+
+```text
+M_new(k) = M_parent(k) + 18 * (2 * 3^(1-k) - 2^(1-k) - 4^(1-k)).
+```
+
+It is strictly larger throughout that range. This is a change to the paid
+profile. It is not extra numerical precision for the same equation.
+
+The exact rational engines give these crossing intervals:
+
+| Word | Lower endpoint | Upper endpoint |
+| --- | --- | --- |
+| PR5569 | 0.00308181851522 | 0.00308181851523 |
+| This word | 0.00308189496866 | 0.00308189496867 |
+
+The raw gain is strictly between 0.00000007645343 and 0.00000007645345.
+The claimed endpoint is 0.00308189; it is tested at 0.0030818905. Its raw
+headroom is between 0.00000000496866 and 0.00000000496867.
+
+The checker also bounds M_new'(k) with rational intervals on [0,0.0034].
+The derivative lies between -255126 and -237752, so the crossing is unique
+on that band. Its upper endpoint is the raw funding ceiling for this fixed
+invoice under the retained BIT cap. A different word, endpoint contract or
+BIT supplier is outside this ceiling. No global optimum is claimed.
+
+## Complete caller and costs
+
+The unchanged caller has 18 forward local calls, 15 query shears and
+3,120 whole idle jobs. It has 66,852 paid jobs, 12,814 productive fields,
+rank-mass surplus 760, maximum paid rank 72 and maximum target rank 145.
+The verifier derives the invoice from the physical event list and checks it
+again from the two controller path lengths. It prices all helper targets,
+normalizers, main adapters, query shears, idles, routes and owned operations.
+
+There are 25,140 local events and 21,686 scalar/owned events. The scalar
+allowance is 217,428, the route allowance is 5,164,000 and the complete
+nonrecursive bound is 184,647,552, below the retained 1,000,000,000 budget.
+Peak owned occupancy stays one. The sum of local paid ranks is 6,013.
+The source report's old literal 5,894 is replaced by this derived sum in
+the native growth bound. This report correction does not change the
+moment or the claimed gain.
+
+Two exact moment engines check the tested endpoint. The compiler checks
+include all three tail ratios, the completion and splitting terms, the
+integer threshold and the retained BIT stock. All 54 strict and four
+functional outer predicates are positive. The source engine rejects its
+insufficient BIT and old-cutoff controls. The new controls reject a missing
+source transport, a wrong contact frame, a wrong coefficient, a descending
+public return and the unchanged word presented as an improvement.
+
+## Scope
+
+This is an author-checked conditional construction. Finite exact replay
+and the chart identity do not prove the full integer multiplication theorem.
+The native all-column realization, owned erasure, uniform compiler closure,
+precision/fixed-tape execution and analytic recovery remain inherited
+assumptions. The free helper endpoints are inherited from PR5561/PR5569;
+this contact changes none of them. The enormous uniform word and a complete
+rounded multiplier are not materialized. Independent scientific review and
+hosted CI are separate from the local checks.
+
+Ali Romman with substantial OpenAI Codex assistance. Apache-2.0.
+All retained source notices and predecessor credit remain in the package.

research/p104-event-contact-step/README.md

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+# Conditional kappa 0.00308189 from one P104 contact change
+
+This construction increases complete conditional kappa from 0.00308181 in
+[PR #5569](https://github.com/CrocSwap/integer-mult-bounds/pull/5569) to
+**0.00308189**. The raw crossing increases by between 7.645343e-8 and
+7.645345e-8. The selected record remains 0.003027288235.
+
+One ADD contact moves from a three-dimensional chart to a four-dimensional
+chart. Each of the 18 local calls replaces two rank-three paid jobs with
+one rank-two and one rank-four job. Strict concavity proves a positive
+signed-moment change for every 0 < kappa < 1. Every public endpoint,
+productive target, scalar instruction and owned lifetime stays fixed.
+
+Read [the proof](PROOF.md), [the four-site construction](construct.py),
+[the complete receipt](RESULT.json), [the source pins](SOURCES.json) and
+[the verification record](VALIDATION.md). The complete bill retains
+66,852 paid jobs and 12,814 productive fields. The exact raw crossing is
+in (0.00308189496866, 0.00308189496867). The claim is tested at
+0.0030818905, below that crossing.
+
+This is a small paid-profile step after the priced helper-706 handoff.
+It composes with that handoff and retains the source's free helper endpoints.
+It is not a new controller or a new selected frontier. No independent human
+review or complete proof-kernel verification is claimed.
+
+## Reproduction
+
+Python 3.12 and the standard library suffice. No optimization solver is
+needed to reconstruct or verify the published word.
+
+```sh
+python3.12 -B scripts/research_package.py --package research/p104-event-contact-step
+```
+
+Both registered modes must print:
+
+```text
+PASS_P104_EVENT_CONTACT_KAPPA_00308189
+```
+
+The launcher must print `PASS_REGISTERED_RESEARCH_PACKAGE`. It runs exact
+source reconstruction, both arbitrary-input endpoints, dense transpose
+columns, all signed native maps, the physical caller, two moment engines,
+the compiler and all 58 outer predicates. It compares the complete result
+with the committed receipt and runs the negative controls.
+
+The PR5545 official source export is retained unchanged as an executable
+dependency. The verifier checks its archive hash, inventory and 33 payload
+files before import. It also checks the PR5569 word and price source against
+their Git blob IDs and SHA256 values. These files are retained sources,
+not new contributions. Compressed word regeneration is compared by its
+complete decompressed payload.
+
+The price implementation retains the source's mathematical tests. Its
+[diff](LITERAL-CHANGES.diff) changes the claim/comparison declarations and
+derives the actual local rank sum in the reported native growth bound.
+The latter corrects the old literal 5,894 to 6,013; it is not the source of
+the kappa gain.
+
+## Limits and ceiling
+
+The five framework assumptions remain: native all-column implementation,
+owned erasure, uniform compiler closure, precision and fixed-tape costs,
+and analytic recovery. Independent acceptance of the source helper-endpoint
+contract also remains inherited. The new change preserves those endpoints.
+The uniform word and complete rounded multiplier are not materialized.
+
+On [0,0.0034], the fixed invoice has a strictly decreasing signed moment.
+Its raw funding ceiling is the crossing interval above. The headroom above
+the claimed endpoint is between 4.96866e-9 and 4.96867e-9. This is not a
+ceiling for other words or suppliers.
+
+The p19 proposals have larger numerical headlines. In particular,
+[PR #5440](https://github.com/CrocSwap/integer-mult-bounds/pull/5440) records
+an unresolved chain-to-native compiler and physical attachment. This package
+improves the complete P104 paid-caller line; it does not claim to exceed that
+proposal's extra-premise numerical model.
+
+## Coordination and credit
+
+Base: current canonical main `5e0052ca0aa3036a3afa8b0438927377c8d97d53`.
+The [canonical claim](https://github.com/CrocSwap/integer-mult-bounds/discussions/5574)
+records the changed scope, initial overlap coverage and test.
+[TASK.json](TASK.json) retains the revision-7 card. The released
+[event-placement handoff](https://github.com/CrocSwap/integer-mult-bounds/discussions/1166#discussioncomment-19181969)
+supplied the research lead. The event-level model in
+[PR #5568](https://github.com/CrocSwap/integer-mult-bounds/pull/5568) by
+@DreamingOfClouds informed discovery. The submitted edit was then isolated
+by a direct single-contact scan and is reconstructed without that solver.
+
+- Joel Pulikkan, @GamingPuzzled, supplied the exact PR5569 word and priced
+  helper-706 handoff, building on his successor-handoff work in
+  [PR #5472](https://github.com/CrocSwap/integer-mult-bounds/pull/5472).
+- @DreamingOfClouds supplied the free-endpoint word in
+  [PR #5561](https://github.com/CrocSwap/integer-mult-bounds/pull/5561)
+  and the event-level toolkit and released handoff.
+- @thu-nmrc supplied the coupled contacts in
+  [PR #5551](https://github.com/CrocSwap/integer-mult-bounds/pull/5551).
+- Ali Romman supplied the complete caller and source closure in
+  [PR #5544](https://github.com/CrocSwap/integer-mult-bounds/pull/5544) and
+  [PR #5545](https://github.com/CrocSwap/integer-mult-bounds/pull/5545).
+- The retained source notices credit Gareth Davidson, David Arias and
+  Cinna Davis for the P104 word, coalescing and private reuse; Cinna Davis
+  for the controller; Jacob Alan Sussman for productive recursion; zxv and
+  Cao Yifan for the interval, compiler and native framework. The official
+  source closure preserves the earlier geometry, BIT and analytic notices.
+
+New construction, proof and verification by Ali Romman with substantial
+OpenAI Codex assistance. Apache-2.0. The search, proof and checks were
+performed by the same assistant; they are not independent review.
+
+## Open next questions
+
+Independently review this contact and the inherited helper-endpoint contract,
+then recompute the complete invoice from the word. A later construction
+must change a paid itinerary or a target contract. Another root digit does
+not change this invoice. No wider optimality or native-admission claim
+follows from the bounded contact search. Structured questions are in
+[TASK.json](TASK.json).