Conditional κ = 0.003288299 (+1.285e-6 over #6453): scaled transport fusion

research/p104-scaled-transport-fusion/NOTICE

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+Scaled transport fusion
+Copyright 2026 Ali Romman. Apache-2.0.
+
+New construction and package: Ali Romman, with substantial OpenAI Codex
+assistance. No subagents were used.
+
+The method extends Rohan Arun's PR6399 donor transport merge to intervals
+with a scalar rescaling. His PR6417 supplies the clean mixed composition.
+Erwan L., with the assistance disclosed in PR6453, supplies the third-anchor
+stack used as the exact source. DreamingOfClouds supplies the PR6375 lifts
+and retained native optimizations. Those contributions are not new here.
+
+Ali Romman's earlier contact basis and mixed caller retain their prior credit.
+Cinna Davis, David Arias, Gareth Davidson, Jacob Alan Sussman, zxv, Cao Yifan,
+Douglas Colkitt, and all retained native, helper, BIT, compiler and analytic
+authors keep their credit. Tekalign's package exporter supplies source.tar.
+The complete original notices and source attributions remain unchanged inside
+that archive and its nested source archives.
+
+The exact source is CrocSwap/integer-mult-bounds PR6453,
+b1a3e525793eca35c56324aa7ffd0b714cf606d4.

research/p104-scaled-transport-fusion/PRICING-EDITS.json

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+{
+  "source_sha256": "93791b1596620f8657450896492e697817b854c2bb3984e8ef2b6c87e44ac4c1",
+  "edits": [
+    [
+      "KAPPA = Q('0.003287014')",
+      "KAPPA = Q('0.003288299')"
+    ],
+    [
+      "TESTED = Q('0.003287019')",
+      "TESTED = Q('0.003288304')"
+    ],
+    [
+      "PREVIOUS = Q('0.003286849')",
+      "PREVIOUS = Q('0.003287014')"
+    ],
+    [
+      "(13652, 67132)",
+      "(13652, 67096)"
+    ],
+    [
+      "'kappa_decimal': '0.003287014'",
+      "'kappa_decimal': '0.003288299'"
+    ],
+    [
+      "Clean donor-transport merge plus third group-1091 anchor, unchanged mixed root.",
+      "Two scaled transport fusions with an output basis correction; unchanged mixed root."
+    ]
+  ]
+}

research/p104-scaled-transport-fusion/PROOF.md

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+# Construction and cost
+
+All event indices in this table refer to the zero-based PR6453 source program.
+The fields and frames retain their source labels.
+
+| Field | First move | Export | New carrier injection | Sign change | Second move |
+| --- | --- | --- | --- | --- | --- |
+| 368 | 8352: 243 to 517 | 8398 | before 9101: add field 368 to field 782 at frame 243 | 12879 | 12893: 517 to 127 |
+| 336 | 8393: 240 to 518 | 8402 | before 9048: add field 336 to field 781 at frame 240 | 12923 | 12924: 518 to 127 |
+
+Each first, intermediate and final frame has dimension 4, 8 and 9. Each
+interval contains one export and one `SCALE -1`, with no other write to the
+held field. The constructor checks every event in each interval.
+
+Delete the first move and the export. Keep the field at its first frame.
+Insert the indicated carrier addition. Move the sign change to the held frame,
+then replace the final move by the direct rank-five move to frame 127.
+Both injections precede their sign change. If a scale preceded an injection,
+the constructor would divide the injection coefficient by that scale.
+All original public boundary frames stay fixed.
+
+## Exact output correction
+
+Let `S` be the desired scalar endpoint on all 770 public inputs. It is the
+identity with the 104 main shears. The constructor starts its row calculation
+in the coordinates `y = Sx`. Thus an unchanged source ends at the identity.
+Owned initialization and erasure keep their literal chronological positions.
+
+After both fusions, every output outside frame 127 is exactly its required
+coordinate. The 572 outputs at frame 127 depend only on those same 572 output
+coordinates. Only 28 rows in this block change. Exact rational elimination
+reduces this block to the identity. It emits 569 dyadic scalar gates, all at
+frame 127. Every pivot inverse is dyadic; the full word checker also verifies
+that each scale is a signed power of two and every coefficient is bounded.
+
+This supplies an explicit inverse for the changed block. It does not infer
+invertibility from a modular rank or a numerical residual. A second replay of
+the emitted correction returns every public row to the required endpoint.
+The separate dense reverse checker then verifies all 799 columns, including
+the owned coordinates. The retained explicit zero-cache check still passes
+at the final frame-127 clear of field 782. Other owned erasures retain the
+source's stated framework assumption.
+
+## Native operators and complete price
+
+Every remaining move has nested frames in its declared direction. The native
+checker lowers each distinct map and checks its signed Pauli action and exact
+global phase. It also checks all helper normalizers and 208 main adapters.
+The scalar endpoint proof and these native identities give the same main and
+independent-helper boundary at every positive tensor width under the retained
+native framework assumptions.
+
+Each fusion replaces a paid rank-four and rank-one job by one rank-five job.
+It adds no productive target, owned lifetime or native boundary adapter.
+Its scalar repair is included in the ordinary-work and coefficient bounds.
+For `Hr = r^(1-kappa)` and `0 < kappa < 1`,
+
+```text
+old paid - new paid = 2(H4 + H1 - H5) > 0.
+```
+
+The unchanged mixed caller makes eighteen native calls. Its queries, idles,
+main targets and ordinary normalizers remain charged. The complete signed
+gain is `36(H4 + H1 - H5)`. The target count remains 13,652, the paid count
+falls to 67,096, and rank-mass surplus remains 760.
+
+`pricing.py` differs from the frozen source only by the six declared edits in
+`PRICING-EDITS.json`: the claim, tested saving, comparison claim, paid count and
+two result descriptions. It retains both rational interval engines, the strict
+root enclosure, completion, compiler, precision and outer inequalities.
+The final verifier also prices the unchanged source at the new claim; both
+engines reject it. The source's inherited improvements are therefore separate
+from the new increment.
+
+This is a conditional construction with local verification. It does not remove
+any of the five framework assumptions or establish independent acceptance.

research/p104-scaled-transport-fusion/README.md

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+# Scaled transport fusion
+
+This construction proposes conditional **kappa = 0.003288299**.
+The direct source is [PR6453](https://github.com/CrocSwap/integer-mult-bounds/pull/6453)
+at `b1a3e525793eca35c56324aa7ffd0b714cf606d4`, with claim `0.003287014`.
+The new increment is `0.000001285`, or about **0.03909 percent**.
+The complete receipt is `RESULT.json`; the run record is `VALIDATION.md`.
+The raw crossing is strictly between `0.00328830463392494440038260` and
+`0.00328830463392494440038261`. Both rational engines certify the signs.
+The strict derivative bound makes this the unique crossing for the complete
+fixed invoice below the admitted BIT cap. The claim is less than `5.635e-9`
+below that ceiling. This changes the native word and its paid profile; the
+historical fixed-local packing model does not apply. No ceiling for other
+words or caller choices is claimed.
+
+Two public fields now stay at their rank-four frames until they can move
+directly to the full frame. Each field has one intermediate export and a
+later sign change. An existing owned carrier delivers the export. The sign
+change remains at the held frame. A joint basis correction at the full output
+frame restores all arbitrary inputs. The complete native word is
+`WORD.json.gz`; `SPEC.json` gives the two changed intervals.
+
+The source method in Rohan Arun's [PR6399](https://github.com/CrocSwap/integer-mult-bounds/pull/6399)
+handles a constant held value. This construction also permits an intermediate
+scalar rescaling. It restores the output basis in place, with no new owned
+lifetime. The source word, helper boundary changes and mixed caller are
+predecessor work. Their gains are not counted in the new increment.
+
+Per native call, the paid change is `2H5 - 2H4 - 2H1`. Every productive target
+stays fixed. All eighteen calls are charged, so the complete paid change is
+`36H5 - 36H4 - 36H1`. There are 67,096 paid jobs, 13,652 productive fields and
+rank-mass surplus 760. For every `0 < kappa < 1`, strict concavity gives
+`H4 + H1 > H5`, where `Hr = r^(1-kappa)`.
+
+The program has 18,493 events. It retains all 770 arbitrary public inputs,
+29 owned labels, 45 owned lifetimes and peak owned storage 13. The correction
+uses 569 scalar gates. The local scalar allowance rises from 131,560 to
+137,218; the complete compiler budget includes that increase.
+
+## Reproduction
+
+Use Python 3.12 and the standard library. The package contains every runtime
+dependency in the unchanged source export. The verifier authenticates the
+archive and all 26 source members before an import. `SOURCE.json` binds each
+member to its original Git blob, path and source head. `SOURCES.json` binds
+the retained archive and manifest to their ancestor commit. No network
+or Git command is used by the scientific verifier.
+
+```sh
+python3.12 -B scripts/research_package.py --package research/p104-scaled-transport-fusion
+```
+
+The registered normal and optimized commands rebuild the source and candidate,
+check all 799 scalar columns, native maps with absolute phases, the complete
+mixed caller and its 7,488 physical contacts, both rational prices, compiler
+and outer inequalities. Controls remove or change each new carrier injection,
+change the sign-change frame, remove correction gates and corrupt source bytes.
+The unchanged source fails at the new claim in both price engines.
+
+## Scope and limits
+
+This is a source-bound conditional construction. All five framework assumptions
+remain: `native_all_columns`, `owned_erasure`, `compiler`, `precision_tape` and
+`analytic_recovery`. The large uniform word and rounded multiplier are not
+materialized. Local replay does not establish independent scientific acceptance.
+The selected frontier is unchanged. No global optimum is claimed.
+
+## Open next questions
+
+- Can several held values share a changed carrier path with a larger signed
+  gain? First require an exact response identity and a legal chronological
+  word. A scalar span or favorable partial invoice is insufficient.
+- Can an independent reviewer verify both fused intervals, the joint output
+  correction and the complete price? Start with `PROOF.md`, `SPEC.json` and
+  the normal and optimized replays. The structured questions are in `TASK.json`.
+
+## Credit
+
+New construction and package: Ali Romman, with substantial OpenAI Codex
+assistance; no subagents. Rohan Arun supplied the donor merge and clean mixed
+composition. Erwan L. supplied the third-anchor stack, with the AI assistance
+recorded in its retained notice. DreamingOfClouds supplied shared-carrier lifts
+and earlier native optimizations. The mixed caller, native, helper, BIT,
+compiler and analytic sources retain their authorship. See `NOTICE` and the
+unchanged notices in `source.tar`. Apache-2.0.