[unpaidmoon]

Change and mathematical scope

Partial certificate. No new κ. The selected conditional result stays 60403/20000000 (0.00302015, #4470).

On the pinned SOURCE87 rank-2 entry, the parent packet is exactly M = 9475 * 3^124 copies of the executed 972-bit fibre. The published extent triple (2, 3 * 3^124, 2) holds for the call (first, second, width) = (0, 126, 2) at parent size 64 and atom size 3 exactly when the plan dimension is 64, and at no smaller positive dimension through 64. Both carrier arms use this same M, so a leaf scan that charges one common per-fibre vector has C-minus-D difference zero on this entry.

The compiler profile still changes by {1: +288, 2: -576, 3: +288}. Gather, routing, parking, and blank-return between the fibres are not priced. The reverse coefficient is not rederived. This is not a supplier admission.

Task and overlap

• Task: r437-carrier-integration, scope refined.
• Base: canonical main ff3cc58e370d0f678e529246f8c73e8094e18fcf, priority revision 7. Head e27d312d693590989f8a89c26b5deb44848bdfd3.
• Ordered eligible list, the priority table in docs/research/current-priorities.md, then catalogue tasks that are not already in that table. A row stays while its stated next decision is still open:
  1. uniform-transfer-audit
  2. supplier-boundary-audit
  3. joint-query-controller
  4. This package. r437-carrier-integration
  5. p104-side-correction
  6. independent-moment
  7. formal-interface-lemma
  8. bit-helper-contract
  9. bit-new-register-model
  10. complex-rank-shape-decoder
• Construct a two-window R437 carrier exchange with a strictly better paid profile #4067 is the paid exchange. Derive the reverse row coefficient of the two-window R437 carrier. #4147 is the reverse coefficient and is not recomputed. Integrate the R437 carrier compiler, numerical invoice and paid local caller #4176 checks the extent triple on one execution and leaves the full spectator bill open. This package names M, classifies the dimension, and separates this entry's zero leaf-scan difference from the nonzero profile delta.
• Price the R437 child-constructor tapes inside Pi_v. #4160 prices a different constructor tape.

Validation

Python 3.12, standard library only, from the repository root:

python3 -B scripts/research_package.py --package research/r437-source87-fibre-multiplicity --check-only
python3 -B scripts/research_package.py --package research/r437-source87-fibre-multiplicity

Both passed. verify.py prints PASS_R437_SOURCE87_FIBRE_MULTIPLICITY. The optimized (-O) run printed the same marker. Controls reject every plan dimension from 1 through 63, atom size 9, and a gap counted twice.

Not run: the integration's physical.py replay, Lean, Docker, the selected cold replay, and check_research_commit.py --check-source-history (this checkout is shallow). The dimension statement is the finite check together with the closed form in PROOF.md.

Credit

Chris R / Clear1nsight, PR #4067 and PR #4176, for the carrier, the compiler receipt, and the extent assertion. The reverse coefficient remains unpaidmoon's PR #4147. The layout and plan sources are the retained selected-bit caller.

Prepared by unpaidmoon with substantial Cursor Grok assistance. Apache-2.0.

Open next questions

1. Price the fixed-tape gather, routing, parking, and blank-return that separate these M fibres. That bill is what the integration still names as blocking a global paid improvement. Start with one spectator step on the pinned layout. Blocked here because no tape machine for the 3^124 gap is executed.
2. Apply the same extent map to one request in the profile delta. SOURCE87 does not account for the 288 extra rank-1 requests or the 576 missing rank-2 requests. Blocked because the compiler receipt does not list those plan coordinates.