[petalas]

Summary

PR2458 forward + PR2712 dual
  -> independent transport/progress recount
  -> p=1 mass test; p=2..7 rational bounds; p>=8 affine proof
  -> no competitive moment for any pair count in this coverage model

Extends Jose Manuel's four-pair screen to every integer p>=1, with the actual width m=16p+9, W=208p, p+1 forward calls and p dual calls. Even forgiving 416 rank units per dual, supplying the other 102 corrections free, allowing full-width idle children and adding any finite number of fully paid banks cannot meet the selected saving.

Only research/p104-all-pair-consumer-budget/ is added. It contains the scoped proof, exact receipt, source pins, retained predecessor notices, standalone checker, tests and opt-in replay hook. Proof and assumptions. Canonical claim.

Credit Jose Manuel/jmbarrancoml for the p=4 calculation and rank-discount argument; ywz65 for #2458/#2712 and the physical-dual lineage; commdata2338 for #2662; Nick Petalas for #2550; Ross Richardson for #2445. Full native-channel, geometry and template credit remains in the package. #2729's local fusion allowance and #2675's monotone-history relaxation concern different questions.

Evidence

• Before, the cited screen covered four pairs. After, exact rational bounds cover six finite base cases and the infinite tail, plus the separately clamped one-pair/bank boundary.
• CPython 3.12.15 registered replay passes on Linux/WSL2:

  python3 scripts/research_package.py --package research/p104-all-pair-consumer-budget

• All 11 package tests pass, including an independent set-span census of all 3,584 transports, source/receipt corruption, typed JSON, optimized Git-free replay and gzip recompression. CPython 3.13.5 optimized replay also passes.
• All 70 research-workflow tests pass with two skips; Ruff E,F,I,UP,B and staged whitespace checks pass.
• Scientific base 0374b3e6a532dac112813523d605288c416418c1, priority revision 5. Refreshed main 7b39515117fe26e75d16c268877391f1bdaa5640 has unchanged guidance, selected record, runner and live inputs. Both dependency heads are unchanged. Final overlap covered 751 open PRs and 1,368 Discussion records with complete pagination, followed by targeted thread reads; it is a metadata search, not proof of novelty.

Merge Danger

Door: two-way. One isolated research package and bounded opt-in replay.

Blast Radius: research.

The result assumes the explicitly stated one-unpaid-coordinate coverage law and endpoint-progress limit. Changed profiles, call multiplicities, paid-work sharing or consumer coverage are outside it. Native correctness remains inherited; physical hosting, precision/tape, all-size admission and a complete multiplication theorem are not verified. No selected-frontier or kappa change, independent human review, formal-kernel proof or hosted-CI success is claimed.

Next useful work needs a changed complete profile or a justified replacement consumer/coverage law, not another pair count or idle repacking of these exact words.