Re-price PR2920's two-history P104 profile under reported lifetime floors (no new kappa)

[Sudarsh3301]

Summary

Audit pending PR #2920's two-history P104 price against the lifetime floors reported in the same X-only monotone model.

#2920 (head b9ea9def) finds the unique cheapest profile (cheap, unit) = (0, 208), with selected moment ≈ 0.998896 and relaxed root ≈ 0.0021042. Its search enforces #2909's endpoint curve and C+U <= 482, but no lifetime floor above the merged 208. Sagar Thakrar's mixer handoff (2245 comment 18960667, fork 743640530) reports written floors of 216 (grammar G′), 219 (shear-only G) and 234 (final-frame words). Each excludes 208 lifetimes.

floor L   cheapest (C,U)   selected moment   relaxed root
  208        (0,208)        0.9988962439     0.0021041528   #2920 control
  216        (8,208)        0.9989395970     0.0020832186   applies to #2920's model
  219       (12,207)        0.9989524538     0.0020770912   shear-only grammar
  234       (28,206)        0.9990303403     0.0020407230   final-frame words
  387      (194,193)        0.9998152606     0.0017346178   unproved relay estimate
first rejecting floor: 423 lifetimes   (232,191), moment 1.0000035

The #2920 decision stands: the restricted route still passes the optimistic screen under every reported floor. But (0, 208) is infeasible under them, and the root falls about 1% under the applicable 216 floor. A future floor rejects this two-type relaxation only at 423 lifetimes or more.

Adds only research/p104-two-history-lifetime-floor/. Credit Nick Petalas/#2920/#2909/#2896, Sagar Thakrar (floors and mixer handoff), Hiroki Kumazaki/#2353/#2889, Philippe Van Velzen, Arham Tahir/#2675/#2682, ywz65/#2614, Douglas Colkitt (ceiling.py) and the retained P104 lineage. Claim.

Evidence

• Same model, template and certified ceiling.relax engine as Certify P104 separate endpoint geometry and two-history budget #2920. The recomputed endpoint curve equals Certify P104 separate endpoint geometry and two-history budget #2920's RESULT.json in both orientations; the (0, 208) moment is byte-identical to Certify P104 separate endpoint geometry and two-history budget #2920's receipt.
• The moment is affine in (C, U). Three relax enclosures give exact-interval coefficients; each optimizer is certified unique over all feasible minimal-cheap pairs (U = 0..482) and re-evaluated directly with relax. Root brackets on a certified 1e-12 grid; the 422/423 threshold by certified bisection.
• Six controls: no floor returns (0, 208); a changed endpoint capacity at equal total demand fails the Certify P104 separate endpoint geometry and two-history budget #2920 curve binding; a wrong affine coefficient fails the direct re-evaluation; 422 passes and 423 rejects; an altered receipt fails; a changed pinned ceiling.py fails before use.
• Registered CPython 3.12 replay, metadata check and 144 research-workflow tests (5 skips) pass locally. A separate review agent found no soundness error; its applicability point was resolved by reading the fork commit (G′ contains Audit P104 relay floor with an explicit monotone-lifetime model #2353's copies and clears; its proof uses no restoration or cut order).

git fetch --no-tags https://github.com/CrocSwap/integer-mult-bounds.git pull/2920/head
python3.12 -B scripts/research_package.py --package research/p104-two-history-lifetime-floor

Base: canonical main 3bee87dc2, priority revision 5. Live overlap was checked at 11:28 UTC with gh (open/merged PRs and the #2245, #1166 threads); #2920 had no comments or reviews.

Merge Danger

Door: two-way. One new opt-in package; predecessors, frozen inputs and the selected frontier are unchanged.

Blast Radius: scoped. The 216/219/234 floors are imported as reported (author-checked, unmerged fork), not re-proved; the 219 row is conditional on shear-only mixing. Everything else is #2920's relaxation: two named histories, separate endpoints and favorable fractional idle. No construction, new floor, supplier, kappa or human review is claimed.

Prepared by Sudarsh Chaturvedi with substantial Anthropic Claude assistance.

🤖 Generated with Claude Code