Certify the changed-history boundary of P104's lifetime screen

[petalas]

Summary

Certify a changed-history boundary of #2924, not an error in its explicitly two-history result.

 C = (1,7,1)
 U = (1,1,1,1,1,1,1,1,1)
+M = (1,1,2,1,1,1,1,1)

Adding M preserves nine rank units per lifetime and the checked endpoint signatures. Eleven replacements make the 423-lifetime profile pass the selected-saving optimistic moment. The first rejecting floor becomes 436 within this three-history endpoint/cut/ideal-idle relaxation. Neither threshold is an all-P104 barrier.

Adds only research/p104-three-history-threshold/: proof, exact receipt, independently implemented binomial checker, source pins and bounded replay. Canonical claim.

Evidence

• Before: reproduce Re-price PR2920's two-history P104 profile under reported lifetime floors (no new kappa) #2924's exact rational enclosure for (C,U,M)=(232,191,0), moment approximately 1.000003548402828.
  After: (232,180,11) gives approximately 0.999999737314690. Ten replacements still reject; all 192 fixed-count profiles satisfy the seven cuts and separate endpoint constraints.
• Certify unique three-history optima at floors 423,435,436. A separate positive-binomial implementation checks signs without the retained logarithm engine. Tests independently check the endpoint curve by DP and optimize including nonminimal cheap counts.
• Registered CPython 3.12.15 replay, 10 behavioral test groups, Python 3.13.5 checks, lint, warning-as-error compilation and committed-byte preflight pass locally. The 144-test research-workflow suite passes with five skips. Hosted CI is not claimed.

python3.12 -B scripts/research_package.py --package research/p104-three-history-threshold

Scientific base main 914cd73f563acaaa682d733a9fbfcc07272336a3, priority revision 5; refreshed main f3894fbf0ad3012ff294e1673fdbb3e1c4a92225 has unchanged guidance and live inputs. #2924 is pinned at d1660ed0a17b66ad0c86cd4aaea724926134e362; #2920 at b9ea9def949f9d71d59e21294d0e6cfbe0692a73.

Credit Sudarsh Chaturvedi/#2924, Nick Petalas/#2920/#2909/#2896, Arham Tahir/#2675/#2682, Hiroki Kumazaki/#2889/#2353, ywz65/#2614, Sagar Thakrar's mixer handoff, Philippe Van Velzen, Douglas Colkitt's interval engine and the retained P104 geometry/native lineage. Exact predecessor evidence is retained unchanged.

Merge Danger

Door: two-way. One new opt-in package; frozen sources and the selected frontier remain unchanged.

Blast Radius: scoped. Endpoint geometry and cut implications are inherited, not independently rederived here. No compatible joint flags, acquisition program, dirty restoration, native lowering, complete physical/consumer bill, supplier or new kappa is established. The missing dimension-three contact may block acquisition. Next useful work is one actual joint endpoint/dependency assignment, not further numeric threshold refinement. This audit ends without construction expansion; no independent human or proof-assistant review is claimed.