Certify P104 separate endpoint geometry and two-history budget

[petalas]

Summary

Close PR #2909's separate-endpoint geometric coverage and pricing handoff for the two named P104 helper histories.

odd affine residual set
  -> ker(f), ker(f+q) partition every endpoint's demands
  -> endpoint-count curve is attained by actual subspace unions
  -> cheapest two-type multiplicities: 0 cheap + 208 unit-step

The optimistic transport/ideal-idle moment is about 0.9988962438816702 at the selected complex saving. Its exact relaxed root lies between 0.002104152801941 and 0.002104152801942. The screen therefore keeps this restricted route open.

Adds only research/p104-endpoint-geometric-budget/, with the written affine-complement and price-dominance proofs, original-input reconstruction, exact receipt, source pins, controls and registered replay. Credit Nick Petalas/#2909/#2896, Hiroki Kumazaki/#2889/#2353, Arham Tahir/#2675/#2682, ywz65/#2614, Philippe Van Velzen, Sagar Thakrar and the retained geometry/native lineage. Full scope, assistance disclosure and predecessor pins are in TASK.json and README.

Canonical claim and handoff. Publication commit: b9ea9def949f9d71d59e21294d0e6cfbe0692a73.

Evidence

• Before: Reject the P104 253/147 profile by endpoint demand saturation #2909 gives sharp separate endpoint counts but leaves actual subspace unions and replacement-profile pricing open. After: all 208 endpoints have explicit complementary covers, and a symbolic inequality proves the unique cheapest two-type multiplicities for every positive saving.
• Exhaustive restricted-hyperplane pair enumeration agrees on every one/two-plane optimum. Exact rational intervals verify the selected moment and strict root signs; 23 feasible minimal count profiles provide a finite price cross-check.
• Registered CPython 3.12.15 replay and four behavioral groups pass, including missing-affine-hypothesis rejection, optimized Git-free replay, source-before-import corruption and typed receipt corruption. Optimized CPython 3.14.8 replay, Ruff 0.17.1, warning-as-error compilation and committed-byte checks pass.
• Two scoped internal audits found no actionable defect. The pair oracle shares reconstructed inputs, and interval arithmetic is inherited; no independent human or formal-kernel review is claimed.

python3.12 -B scripts/research_package.py --package research/p104-endpoint-geometric-budget

Started from canonical main 5a0dc2c0f; refreshed d98c98262 has unchanged relevant guidance, inputs, selected record and package runner. Final overlap has complete pagination for 496 open PRs, 2,117 closed PRs and 1,593 Discussion records, without warnings. Arbitrary diffs and unpublished work remain outside coverage. Hosted CI is separate from these local checks.

Merge Danger

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

Blast Radius: scoped. Attainment is for each endpoint independently. Flags do not establish joint source acquisition, coefficients, chronology or dirty restoration. The optimum covers only the two named histories, not all 256 histories. Native execution, ownership/routing, precision, all-size admission and the complete consumer bill remain open. No supplier, new kappa or full multiplication theorem is claimed.