[petalas]

Summary

 Sharp pooled T16 integer inventories on selected1094 supplied windows
- temporal assignments relax distinct physical families within a call
+ both inventories have complete distinct-family, active-pair-safe assignments

The new per-pattern flow constraint and bipartite multigraph colouring reconstruct both 69,120-helper maps. Combining this attainment with the separately replayed PR3378 pooled lower bound proves the exact finite-hosting idle-cost envelope for every real 0<=a<=1/2, with p=1-a:

min(2431+17^p,2429+5^p+14^p)+4887*48^p.

Only research/t16-distinct-call-attainment/ is added. The model takes selected1094's supplied windows as hypotheses. Complete chart/native/controller/stock admission and independent program-derived windows remain separate. No supplier, new kappa or selected-frontier change is claimed.

Evidence

• Before: PR3395's old/new relaxed flows place up to 331/296 helpers of one call in 224 physical bins. After: both new assignments satisfy every actual helper width, call/window, disjoint prefix reservation, distinct physical family and active-pair check. The inherited source-bound audit_roles separately accepts both exported original-schema maps, with 480 distinct families per call.
• Exact CPython 3.12.15 registered replay, code-disjoint sufficient-degree audit, six behavioral groups, 120 tiny pattern systems, 86 exhaustive regular-multigraph matching oracles and optimized actual-CLI source/certificate controls pass. Ruff diagnostics and formatting pass.
• Exact committed PR3378 export separately returns PASS_T16_INTEGER_PHASE 56987, with 6850 concavity, 330 Bernstein and one symbolic comparison types. Its proof is an explicit external dependency with exact public source pins and replay commands, rather than a hidden pending-Git dependency of the new verifier.
• Publication-byte/source-history preflight and six normal/optimized commands on the Git-free committed export pass with all 15 files unchanged, including the transport manifest. Replay: python3 -B scripts/research_package.py --package research/t16-distinct-call-attainment.

Credit Ali Romman/PR1129, Hanson Sun/PR1914, PR3352/3364/3378/3395, Rohan Arun, Jeremy Kothe, Hao Yan/FanPUYen, Philippe Van Velzen and the retained owner/compiler/bit/geometry lineage. PR3390's physical augmentations and PR3396's transport cut remain complementary. Proof, machine certificate, literal-map export command, source pins, rejection controls and open next questions are included.

Canonical investigation: #1885 (comment)

Merge Danger

Door: two-way

One isolated proof/certificate package. Frozen predecessors, shared checkers and selected results are unchanged.

Blast Radius: research

This proves a supplied-window finite optimum. It does not price charts/native adapters/controller storage, certify the full multiplication theorem, or claim hosted CI or independent human review. The next useful test is complete physical admission of one exported nomination, stopping at its first failing budget.