Certify PR2339's whole-helper T74 packing cap below 0.0016870

[jeremydiviney]

PR2339's low-alias construction saves local rank mass but changes the helper widths. Its favorable rank-48 cap and calibrated refill models do not enforce the actual T74 bin inventory. This package certifies primitive b < 0.0016870 for either of its two pinned 400-helper words, or any mixture across 666 calls, with unsplit helpers and the unchanged PR2269 bin stock. It is a scoped cost barrier, not a new κ or a criticism of PR2339's correctly qualified local construction.

The relaxation allows arbitrary fractional counts of integer bin patterns and discards chronology, owner-family and physical-port coupling restrictions. An exact rational dual checks all 1,163 patterns and forces the recurrence moment above 1 by more than 6.4e-8 at b = 1687/1000000. Therefore no integral owner reassignment with this same inventory can beat that cap. A changed local contract, partial alias subset, split reservation or different parent stock remains open.

Added only research/t74-low-alias-width-cap/: pinned source words and parent plan, an independent explicit-subspace frame invoice, the nine rational dual coefficients, a directed exact certificate, proof, meaningful controls and a registered standalone replay. No optimizer or network is used during verification. The attained PR2269 profile passes the positive control at the same threshold. No selected pointer or predecessor package changes.

Validation on Linux CPython 3.12.3: registered package metadata and both commands pass; eight mathematical mutations reject under -O; read-only source export, input/receipt tampering and no-clobber checks pass. A fresh archive of committed head 16d4ea6c passes both commands, with all five immutable source byte hashes preserved, including original CRLFs. The exact verification takes under one second locally; CI is not claimed in advance.

Credit: Sagar Thakrar/PR2339 for the 400-helper words; Cinna Davis/PR2226 for anticipatory borrowing; Jeremy Kothe/PR2269 and Rohan Arun's T74 lineage for the parent; Vlado Vojdanovski/PR2322 for the reference frame accounting and directed moment engine. Ali Romman/PR1129 and the incorporated R480 pattern-dual audit already use this relaxation on an older inventory: the method and 1,163-pattern domain are inherited, the application to PR2339 is new here. Concurrent PR2359 audits different raw words and does not claim this cap. Original notices and Apache-2.0 retained. Prepared by Jeremy Diviney with substantial OpenAI Codex assistance; no independent human review claimed.

Latest observed conditional claim is PR2349 at 0.001697065994108880. Canonical main remains 0fdd7d82; live PR/Discussion overlap coverage and scope are recorded in TASK.json. The next constructive target is a narrower lender contract or a changed parent capacity inventory, screened with whole-width costs before native/global replay.

[thakrarsagar]

Independent cross-check from #2387. Your DUAL.json (head 16d4ea6) was re-checked with a separate 1,163-pattern enumeration and 800-bit enclosures. All inequalities hold, and the lower bound of 66304·mu is 66304.0043 under your all-extra envelope (66304.068 with the actual 249/417 dispatch). A dual tampered past its minimum slack is rejected.

#2387 also builds the attainable side. A legal 266,400-role fill of the same words reaches b = 0.00168654324, which is 99.994% of the LP ceiling (certified b < 0.0016867 with the real dispatch). So the cap is essentially tight. Thanks for the clear writeup; it is credited there.