Conditional bound: four aliases + 24 entrance raises give κ = 0.001699160892139825

[tekuuu]

This conditional construction composes our four lifted-target aliases with Jeremy Kothe’s PR2435 entrance-frame improvement, then makes six explicit owner-slot replacements per call. The resulting κ is 0.0016991608921398251600279999999999999999999998999999999999999999999999, approximately 6.4954844219583e-7 (0.03824%) above pinned PR2435. This is a modest gain; it does not reach κ > 0.01.

Base: 7ee02b7c96d85f22b38d28bd7ed49bb8c1aeb261; OS assignment seed39, complex supplier. PR2435 source: 324d7d3590dc21003940a44cb0cbdc32b3620f25. The earlier verified FOUR428 snapshot remains intact and independently reviewable. The new package is research/complex-structure-seed39/nonzero-lender-evidence/composition2435/.

The complete construction has428 helpers,652 arbitrary local input columns,666 calls,285048 explicit owner roles and66818 physical fields, including all76 private cleanup buffers. It prices every local frame change, COPY split, source restoration, warp, helper embedding, padding child and physical CLEAR. Prefix1442<2048 and row19545<20161. Reusing the old owner packing failed the cost screen; the submitted construction uses an actual checked owner assignment.

Verification passed:

• All15 fresh changed-word native stages, both orientations, exact phases, residual wrappers, arbitrary-column replay and Lemma G.
• Complete owner geometry with9 rejecting controls; strict global admission with21controller,6buffer,114assembly,12bit,8independent-owner,5interface and6geometry controls.
• Modern outer transfer:63 strict inequalities,17 rejecting controls,19 retained evidence replays; an independent checker rederives nine cost terms and exact κ.
• The one-command global/outer replay passed from a clean temporary-index export, using explicitly hash-bound complete native evidence. An exported independent outer check also passed.

Reproduce from repository root (Python with NumPy and SymPy1.14):

python3 -B research/complex-structure-seed39/nonzero-lender-evidence/composition2435/verify_global.py --out /fresh/absolute/output

Expected: PASS_COMPOSED_FOUR428_ENTRANCE24_CONDITIONAL_BOUND. Native regeneration is available separately via that package’s replay_native.py; receipt reuse is not described as fresh native compilation.

The required broad make verify was run once and failed in historical frontier741/bit589 at a bytewise gzip comparison. The generated and pinned files have identical decompressed bytes and parsed JSON. This is recorded as a failed broad suite, separately from the successful focused replays; no baseline test was changed.

PR2442’s fixed-word owner-fill ceiling does not cover this changed word and428-helper inventory. PR2446 independently corroborates PR2435 and explicitly excludes entrance delivery from its own audit; our finite checks cover the rank-two residual adapters and seven-active/two-spectator embeddings. Uniform common-label/mutable-source realization, whole-call hosting, precision/tape, exact recovery and the retained analytic/outer assumptions remain conditional. These finite certificates do not formally prove the full multiplication theorem. No selected frontier or upstream/ file is changed, and no merge is requested.

Prepared for Tekalign (@tekuuu), with substantial OpenAI Codex assistance; Apache-2.0. Credit Jeremy Kothe/PR2435 for the24 entrance raises, call order and source fill; Cinna Davis/PR2226 for anticipatory borrowing; Sagar Thakrar/PR2339 for the low-alias predecessor; Jeremy Kothe/PR2269 and the retained T74/native lineage; Vlado Vojdanovski/PR2322 and the PR2349/PR2363 owner lineage; PR2374 and the retained outer, private-buffer and proof predecessors. Exact notices, source pins, negative controls and scoped concurrent-review records are preserved in the package.