Consume retimed staged releases with smaller T360 stock

[zxv]

Change and mathematical scope

Compose the two commuting staged-release retimings with the literal T360 allocation. The complete conditional finite release supports κ = 0.001730418899766071163804 − 10^-46 − 10^-70, matching the endpoint reported by PR3653 with 323,069 instead of 437,757 physical families, 3,240 instead of 4,392 calls, and 1,321,920 instead of 1,791,936 helper roles. The normalized profiles are identical; smaller stock changes finite constants. No priority or further frontier gain over PR3653 is claimed.

In PR3605's words, move 640 += 2*644 and 656 -= 660 to immediately before the pivots' first producer updates. Exact commutation preserves the full arbitrary-dirty operator, while each donor pays H3 instead of H1+H2. Both providers have local profile {1:2437,2:724,3:226,4:102,5:20,8:8}. The complete paid profile is {1:7980120,2:2345760,3:755730,4:330480,5:69930,8:25920,48:137790} across 322,560 live families, with 509 additional private families. The invoice includes both providers, all literal roles, 91 zero buffers, and the charged 2,048-bit prefix reserve.

All-size/compiler, uniform source/hosting, recursive precision/tape/recovery, bootstrap, analytic and BIT hypotheses remain inherited. This is a conditional finite construction, not an unconditional multiplication theorem or a selected-frontier update.

Task and overlap

Explicitly assigned staged-release consumer work; task independent-moment, changed scope: change and fully price an actual word, rather than only audit an unchanged moment. See research/staged-donor-release/TASK.json for the original card and scope rationale.

Base: 20ecf2891d80b5acf18d980b2164fb44ea7faa90. Exact predecessor inputs are retained with source hashes and notices:

• PR3605 staged words: 3efbb5de06a49ffeea6684482f2d3fe48cdca3fb.
• PR3638 T360 allocation: d62e1acd7518a231440383f0d0dddf54d6edf8c1.
• PR3633 packing comparison: 72c268f113368ea0387d188225e3f81ba6d6ef73.

Concurrent PR3642 reports the same retiming mechanism; PR3653 composes it with T488. This independently constructed package contributes the smaller T360 consumer and its source-bound validation. The strict gain of 0.000000322536237447629574 is relative only to the pinned PR3638/PR3633 predecessor on the common release grid. The final full overlap search covered 374 open PR bodies and 2,464 Discussion records; the related PR heads were rechecked during preparation. Coverage is not a novelty proof. See CONCURRENT-WORK.md for exact heads and comparisons.

Validation

• Both changed providers passed fresh five-stage native replay: 632 arbitrary columns in both orientations, phase/warp recipes, and actual omission/sign controls.
• The complete original release passed all strict finite margins, with the predecessor edit chain retained and a separately checked retiming stage. The original run explicitly reused authenticated unchanged native/parent evidence and preparatory discovery after a declared-stage binding repair.
• Exact dual calibration, integral T360 fill, independent frame/invoice checks, and owner-transfer/source-closure checks passed. Fresh Astra medium review approved the scoped scientific result at a3bdc591920a4b9003d8442d1fcca24218153661; a follow-up review approved the concurrent-work framing. These are independent AI reviews, not human or formal-kernel approval.
• Bounded registered replay, committed-byte comparison and Git-free committed export replay pass for the prepared package. The new full-wrapper evidence is separate from the frozen original scientific evidence.

Reproduce the bounded package with Python 3.12 (standard library only):

python3.12 -B scripts/research_package.py --package research/staged-donor-release --check-only
python3.12 -B scripts/research_package.py --package research/staged-donor-release

Full replay: Python 3.12.8, NumPy 1.26.4, SciPy 1.15.3, SymPy 1.14.0, mpmath 1.3.0; assertions enabled, one heavy replay at a time:

python3.12 -B research/staged-donor-release/full_replay.py --work /tmp/fresh-staged-release

The default full wrapper passed end to end, including both fresh changed native providers, fresh preparation and all seven complete-admission stages. The wrapper and scientific inputs match commit 74afc9ff5cb437d3112c6279216d10250775cd98 and are unchanged in this preparation update. Raw receipts, logs, environment versions and hashes are retained in research/staged-donor-release/evidence/full-wrapper/; the bounded verifier authenticates them and rejects four targeted receipt inconsistencies. This later run retains explicitly authenticated unchanged parent/native ancestry; it is execution evidence subsequent to the cited independent AI review. A no-reuse retained-parent cold run and hosted CI have not been run. Source-history preflight refused the shallow checkout; the self-contained archive instead reconstructs all required source bytes without foreign Git objects. No Lean or Docker was run.

Credit

Credit Ross Richardson/PR3605, roger-sato's concurrent PR3642, Rohan Arun's PR3653, Pierre-Loic Doulcet's PR3633, PR3638's T360 allocation, dcharb78/PR3133, Marius-Paul Dumitrean/PR2979, Jeremy Kothe, and the retained native, owner, block-norm and outer authors. Exact source notices remain in the package. Apache-2.0; substantial OpenAI Codex assistance and independent AI review.

Open next questions

See the package README and structured TASK.json questions. A useful next construction would identify one compensated later release or changed joint consumer, prove its arbitrary-dirty identity, and price its complete invoice before synthesis. The inherited uniform/all-size premises remain separate open obligations.