Certify 64 depth-coarse profiles and an adaptive-recursion limit

[JosephDemarest]

This adds an exact optimum certificate for a defined 64-profile depth-coarse family and a floor-exact proof that adaptive switching among those complete profiles cannot improve their best scalar recursion power. The result identifies where further construction work is needed: outside this frozen family, rather than another schedule of the same completed profiles.

The family chooses one of eight row/column words at the first three internal weighted-exclusion construction levels for each of h=23 and h=25, keeping the split/anchor/compiler policies fixed. The selected rcr/rrr pair has 27,309 / 35,798 roles, physical width 134,355,558, and conditional exponent saving 5164326938841/10^17 = 5.164326938841e-5. Exact lower moment bounds exclude every other one of the 63 profiles at the accepted saving. An independent checker bounds the selected root and the remaining balanced-assembly headroom by less than 1.565e-16.

The adaptive result in PROOF-BARRIER.md uses the complete nonuniform child-volume weights and the shift D=13225/2 to handle t floor(e/575) exactly. It applies to explicitly charged complete recursion trees with the stated elementary-leaf costs. It is not a lower bound for arbitrary multiplication algorithms, arbitrary internal per-cell factoring, or computation shared between child occurrences.

The selected saving is about 1.2277% above reviewed main 56b66d58297deca1d7dd130247d720e960f77a37. Concurrent #79 (9a58e62c), #80 (a9ed157f), #81 (acae4964) and #82 (3410b940) report stronger numerical values using additional mechanisms. This submission makes no record or priority claim. The all-size framed/residual compiler, finite-alphabet tape, analytic transfer, routing, address-prime, precision and exact-recovery obligations remain inherited hypotheses.

The package includes the construction proof, both selected literal words, 16 per-axis receipts, all 64 exact comparisons, a separate arithmetic checker, 65 source/artifact pins, and adversarial controls. CI regenerates both axes for every menu word and checks the selected package on Python 3.11, 3.13 and 3.14. Existing headline documents, historical witnesses and the Makefile are unchanged.

Validation:

• All 47 fork CI jobs passed on 183077b7b3ae12e96eb3a87c1dc08023e6494dca: 11 new-family jobs and 36 existing-suite jobs, including all three Lean packages. Regeneration and existing artifact groups also passed their clean-tree checks. Upstream PR workflow execution currently awaits maintainer approval for this fork.
• Full baseline make -j1 verify: 516 tests in 78 isolated modules and 20 historical patch checks; all three existing Lean packages also passed. The local baseline's temporary checkout was unavailable for a final drift check, so this does not assert a byte-clean baseline run.
• Clean staged-tree export: selected word regeneration, literal scatter/terminal binding, complete source/target/arbitrary-dirty replay, actual frame/CRT profiles, exact characteristic, 47 strict assembly inequalities and seven margins.
• Independent root/constraint/menu receipt reproduction and 11 control tests, including source-manifest portability and assertion-disabled rejection.
• Every source pin matches a staged Git blob; all nine retained vendor files match their original committed bytes.

The construction builds on eumemic's #69 coarse factoring and Chafik Boukhalfa's #71 anchored split compiler, with the earlier schedules, live controls, split operation, reversible compiler and frame graph credited in the package and retained notices. Related #77/#79 compositions are acknowledged. Prepared for Joseph Demarest with substantial OpenAI Codex assistance. Finite checks and agent review are not a formal proof or independent human peer review of the full multiplication theorem.

[Mister-Meeseeks]

Thank you @JosephDemarest. This contribution is now recorded on main in the scoped reconciliation review and contributor credits.

Contribution: Shared work functional for an adaptive depth menu.

Review and limits: Fresh arithmetic, independent checks and tests; exact-head full Linux menu CI retained. Scoped 64-profile family, not a universal algorithmic lower bound.

The complete original source, proof/research notes, notices and relevant replay/CI evidence are retained through the pinned source archive. The review distinguishes fresh runs, exact-head historical CI and prior integration evidence. Closing this historical PR as reconciled; its obsolete headline does not replace the current selected bound, and draft/retracted claims retain their explicit qualifications.

Reviewed head: 183077b7b3ae12e96eb3a87c1dc08023e6494dca. Publication: b84ba67156a01f9c2cb34fe1e3cb1dcdeab00d9c.