CLAIM: fixed-point exponential for the first selected ceiling evaluation

[hevlyo]

CLAIM — verifier-engineering, card replay-runtime, scope refined.

Seed 72c78c29f4a732aee66d631374cb276c, catalogue scope key b1dd41940c60d240b47a. Base 20ecf2891d80b5acf18d980b2164fb44ea7faa90, priority revision 6. The selected record hash is unchanged.

scripts/research_baseline.py cannot bind the selected frontier in this checkout: it needs the frontier1094 package roots. The profiled stage is one ceiling() evaluation of the selected complex local word in the unchanged research/complex-local-word-ceiling/ceiling.py (SHA-256 86a1432870b3b21d8454106ec9162fddc0471472d9214c590a1420f2426cedfc). cProfile shows math.gcd inside that exponential as the dominant cost.

Question: can an opt-in fixed-point series speed that first evaluation and still return the same 256-bit bounds on every argument the selected screen visits? The pinned file is not edited. This is not the warm child_cost memoization in research/exact-child-interval-reuse, the degree-16 owner-check kernel in research/exact-exp-performance, or the domain extension in research/ceiling-range-reduction.

No new kappa and no selected-frontier change. Substantial AI assistance; no independent human review claimed. Apache-2.0.

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[hevlyo]

DONE. PR #3662, exact head aa6f513720ad8de12d678f24f90ea17576e31d52.

Python 3.12 replay: PASS_CEILING_EXP_FIXED_POINT ref_s=0.801109 fast_s=0.017200 ratio=46.58 visited=672 mismatches=0 bracket=1690054109089/1000000000000000. The pinned ceiling engine is unchanged. Universal equality on every rational in [0, 1/2] remains open. No new kappa and no selected-frontier change.

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