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Integrate exact FFT scalars into the physical Full caller (no new κ) - #6898
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Mister-Meeseeks merged 1 commit intoNov 10, 2026
Merged
Mister-Meeseeks merged 1 commit into
Mister-Meeseeks merged 1 commit into
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Summary
Join the exact #3787 FFT scalar service to the actual physical Full caller, including radius admission, coefficient expansion, every diagonal product, protected returns and private tape ownership. All eight consumer methods retain the established numerical semantics.
The complete scalar contribution becomes O((D+1)V log²p) under the stated source-width premises. This removes the earlier Karatsuba restriction beta>0.585975647 for fixed positive polynomial axis growth. Native-H, source construction and outer admission remain explicit. No new κ.
Evidence
Base:
7c49fe32c55de02c2c873655c804b16e4c3fef0a. SOURCES.json pins 42 canonical inputs and ten unchanged files from the physical Full caller. The independent numerical refinement supplies the retained scalar numerical audit.Expected:
PASS_FULL_FFT_SCALAR_JOIN. Author and lead normal/optimized replays passed, with frozen scientific bytes and committed file modes checked.The actual 21-stage Full fixture executes ten H events, eleven diagonals and 92 scalar calls. At the fixed production cutoff 4096 these are base cases. A separately disclosed width-three fixture with cutoff two executes four genuine FFT products and two nonzero truncations. Observed and erased executions agree on their literal action counts.
Controls reject twenty private-tape aliases, five stale source cohorts and two protected-return violations. Source authentication includes the new adapter itself. The full bill retains scalar setup, 1,024 private roles, historical backing, metadata, all H events and all source preparation.
Scope and open next questions
This is a completed service join with an all-width proof, not a full accelerated native implementation or outer multiplication theorem. The existing Full constructor remains unchanged. Exact integer, codec, owner and native contracts remain explicit. The optional full-history check refused this shallow checkout and is not reported as passed; direct source/blob/tree checks passed. Next: establish the remaining native and complete outer-caller admissions.
Credit
Prepared for @CubeJerry with substantial OpenAI Codex assistance and separate AI review; no human or proof-kernel acceptance is claimed. Credit Jose Manuel/jmbarrancoml, Vlado Vojdanovski and #3709, #3787, #3808, #3935, #5110, #6252 and #6024. Their FFT, carry, setup and prior Gaussian results are inherited. Full proof, pins, receipts and limitations: research package.