perf(number-field-tower): complete core Phase-4 scientific evidence - #9889
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kim-em wants to merge 14 commits into
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perf(number-field-tower): complete core Phase-4 scientific evidence#9889kim-em wants to merge 14 commits into
kim-em wants to merge 14 commits into
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added 9 commits
September 1, 2026 09:42
Derive subtraction, negation, and scalar action as linear in D=2n bounded-height coordinates, and division as the existing n^2 log n recursive inversion term plus lower-order quadratic multiplication. Replace the invalid Trager/BHKS two-sided declaration with a zero-grace mode-3 degree-24 Selmer budget because the inclusive dominant gcd, resultant, and replay phases are outside BHKS. Use the single-root HexRoots certificate to keep fixture construction out of the ladder cost.
Model coordinate negation with its measured fixed result/checksum intercept, and give the identity-adjoin and recursive-factor fixed cases one-second whole-child budgets that cover certified fixture construction and their steady-state batches.
Raise the bad-first-shift whole-child ceiling to one second after a clean five-repeat run exposed that its certified fixture startup can cross the former 0.5-second zero-grace cap. The steady-state median remains 0.813 ms.
Record seven passing ordered mode-1 arithmetic models, eight canonical zero-grace mode-3 budgets, and a refreshed inclusive profile at the degree-24 factorization case. Separate performance modes from correctness, hash, protocol, comparator, and attribution anchors; leave the headline report with no concerns and promote HexNumberFieldTower to Phase 4.
For each coordinatewise operation on the dimension D=2n bounded-height family, the timed call has fixed dispatch/result construction plus a single D-coordinate pass, so use the uniform positive affine proxy n+1 for add, subtract, negate, and rational scalar action. This is a structural finite-range model; the checksum remains part of the linear pass.\n\nofQAdjoin constructs exactly n defining coefficients from an already certified degree-n presentation and its checksum walks the resulting generator and polynomial once, giving a linear mode-1 model. Add temporary candidate-parameter ladders for the remaining composed operations so their ordered-mode exclusions can be measured and retained before the diagnostic registrations are removed from merge smoke.
Retain the failed diagnostic schedules that justify each mode-3 selection, add a canonical checked-replay budget, and classify retry and recursion as branch anchors covered by the inclusive factor case. Derive and register full-basis coordinate-map models: toPrimitive performs Θ(D³) work and fromPrimitive Θ(D⁴).
Record the six attempted parameterizations that rule out direct wall models for the composite fixed surfaces. The map diagnostic also motivates the separately derived cubic and quartic full-basis conversion registrations.
The independently repeated linear run resolves a stable fixed constructor cost: normalizing by n gives beta -0.153, while the code-derived fixed setup plus n coefficient writes gives n+1. Retain that discovery export, the nine already-consistent surface results, all six final mode-3 budgets, and the preregistered CPU host state.
Record ten passing mode-1 surfaces, six independently budgeted mode-3 composites, all failed candidate schedules, inclusive profile denominators, measured host state, and the distinction between performance evidence and branch/hash/comparator anchors. Remove superseded timing exports and retain the model-discovery run.
added 5 commits
September 1, 2026 10:33
Restore the independently derived linear declarations, remove widened slope gates, and extend schedules where fixed terms obscured the asymptotic range. Negation records the resulting unreachable mode-1 rung and selects a canonical mode-3 case. Add a temporary executable degree diagnostic for non-short-circuit height-two factorization.
Commit the clean height-two recursive-factor and negation schedules, including the dimension-32 fixture cap, then remove their temporary registrations from the merge-facing target set.
The clean extended schedules reject the original dimension-only models at default tolerance: division has residual +0.594 and full-basis toPrimitive +0.521. Preserve those diagnostics and select canonical zero-grace fixed budgets without changing either declaration.
Record the seven source-derived passing complexity models and the ten canonical zero-grace mode-3 budgets selected after the retained diagnostic schedules. Correct the inclusive factor-profile attribution, catalogue the input families, and retain clean scientific exports.
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Closing after the final ordered-mode audit reproduced a real |
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Summary
isolateOne?seeds and hold rational coefficient height fixed as tower dimension growsfromPrimitivetoPrimitive, recursive relative factorization, and all six composite surfaces; enforce ten canonical zero-grace mode-3 budgetsPerformance rationale
No mode-1 declaration or slope tolerance is fitted after measurement. The seven final ladders pass their original source-derived models over extended schedules. The other ten surfaces follow the ordered rule to mode 3 only after retained executable parameterizations fail and no published mode-2 bound covers their inclusive dominant phases.
The realized Trager route is dominated by rational-polynomial gcd, shift search, and checked replay rather than integer factorization. In the unfiltered canonical profile, gcd alone occupies 47.28% of the whole capture,
factor?occupies 58.24%, andHex.ZPoly.factorizeonly 1.42%. GMP stack-unwind truncation makes within-target renormalizations qualitative, but the direct shares already exclude a BHKS-only mode-2 envelope. The degree-24 Selmer case therefore has a canonical 2 s mode-3 budget, and an independent height-two case budgets genuine recursive relative factorization.Verification
lake build HexNumberFieldTower HexNumberFieldTower.Conformance hexnumberfieldtower_emit_fixtureslake build(10,500 jobs)list: 7 parametric plus 39 fixed registrationsverifywith cypari2: 46/46 in 14.1 spython3 scripts/check_phase4.pypython3 scripts/check_dag.pyFixes #9665