research: kernel scaling under repeated cubic folds #33

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opened 2026-07-02 14:03:40 +00:00 by toph · 1 comment

toph commented

2026-07-02 14:03:40 +00:00

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Open questions from the kernel review (aborted mid-run) — measure before more axiom-6/7-heavy features build on the kernel:

Axiom 6/7 timing on algebraic inputs: with one or two prior square-root folds feeding the cubic (e.g. p.x = √2/4, p.x = (√2+√3)/8), do beloch6/beloch7 stay usable? Rational-input baselines exist; the algebraic-input probe was interrupted.
Degree growth: repeated cubic folds tower field extensions multiplicatively. Does the shared-field/RUR approach (notes/2026-06-30-shared-field-rur.md) actually contain this, or does a ~20-step model with a few cubic folds explode?

Deliverable: a small benchmark suite over representative fold sequences (budget: a 20-step model with cubic folds stays interactive) and a verdict on whether ADR 0012 needs adjusting. Feeds #23's real_roots findings.

Open questions from the kernel review (aborted mid-run) — measure before more axiom-6/7-heavy features build on the kernel: - Axiom 6/7 timing on *algebraic* inputs: with one or two prior square-root folds feeding the cubic (e.g. `p.x = √2/4`, `p.x = (√2+√3)/8`), do `beloch6`/`beloch7` stay usable? Rational-input baselines exist; the algebraic-input probe was interrupted. - Degree growth: repeated cubic folds tower field extensions multiplicatively. Does the shared-field/RUR approach (notes/2026-06-30-shared-field-rur.md) actually contain this, or does a ~20-step model with a few cubic folds explode? Deliverable: a small benchmark suite over representative fold sequences (budget: a 20-step model with cubic folds stays interactive) and a verdict on whether ADR 0012 needs adjusting. Feeds #23's `real_roots` findings.

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2026-07-03 07:17:11 +00:00

docs(notes): #33 verdict — kernel scaling with qqbar backend

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2026-07-03 07:17:26 +00:00

feat(kernel): back irrational numbers with FLINT qqbar #41

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2026-07-03 07:21:58 +00:00

docs(notes): #33 verdict — kernel scaling with qqbar backend

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2026-07-03 13:06:52 +00:00

docs(notes): #33 verdict — kernel scaling with qqbar backend

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2026-07-03 13:07:15 +00:00

feat(kernel): back irrational numbers with FLINT qqbar (#41)

toph commented

2026-07-03 13:19:35 +00:00

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Answered by #41 (FLINT qqbar backend + 3.6 roots-first). Measured verdict in notes/2026-07-03-33-verdict.md: axiom 7 with algebraic inputs is fixed (√2/4: >120s → 5ms; (√2+√3)/8: never completed → 0.113s), stacked cubics are interactive through round 3 (0.068s). Round 4 (degree-81 minimal polynomials) remains a genuine wall — it grinds in FLINT's canonical representation too, so it is a property of exact arithmetic at that degree, not of our pipeline; documented in the note and ADR 0013. The 20-step-with-a-few-cubics budget is met as long as cubic folds don't stack more than three deep, which no classical construction does.

Answered by #41 (FLINT qqbar backend + 3.6 roots-first). Measured verdict in `notes/2026-07-03-33-verdict.md`: axiom 7 with algebraic inputs is fixed (√2/4: >120s → 5ms; (√2+√3)/8: never completed → 0.113s), stacked cubics are interactive through round 3 (0.068s). Round 4 (degree-81 minimal polynomials) remains a genuine wall — it grinds in FLINT's canonical representation too, so it is a property of exact arithmetic at that degree, not of our pipeline; documented in the note and ADR 0013. The 20-step-with-a-few-cubics budget is met as long as cubic folds don't stack more than three deep, which no classical construction does.

toph closed this issue

2026-07-03 13:19:35 +00:00

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2026-07-03 21:22:12 +00:00

test(num): #33 deep-stack perf + verdict update for PE tier

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2026-07-03 21:22:12 +00:00

docs(verdict): distinguish measured deg-8 result from extrapolated #33 round-4 estimate

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2026-07-03 21:23:45 +00:00

feat(num): primitive-element tier in real_roots for compositum fields #56

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