feat(kernel): back irrational numbers with FLINT qqbar

toph commented

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

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For #33. Replaces the kernel's Alg representation (resultant arithmetic) with a FLINT qqbar backend behind the unchanged Num API; Rat and same-generator Field stay pure OCaml fast paths. Drops the H(Y)/certify pipeline (candidate roots are verified by exact qqbar evaluation instead), swaps Mpoly.resultant's Laplace determinant for evaluation+interpolation, and — new in the last commit — bumps FLINT to 3.6.0 to use _qqbar_roots_poly_squarefree (roots of polynomials with algebraic coefficients) as the primary path for the axiom-6/7 cubics, with the elimination pipeline as fallback behind an exact discriminant guard.

Measured: cross-field compare >120s → 1ms; axiom 7 with √2/4 input >120s → 5ms; (√2+√3)/8 never completed → 0.113s; stacked cubics round 3 at 0.068s, round 4 walls (intrinsic — canonical degree-81 minimal polynomials are heavy even for FLINT; documented). Full history and verdict in notes/2026-07-03-33-verdict.md, decision in ADR 0013 (supersedes the Alg part of 0012). New dependency: flint 3.6.0 (LGPL, flake source override until nixpkgs catches up — first build compiles FLINT, ~10 min). The num suite drops from 76s to 0.5s; goldens: cube-root.fold re-baselined (qqbar to_float is correctly rounded; old value was the midpoint of a 1e-12 interval, deltas ~4e-13).

For #33. Replaces the kernel's `Alg` representation (resultant arithmetic) with a FLINT `qqbar` backend behind the unchanged `Num` API; `Rat` and same-generator `Field` stay pure OCaml fast paths. Drops the H(Y)/certify pipeline (candidate roots are verified by exact qqbar evaluation instead), swaps `Mpoly.resultant`'s Laplace determinant for evaluation+interpolation, and — new in the last commit — bumps FLINT to 3.6.0 to use `_qqbar_roots_poly_squarefree` (roots of polynomials with algebraic coefficients) as the primary path for the axiom-6/7 cubics, with the elimination pipeline as fallback behind an exact discriminant guard. Measured: cross-field compare >120s → 1ms; axiom 7 with √2/4 input >120s → 5ms; (√2+√3)/8 never completed → 0.113s; stacked cubics round 3 at 0.068s, round 4 walls (intrinsic — canonical degree-81 minimal polynomials are heavy even for FLINT; documented). Full history and verdict in `notes/2026-07-03-33-verdict.md`, decision in ADR 0013 (supersedes the Alg part of 0012). New dependency: flint 3.6.0 (LGPL, flake source override until nixpkgs catches up — first build compiles FLINT, ~10 min). The num suite drops from 76s to 0.5s; goldens: `cube-root.fold` re-baselined (qqbar `to_float` is correctly rounded; old value was the midpoint of a 1e-12 interval, deltas ~4e-13).

toph added 29 commits

2026-07-03 07:17:27 +00:00

test: add test_num_close_roots_distinct for #23 9ab016737b

fix(num): select_root decides zero via isolating intervals (#23 ) 191dca5345

perf(num): continued-fraction rational-root search, drop trial division (#23 ) 30ead45f61

perf(poly): Descartes/VCA root isolation replaces Sturm bisection (#23 ) eab94a0315

test(num): epsilon-ladder regression for close-root isolation (#23 ) 7d43ce839e

perf(num): drop exact-compare sort of already-ascending real_roots (#23 ) 43b3c8b162

test(num)+docs: final-review follow-ups — nudge loop, boundary-root test, breadcrumbs (#23 ) 1ae7cac3d4

docs(ideas): approx-mode verdict — float filter over float kernel 7dd21a6a6b

docs(spec): material creases + first-class flaps design (#26 , #28 ) 5f5c8c8106

Combined design: first-class faces/edges entity in Fold_state, material
creases resolved per-flap (bent -> error), #(.a .b .c) flap operand as the
escape hatch. Staged as two PRs (entity plumbing + principled #27; then
material-crease semantics + area syntax). Retires the #27 tactical patch.

Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01Jfw5BuRgc2vq3j6zckY867

docs(spec): slice 2 pivots to FLINT qqbar backend; D5 design kept as fallback appendix e99397c78a

docs(spec): note no kernel surface — orthogonal to FLINT migration 13d9f2bfa8

Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01Jfw5BuRgc2vq3j6zckY867

docs(plan): qqbar kernel backend (slice 2) implementation plan bcb844672d

docs(plan): PR1 crease/flap entity plumbing (#26 , principled #27 ) d30fe6192b

Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01Jfw5BuRgc2vq3j6zckY867

docs(notes): two-layer principle — capability (all 7) vs surface sugar (by frequency) ea81d9d5a9

docs(plan): PR1 fixes — real #27 assertion, golden harness excludes through.bel + captures error examples, fold_string returns Yojson 9bda97e14c

Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01Jfw5BuRgc2vq3j6zckY867

docs(spec): §0 primer — material entities & addressing (#26 , #28 ) 8a0d9f309c

Version-tagged v0.10-dev preface: point/crease/flap as material paper
geometry, creases carried as per-flap pieces (bent → error), the #(…)
and --(--d #(…)) operands. Entity-model altitude; §3/§4 reconciliation
deferred to #28 PR 2.

Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01QJW3X1XNaTL81UmjD5dm5m

docs(spec): two-layer principle — capability (all 7) vs frequency-driven sugar {①②③⑤} 7d037ff1c4

docs(plan): PR1 Task 3 absorbs edge accumulation+splitting (golden net = oracle) 851ba47450

Per Task 2 implementer's flag: edges must persist and split across folds for
emit-from-edges to keep multi-fold goldens byte-identical. Merged into Task 3.

Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01Jfw5BuRgc2vq3j6zckY867

docs(notes): per-step DOF management for realistic fold-collapse rendering ab40f3a34a

docs(plan): PR1 Task 3 post-rebase note (#35 ctx wrapper; fold_emit region unchanged) 44a0bc6c3d

docs(plan): PR1 Task 4 rescoped to oracle+unit coverage (upgrade landed in Task 3) 88bb684d31

docs(plan): PR1 Task 5 post-rebase consumer map (#35 tests, ctx.recs, abut_edge removal) 1e2602571b

feat(kernel): FLINT qqbar FFI module ac15f39b96

feat(kernel): back irrational Num values with FLINT qqbar, drop Alg 36f0facbee

docs(adr): 0013 FLINT qqbar backend; kernel identity tests 55e6014aab

docs(notes): #33 verdict — kernel scaling with qqbar backend 82a2691db5

perf(num): verify real_roots candidates via exact qqbar evaluation, drop H(Y)/certify 4c0b8f87d8

Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>

perf(mpoly): evaluation-interpolation Sylvester resultant; dedup FLINT roots exactly 1c59dd6660

Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>

docs: align ADR 0013 + verdict note with final real_roots pipeline dfaa422e18

toph force-pushed feat/qqbar-kernel from dfaa422e18 to 03acbc9b72

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

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toph added 1 commit

2026-07-03 11:33:55 +00:00

perf(num): FLINT 3.6 qqbar-poly roots first, Mpoly elimination as fallback 9ed72cbf79

Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>

toph force-pushed feat/qqbar-kernel from 9ed72cbf79 to 10d2c2642e

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

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toph merged commit 8dca67316b into main

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

toph deleted branch feat/qqbar-kernel

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

toph referenced this pull request from a commit

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

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

toph referenced this pull request

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

research: kernel scaling under repeated cubic folds #33

toph referenced this pull request from a commit

2026-07-03 18:27:22 +00:00

test(golden): include through.bel now that the FLINT kernel folds it (#41)

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