hex-roots: tighten the reality-anchored time-budget ceilings (Graeffe, soft-Pellet, Taylor-shift reuse)

[kim-em]

Measured on chungus2 (PR #8749): degree 10 / prec 32 in 0.137 s (budget 1 s, passes); degree 50 / prec 64 in 495.85 s (budget 10 s, 49.6x over); degree 100 / prec 128 did not complete in 19 min (budget 1 min). The dominant costs per the report's profile are deep subdivision near the separation floor and witness evaluation at large working bit-length. Candidate work, in SPEC-anticipated order: Graeffe iteration (SPEC 'Differences from BSSY' names it as the deferred optimisation that turns the ceilLog2(deg) isolation-ratio term into a constant), cheaper T0 discards on far squares, and a re-appraisal of the SPEC time budgets if they prove miscalibrated for the no-Graeffe design. Phase-4 exit is blocked on this plus the bench re-scaffolding issue.

🤖 Prepared with Claude Code

[kim-em]

Owner decision: the SPEC's rough-first-guess budgets are replaced by regression ceilings anchored to the measured reality (PR #8762): 1 s at degree 10 / prec 32, 30 s at degree 20 / prec 32, 15 min at degree 50 / prec 64, and no pinned budget at degree 100 / prec 128 until this issue's work makes that scale practical. This issue therefore no longer blocks Phase-4 exit on its original terms; it becomes the tightening programme:

• Goal: land the optimisations, in expected-value order — Graeffe iteration (the SPEC's named deferred optimisation; turns the witness's degree-proportional isolation-ratio requirement into a constant, cutting both subdivision depth and certification lag), soft-Pellet filtering per Imbach-Pan-Yap (outward-rounded coefficient bounds at reduced working precision keep witnesses exact-dyadic while decoupling their cost from centre bit-length), and Taylor-shift reuse in certify? (the enclosing square and each Newton candidate currently recompute the shift every round).
• Ratchet rule: every landed improvement re-measures the SPEC's time-budget table on a quiet machine and tightens the ceilings to the new measurement with roughly 2x margin — the ceilings must track the implementation, never accumulate slack. When degree 100 / prec 128 becomes practical, pin its row.
• Success yardsticks: restoring the original aspirations (10 s at degree 50, 1 min at degree 100) is the stretch target; the measured python-flint ratios in reports/hexroots-performance.md are the informational orientation, not a gate.
• Side effects to collect when the tightening lands: hex-roots: restore the SPEC's 50-case degree-20 ci fixture tier #8744 (degree-20 fixture tier) becomes cheap, and the demoted fixed benchmarks from hex-roots: Phase-4 bench re-scaffolding to clear the inconclusive verdicts #8750 can be revisited if the kernels' constant factors change materially.