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§3.1 and Tables 2-3 of the canonical .md brought to current data (Valeri's request). §3.1 said the projection's doubling 'is not a tuning constant' and that zero slack 'behaves as bisection'; both are refuted by measurement (stage12 part 3, rerun as measure_budget_factor.py): the canonical total is 2806 for every multiplier >= 1.25, but the wide-bracket total moves monotonically, 2752 at 1.25 to 4006 at 4, and multiplier 1 costs 4817/2997, nowhere near bisection's 7530/3090. So the proposed safeguard is the EARNED projection (credit, C0 = 1 bit: bisection + 1 step, the cheapest endowment within that promise, 8395 -> 7658 -> 6588), as code and verifier had already fixed but no text said; the scheduled projection stays as the one-constant end of the trade. The text says openly that this choice was made after a question, and that it was not made for the numbers - on the canonical set it costs 762 more.

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Tables 2-3 regenerated from sweep_full.json by tables_for_md.py with the verifier's own ranking: Chandrupatla's method, missing from both, is FIRST on the canonical set (2785) and second on the wide-bracket set (2423); the proposed rule is 29th (3568) and 10th (3020); Brent 2889/4099 (was 2890/4101). The abstract, §5 text, §5.1, §5.2 (timed configuration named), §7 (records 2527/2523 are under the scheduled projection: 2523 flat for every multiplier 1.25-4, 2527 becomes 2541 at 1.25; under credit the readings give far less, best constant-free total 6494 by 'defect'), §8.4, §8.11 and the conclusion now say so: parity with the tuned methods at the price of one constant, or a constant-free rule with a tighter guarantee that trails on the canonical set. verify_article.py: 279 checks, measured tables recomputed from fresh runs; 762 tests pass twice.

Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>
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2026-09-21 08:03:21 +01:00
co-authored by Claude Opus 5
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results_tables_for_md.txt
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configurations in the sweep: 264
APS, 154 problems
| # | configuration | tuned | solved | total evals | $>2\times$ |
|---|---|---|---|---|---|
| 1 | Chandrupatla | no | 153/154 | 2785 | 0 |
| 2 | the same rule with no safeguard at all | no | 153/154 | 2806 | 0 |
| 3 | projection variant (tent, 3-point, projection) | no | 153/154 | 2806 | 0 |
| 4 | TOMS 748 | yes | 153/154 | 2820 | 0 |
| 5 | Brent | yes | 153/154 | 2889 | 0 |
| 12 | Dekker | no | 153/154 | 3158 | 0 |
| 13 | ITP, per-problem oracle | yes | 153/154 | 3260 | 0 |
| 20 | Ridders | no | 153/154 | 3313 | 0 |
| 29 | **proposed: tent, 3-point, credit** | no | 153/154 | 3568 | 0 |
| 34 | ITP, recommended constants | yes | 153/154 | 3957 | 0 |
| 73 | Illinois | yes | 153/154 | 7045 | 0 |
| 79 | bisection | no | 153/154 | 7530 | 0 |
| 244 | false position | no | 127/154 | 10560 | — |
CHA, 45 problems
| # | configuration | tuned | solved | total evals | $>2\times$ |
|---|---|---|---|---|---|
| 1 | similarity, $1-\sqrt{|z|}$, bracket scale, projection | no | 41/45 | 4516 | 0 |
| 2 | Chandrupatla | no | 40/45 | 2423 | 0 |
| 3 | ITP, per-problem oracle | yes | 40/45 | 2611 | 0 |
| 4 | similarity, $e^{-|z|}$, bracket scale, both guards | no | 40/45 | 2733 | 0 |
| 6 | ITP, recommended constants | yes | 40/45 | 2857 | 0 |
| 10 | **proposed: tent, 3-point, credit** | no | 40/45 | 3020 | 0 |
| 16 | bisection | no | 40/45 | 3090 | 0 |
| 47 | projection variant (tent, 3-point, projection) | no | 40/45 | 3220 | 0 |
| 164 | TOMS 748 | yes | 40/45 | 4000 | 15 |
| 226 | Brent | yes | 38/45 | 4099 | 18 |
| 228 | the same rule with no safeguard at all | no | 35/45 | 4104 | 10 |
head to head, pure.ratio.derived3.credit (wins/ties/losses on problems both solve)
APS: chandrupatla 79/3/71, toms748 77/9/67, brent 78/5/70, itp 103/10/40, itp_oracle 86/6/61, bisection 122/1/30
CHA: chandrupatla 5/0/35, toms748 24/0/16, brent 18/0/20, itp 12/20/8, itp_oracle 2/3/35, bisection 5/0/35
head to head, pure.ratio.derived3.project (wins/ties/losses on problems both solve)
APS: chandrupatla 86/25/42, toms748 86/16/51, brent 102/11/40, itp 132/3/18, itp_oracle 121/4/28, bisection 152/1/0
CHA: chandrupatla 9/5/26, toms748 31/1/8, brent 30/4/4, itp 17/0/23, itp_oracle 16/0/24, bisection 21/0/19
both sets pure.ratio.derived3.credit 6588
both sets pure.ratio.derived3.project 6026
both sets chandrupatla 5208
both sets toms748 6820
both sets brent 6988
both sets itp_oracle 5871