Sign tests by product underflowed: FIXED everywhere (branch, not master - the paper is not yet updated). FA * fnew < 0.0 with FA ~ -1e-200, fnew ~ 1e-150 is -0.0 and '-0.0 < 0.0' is False, so on flat functions (x^19) the bracket update moved the wrong end, the root left the bracket and the run still reported convergence - the proposed rule returned 4.9e-9, bisection 3.5e-9, ITP 1.6e-8 with a claimed 1e-12 bracket; the 1e-6 harness scored them solved. Same defect in our bisection, false-position family, Ridders, Brent, ITP and twelve copies in stage scripts, simroot/sim.py and one test; all replaced by _opposite / _same_sign, pinned by test_sign_underflow.

Impact, every sweep regenerated: the paper's key configurations are unchanged to the evaluation (proposed 2806/3220, credit 3568/3020, Chandrupatla, TOMS 748, Brent, bisection); 46 stated numbers move (ITP CHA 2857 -> 2896, ITP oracle 2611 -> 2647, record CHA figures by 14-18, the grid means by ~1%) and one finding weakens: the measured-order exponent of section 7.1 was cheaper in 29 of 60 far cells and 7 of 7 safeguards; with the fix 12 of 61 and 6 of 7, and on the wide-bracket set it now loses in every safeguard and drops 5 problems.

PREREG G1-G3 outcome on the fixed code: G2 (repeating step pattern, period from the data) PASSES Y1-Y4 and is ACCEPTED by the stop rule - proposed rule APS 2806 -> 2782 (below Chandrupatla's 2787), CHA 3220 -> 3169, both 6026 -> 5951, per problem vs Chandrupatla on APS 95/20/38 p = 8e-7. G1 fails Y1/Y2 (its Y3 miss was the sign bug), G3 fails Y2, A fails Y2. Regression 887 pass; the two red tests are the paper-number check (awaiting the paper update) and test_blend (fixed since, copy in stage16).

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

results_analyze_extrap2.txt

@@ -0,0 +1,22 @@
+A and no-lengthening cells identical to sweep_extrap.json: 182 same, 0 differ
+
+PROPOSED RULE (tent, 3-point, projection), by mode:
+  mode                 APS   CHA  both  flat  Y1 Y2 Y3 Y4   vs Chandrupatla APS (w/t/l, p)
+  no lengthening      2806  3220  6026  1823   -  -  ✓  -   87/24/42 p=9.2e-05
+  A                   2967  2926  5893  1525   ✓  ✗  ✓  ✓   42/62/49 p=0.53
+  G1 confirmed        2933  3281  6214  1859   ✗  ✗  ✓  ✗   81/28/44 p=0.0012
+  G2 pattern          2782  3169  5951  1780   ✓  ✓  ✓  ✓   95/20/38 p=8.2e-07   ACCEPTED
+  G3 steps+results    2953  3205  6158  1804   ✓  ✗  ✓  ✓   79/28/46 p=0.004
+
+Y6 best cell over both sets, per mode (guarantee family, >= 193 solved):
+  no lengthening     pure+dissim+slope.ratio.derived3.project             2726+2799=5525
+  A                  pure+dissim+ext+slope.ratio.derived3.project         2859+2553=5412
+  G1 confirmed       pure+dissim+extC+slope.ratio.derived3.project        2882+2757=5639
+  G2 pattern         pure+dissim+extP+slope.ratio.derived3.project        2759+2789=5548
+  G3 steps+results   pure+dissim+extR+slope.ratio.derived3.project        2808+2785=5593
+
+readings under the projection, APS/CHA by mode:
+  slope         no 2848/3114  A 2971/2763  G1 3004/2993  G2 2809/3033  G3 2934/3043
+  shape+slope   no 2675/3498  A 2930/3506  G1 2800/3511  G2 2894/3483  G3 2944/3477
+  dissim+slope  no 2726/2799  A 2859/2553  G1 2882/2757  G2 2759/2789  G3 2808/2785
+  defect        no 2523/3210  A 3180/2955  G1 2667/3260  G2 2580/3183  G3 2684/3210