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Valeri's second point measured: the similarity function belongs to the PLACE it is read in, not to the method. False position's three-century stall is a similarity read at order one on an approach of order m: with sigma = |f(far)| the residual ratio is (e/E)^m, so raising it to the measured 1/m recovers the distance ratio exactly. Paired inside each cell, the correction is cheaper in 7 of 7 safeguards for S = 1/(1+z) - the one function that makes that place exact inverse interpolation - and in only 29 of 60 cells over all nine functions, i.e. a coin. It does NOT beat Chandrupatla (2884 against 2683 and 2423), it HARMS the slope reading (2806 -> 2854), and it does not cure false position: 127/154 and 10676 become 128/154 and 10043, where Illinois buys 153/154 and 7045 with one constant. Estimator bias measured and stated: a pure cube reads 2.830, not 3

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Also fixes a real regression from cc2c499: the derived3_cap branch was inserted in front of the derived3_m note and swallowed its division, so derived3_m silently became derived3 (2806 against 2806) and a refutation recorded in the paper stopped being reproducible. The full pin caught it; a cheap pin now guards it too. And \label{sec:method} never existed while the table on page 7 referenced it.

Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>
This commit is contained in:
vvs
2026-09-21 01:17:25 +01:00
co-authored by Claude Opus 5
parent cc2c499f63
commit 15b94242e0
13 changed files with 756 additions and 11 deletions
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results_sweep_order.txt
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sweep: 252 configurations x 199 problems (FULL)
10/252 done, 0s elapsed
20/252 done, 0s elapsed
/home/valeri/sim-numerics/simroot/pure.py:116: RuntimeWarning: overflow encountered in scalar multiply
"cosine": lambda z: 1.0 / math.sqrt(1.0 + z * z),
30/252 done, 1s elapsed
/home/valeri/sim-numerics/simroot/pure.py:116: RuntimeWarning: overflow encountered in scalar multiply
"cosine": lambda z: 1.0 / math.sqrt(1.0 + z * z),
/home/valeri/sim-numerics/simroot/pure.py:116: RuntimeWarning: overflow encountered in scalar multiply
"cosine": lambda z: 1.0 / math.sqrt(1.0 + z * z),
/home/valeri/sim-numerics/simroot/pure.py:116: RuntimeWarning: overflow encountered in scalar multiply
"cosine": lambda z: 1.0 / math.sqrt(1.0 + z * z),
40/252 done, 1s elapsed
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/home/valeri/sim-numerics/simroot/pure.py:115: RuntimeWarning: overflow encountered in scalar multiply
"exp_sq": lambda z: math.exp(-z * z),
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/home/valeri/sim-numerics/simroot/pure.py:114: RuntimeWarning: overflow encountered in scalar multiply
"rat_sq": lambda z: 1.0 / (1.0 + z * z),
/home/valeri/sim-numerics/simroot/pure.py:114: RuntimeWarning: overflow encountered in scalar multiply
"rat_sq": lambda z: 1.0 / (1.0 + z * z),
120/252 done, 3s elapsed
/home/valeri/sim-numerics/simroot/pure.py:114: RuntimeWarning: overflow encountered in scalar multiply
"rat_sq": lambda z: 1.0 / (1.0 + z * z),
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/home/valeri/sim-numerics/simroot/pure.py:110: RuntimeWarning: overflow encountered in scalar power
"ratio_soft": lambda z: 1.0 / (1.0 + abs(z)) ** 2,
/home/valeri/sim-numerics/simroot/pure.py:110: RuntimeWarning: overflow encountered in scalar power
"ratio_soft": lambda z: 1.0 / (1.0 + abs(z)) ** 2,
/home/valeri/sim-numerics/simroot/pure.py:110: RuntimeWarning: overflow encountered in scalar power
"ratio_soft": lambda z: 1.0 / (1.0 + abs(z)) ** 2,
/home/valeri/sim-numerics/simroot/pure.py:110: RuntimeWarning: overflow encountered in scalar power
"ratio_soft": lambda z: 1.0 / (1.0 + abs(z)) ** 2,
170/252 done, 4s elapsed
/home/valeri/sim-numerics/simroot/pure.py:110: RuntimeWarning: overflow encountered in scalar power
"ratio_soft": lambda z: 1.0 / (1.0 + abs(z)) ** 2,
/home/valeri/sim-numerics/simroot/pure.py:110: RuntimeWarning: overflow encountered in scalar power
"ratio_soft": lambda z: 1.0 / (1.0 + abs(z)) ** 2,
/home/valeri/sim-numerics/simroot/pure.py:110: RuntimeWarning: overflow encountered in scalar power
"ratio_soft": lambda z: 1.0 / (1.0 + abs(z)) ** 2,
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wrote sweep_order.json (5s total)
====================================================================================
APS: 154 problems (top 20 of 252)
====================================================================================
configuration solved total fev over 2x
------------------------------------------------------------------------------------
pure.ratio.derived3.none 153/154 2806 0
pure.ratio.derived3.project 153/154 2806 0
pure+ord.ratio.derived3.none 153/154 2854 0
pure+ord.ratio.derived3.project 153/154 2854 0
pure+ord.ratio.derived3.step 153/154 3000 0
pure+ord.ratio.derived3.safe 153/154 3000 0
pure.ratio.derived3.step 153/154 3036 0
pure.ratio.derived3.safe 153/154 3036 0
pure+ord.exp_abs.derived3.project 153/154 3227 0
pure+ord.exp_abs.derived3.none 153/154 3227 0
pure.exp_abs.derived3.none 153/154 3264 0
pure.exp_abs.derived3.project 153/154 3264 0
pure+ord.exp_abs.derived3.step 153/154 3308 0
pure+ord.exp_abs.derived3.safe 153/154 3308 0
pure.exp_abs.derived3.step 153/154 3312 0
pure.exp_abs.derived3.safe 153/154 3312 0
pure.rational.derived3.none 153/154 3356 0
pure.rational.derived3.project 153/154 3356 0
pure.rational.derived3.step 153/154 3420 0
pure.rational.derived3.safe 153/154 3420 0
====================================================================================
CHA: 45 problems (top 20 of 252)
====================================================================================
configuration solved total fev over 2x
------------------------------------------------------------------------------------
pure.sqrt.far.project 41/45 4516 0
pure+ord.rational.far.credit 40/45 2884 0
pure+ord.ratio.derived3.credit 40/45 2994 0
pure.rational.far.credit 40/45 3013 0
pure.cbrt.derived3.credit 40/45 3016 0
pure.ratio.derived3.credit 40/45 3020 0
pure+ord.cbrt.derived3.credit 40/45 3029 0
pure.exp_abs.far.credit 40/45 3034 0
pure+ord.exp_abs.far.credit 40/45 3035 0
pure+ord.ratio_soft.derived3.credit 40/45 3039 0
pure.exp_abs.derived3.credit 40/45 3049 0
pure.ratio_soft.derived3.credit 40/45 3054 0
pure+ord.exp_abs.derived3.credit 40/45 3067 0
pure.sqrt.far.credit 40/45 3094 0
pure+ord.sqrt.far.credit 40/45 3096 0
pure.ratio.far.credit 40/45 3113 0
pure.cbrt.far.credit 40/45 3127 0
pure+ord.rat_sq.far.credit 40/45 3128 0
pure.rat_sq.far.credit 40/45 3129 0
pure+ord.cbrt.far.credit 40/45 3130 0
====================================================================================
THE STAGE-0C LAW ACROSS THE GRID
====================================================================================
scale=derived3 slope c=1 (linear) mean total 6910 mean solved 192.2/199
scale=derived3 slope c=0 (quadratic) mean total 22334 mean solved 192.8/199