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Outcome of PREREG_empty_step: both features FAIL by the declared criteria. Empty step (similarity of |f_n| to |f_n-1|): AUC 0.45/0.53/0.34 (proposed) and 0.46/0.51/0.31 (reading 3) against APS/fun1/other CHA; on the proposed rule it fires MORE on APS (36.0%) than on the flat families (18.9%). Repeating pattern with the period chosen from the data: separates the flat families from APS and fun1 (AUC 0.69/0.77 and 0.66/0.67; fires 77.1% vs 37.7%/38.2%, and 18.0% vs 6.2%/9.5%) but not from the other CHA families (AUC 0.41 and 0.22; fires 72.4% and 68.6%), so R1 fails and no rule is built.

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Seen after the result and therefore NOT claimed: the 'other' group contains fun7 = x exp(-1/x^2), itself a flat function whose derivatives all vanish at the root. A fair re-test needs a new pre-registration with flatness defined in advance by a property of f (f'(r) = 0), not by the grouping that just failed.

Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>
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2026-09-21 11:23:47 +01:00
co-authored by Claude Opus 5
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results_diag_empty_step.txt
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== proposed (projection)
group states E: S_E > 1/2 R: S_R > 1/2 (R defined)
APS 1429 36.0% 37.7% 977
CHA fun1 83 18.1% 38.2% 68
CHA flat fun3-6 1763 18.9% 77.1% 1703
CHA other 237 50.6% 72.4% 192
AUC, flat states against: E R
APS 0.447 0.691
CHA fun1 0.529 0.771
CHA other 0.344 0.408
== reading (3), as for m>=2
group states E: S_E > 1/2 R: S_R > 1/2 (R defined)
APS 990 19.0% 6.2% 536
CHA fun1 36 13.9% 9.5% 21
CHA flat fun3-6 659 27.9% 18.0% 599
CHA other 204 54.9% 68.6% 159
AUC, flat states against: E R
APS 0.460 0.656
CHA fun1 0.512 0.674
CHA other 0.310 0.219
bars: m>=2 fires 0.2% canonical / 5.8% flat; successive-ratio similarity AUC 0.28-0.42