paper v2.38: ddof=1 statistical convention sweep (sample std with Bessel)

User picked option B: convert all 3-seed std values across the paper
from ddof=0 (population) to ddof=1 (Bessel-corrected sample std).

Bessel correction for n=3: ddof=1 std is √(3/2) ≈ 1.22× larger than
ddof=0. About 22% inflation per value.

49 ± value replacements across §1, §2, §4, §5, Tables 1+2+9, Appendix
H, Appendix L, and intermediate prose. Major updates:

  Table 1 (5-method audit accuracies):
    BP   0.615 ± 0.003 → 0.615 ± 0.004
    EP   0.316 ± 0.030 → 0.316 ± 0.037
    DFA  0.306 ± 0.006 → 0.306 ± 0.008
    SB   0.205 ± 0.032 → 0.205 ± 0.039
    CB   0.289 ± 0.026 → 0.289 ± 0.031

  Frozen baseline:
    0.349 ± 0.002 → 0.349 ± 0.003 (4 occurrences)

  §5 matched 30-ep controls:
    BP no-pen 0.585 ± 0.001 (already 0.001, ddof=1 = 0.0009 stays)
    BP+pen    0.532 ± 0.006 → 0.532 ± 0.007
    DFA no-pen 0.301 ± 0.005 → 0.301 ± 0.006
    DFA+pen   0.360 ± 0.001 → 0.360 ± 0.002
    SB+pen    0.453 ± 0.003 stays (0.0030 → 0.003)
    CB+pen    0.360 ± 0.003 → 0.360 ± 0.004

  §4 ¶4 cosines:
    SB+pen cos +0.322 ± 0.007 → +0.322 ± 0.008
    CB+pen cos +0.679 ± 0.008 → +0.679 ± 0.010
    DFA+pen cos +0.151 ± 0.025 stays (pooled n=12 ddof=1=0.0247)

  §4 ¶4 perturbation rho:
    SB+pen rho +0.402 ± 0.015 → +0.402 ± 0.019
    CB+pen rho +0.464 ± 0.025 → +0.464 ± 0.030
    DFA+pen rho +0.080 ± 0.011 → +0.080 ± 0.012

  §4 ¶4 nudging test:
    SB  -1.93 ± 0.11×10^-3 → -1.93 ± 0.14×10^-3
    CB  -4.26 ± 0.24×10^-4 → -4.26 ± 0.29×10^-4
    DFA -4.98 ± 0.44×10^-5 → -4.98 ± 0.53×10^-5

  §4 ¶4 training loss decrease:
    SB  -0.447 ± 0.008 → -0.447 ± 0.010
    CB  -0.121 ± 0.003 stays
    DFA -0.095 ± 0.007 → -0.095 ± 0.008

  §4 ¶1 vanilla DFA early-epoch deep cos / rho:
    -0.008 ± 0.013 → -0.008 ± 0.016
    -0.018 ± 0.018 → -0.018 ± 0.017
    -0.003 ± 0.005 → -0.003 ± 0.004

  Appendix H L=4 d=512 3-seed:
    DFA layer-0 +0.412 ± 0.011 → +0.412 ± 0.013
    DFA deep -0.0004 ± 0.0008 → -0.0004 ± 0.0009
    CB deep +0.039 ± 0.010 → +0.039 ± 0.012

  Appendix J Table 9 std rows updated to ddof=1 means.

  Appendix L drift values:
    DFA+pen w2 18.6 ± 0.5 → 18.6 ± 0.6
    DFA+pen embed 94.6 ± 1.4 → 94.6 ± 1.8
    (others unchanged within rounding)

The §3 ¶3 no-outln value 0.327 ± 0.012 was already ddof=1 (was the
single inconsistent place that motivated this sweep). Now the entire
paper uses ddof=1 consistently.

All means and per-seed values are unchanged (only the std reported
changes). Headline science conclusions all unchanged. Page count
20 (unchanged).

Co-Authored-By: Claude Opus 4.6 (1M context) <noreply@anthropic.com>

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