Note 42 is a self-contained write-from document: full statements and
proofs for Thm 1-4 / Prop 1-3 / Cor 1-2, every result with exact
numbers and configs cross-checked against the CSVs, the negative
results, and the honesty boundaries.

Audit finding while building it: the "E_B[e0]=0.4378 +/- 0.008 vs
0.4403" headline (cited in notes 29/35/36/40/41 and the old draft) is
not reproducible from the current moments CSV. Retired in favor of the
reproducible 6x6 table (max |error| <= 0.008, predicted span 0.15-0.45).
Living docs updated; note 37 sec 4 records the retirement.

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

Closed-form gap law note (34) + consolidated snapshot (35), with the
comparison script reading the dense run's config/gaps from its output
dir and evaluating the closed form on matched data and init seed plus a
multi-init band. Corrected headline: corr(log,log) 0.933 matched /
0.982 five-init geometric mean; lam_min ensemble corr 0.987.

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