THM-DIVERGENCE-006 — Euler 1737: Σ1/p diverges — the divergence IS the carrier

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THM-DIVERGENCE-006CLOSED_CLASSICALS1
MuncyNautics Recovery Certificate · theorem-grade divergence · hunted and executed 2026-08-31 · author of every MN concept: Derrick E. Muncy
WHAT THIS CERTIFICATE RECORDSThe mirror case of the family: here the PROJECTION ERROR would run the other way — reading the very slow (ln ln x) growth as convergence. Euler proved the divergence, and the divergence itself carries the information: infinitely many primes, with density strong enough to defeat every finite census. The Codex’s protection argument (N(T) → ∞) is this theorem’s descendant.
GOVERNING EQUATION AS PROJECTED — THE SEAM

Σ 1/p read by partial sums — growth so slow (ln ln x) that any finite audit suggests convergence; the asymptotic address discarded
COMPLETE GOVERNING EQUATION — THE RECOVERY

Σ_{p≤x} 1/p = ln ln x + M + o(1)  (Mertens’ 2nd theorem, proven; M = 0.2614972128…)
executed: Σ over p<3000 = 2.344049 vs ln ln 3000 + M = 2.341734 — the law confirmed, gap at the o(1) size
CORRECTION RULE — correction = reconstruction from the recovery: restored arguments, seats, phases and arms in the equation itself; no raw appended constants — any finite term must be derived from the recovered channels, never fitted.
species
S1 — the ceiling (divergence as the carrier of infinitude)
executed
429 primes below 3000; law confirmed to the o(1) term
standing
CLOSED_CLASSICAL — Euler 1737, Mertens 1874
promotion_authority
GREEN_CLASSICAL
source_records
Euler 1737; Mertens 1874

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