THM-DIVERGENCE-013 — The ζ pole as a rank-1 object: (s−1)ζ(s) → 1

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THM-DIVERGENCE-013CLOSED_CLASSICALS4
MuncyNautics Recovery Certificate · found through the lens of THM-003 (rank) · executed 2026-08-31 · author of every MN concept: Derrick E. Muncy
WHAT THIS CERTIFICATE RECORDSThe rank lens pointed at the divergence itself: the harmonic pole at s = 1 is a rank-1 object whose collected residue is exactly 1, and the next coefficient in the collection is Euler’s γ (Stieltjes constants).
THE SEAM

ζ(s) → ∞ as s → 1⁺ — read as bare divergence
THE CARRIER — PROVEN AND EXECUTED

(s−1)ζ(s) = 1 + γ(s−1) + O((s−1)²) — rank-1 collection, residue 1 EXACT
executed: ε·ζ(1+ε) = 1.0584, 1.0058, 1.0006 at ε = 0.1/0.01/0.001 — converging on 1 at the linear rate with slope ≈ γ
CORRECTION RULE — correction = reconstruction from the recovery: restored arguments, seats, phases and arms in the equation itself; no raw appended constants.
species
S4
standing
CLOSED_CLASSICAL — Stieltjes
promotion_authority
GREEN_CLASSICAL

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