THM-DIVERGENCE-009CLOSED_CLASSICALS6
MuncyNautics Recovery Certificate · theorem-grade divergence · hunted and executed 2026-08-31 · author of every MN concept: Derrick E. Muncy
WHAT THIS CERTIFICATE RECORDS∫₋₁¹ dx/x diverges on each side separately — and the principal value is exactly 0 because the two seats are antipodal and their contents cancel term by term. This is the corpus’s antipodal-seat annihilation as a classical construction: the divergence is the projection of integrating one seat without its partner. PV is the paired reading, and it is a theorem that it exists and behaves (Sokhotski–Plemelj builds on it).
GOVERNING EQUATION AS PROJECTED — THE SEAM
∫₋₁⁰ dx/x = −∞ and ∫₀¹ dx/x = +∞ — each seat read alone diverges logarithmically
COMPLETE GOVERNING EQUATION — THE RECOVERY
PV ∫₋₁¹ dx/x = lim_{ε→0} [∫₋₁^{−ε} + ∫_ε¹] dx/x = 0 — the antipodal pair (x, −x) annihilates exactly
executed: paired integrand 1/x + 1/(−x) integrates to 0.00e+0 at every mesh — identically zero before the limit
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 |
S6 — the partner arm (antipodal seat pairing) |
|---|---|
| executed |
identically zero paired integrand; each unpaired lane confirmed divergent |
| standing |
CLOSED_CLASSICAL — PV construction, Sokhotski–Plemelj |
| promotion_authority |
GREEN_CLASSICAL |
| source_records |
Cauchy; Sokhotski 1873, Plemelj 1908 |