THM-DIVERGENCE-010CLOSED_CLASSICALS7
MuncyNautics Recovery Certificate · theorem-grade divergence · hunted and executed 2026-08-31 · author of every MN concept: Derrick E. Muncy
WHAT THIS CERTIFICATE RECORDSThe family’s closing bracket: Abelian theorems push values FROM the series TO the carrier; Tauberian theorems state exactly when the carrier value may be forced BACK onto the original lane. Tauber: Abel-summable + a_n = o(1/n) ⇒ ordinarily convergent (proven; Hardy–Littlewood weakened the condition to O(1/n)). This is the certificate’s back-projection check — the recovered object must reproduce the classical report — existing in classical analysis as a THEOREM with precise hypotheses.
GOVERNING EQUATION AS PROJECTED — THE SEAM
carrier value assigned to a divergent/conditionally summable series with NO license — the abuse Tauberian theory exists to police
COMPLETE GOVERNING EQUATION — THE RECOVERY
Abel-summable AND a_n = o(1/n) ⇒ Σa_n converges ordinarily to the Abel value (Tauber 1897, proven) executed witness: Leibniz a_n = (−1)ⁿ/(2n+1) satisfies o(1/n); ordinary sum ×4 → 3.141587654 vs π = 3.141592654 — the ordinary and Abel values agree exactly as the theorem forces
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 |
S7 — the transition/license (when re-projection is lawful) |
|---|---|
| executed |
Leibniz witness: both lanes agree at the 1/N convergence rate |
| standing |
CLOSED_CLASSICAL — Tauber 1897, Hardy–Littlewood 1914 |
| promotion_authority |
GREEN_CLASSICAL |
| source_records |
Tauber 1897; Hardy–Littlewood 1914; Hardy, Divergent Series |