THM-DIVERGENCE-001CLOSED_CLASSICALS3
MuncyNautics Recovery Certificate · theorem-grade divergence · hunted and executed 2026-08-31 · author of every MN concept: Derrick E. Muncy
WHAT THIS CERTIFICATE RECORDSA THEOREM-grade divergence: Σ(−1)ⁿ has no ordinary sum — partial sums oscillate 1,0,1,0 forever. Abel’s theorem makes the recovery lawful: the carrier 1/(1+x) is finite on [0,1) and its boundary value 1/2 is consistent with every regular summation method. The divergence was the projection of reading an oscillation as a sum.
GOVERNING EQUATION AS PROJECTED — THE SEAM
S = Σ(−1)ⁿ — partial sums oscillate {1,0}; no ordinary limit (proven)
COMPLETE GOVERNING EQUATION — THE RECOVERY
carrier f(x) = Σ(−1)ⁿxⁿ = 1/(1+x) on |x|<1 (exact); Abel boundary value f(1⁻) = 1/2 EXACT rational executed: 0.50000000 by one divSmall — rank-0 collection; Cesàro mean of 1000 partial sums = 0.500000 (second route)
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 |
S3 — the summation lane (order/method channel discarded) |
|---|---|
| executed |
1/2 exact; Cesàro route agrees — two independent methods (Abel, Cesàro), consistency THEOREM (regularity) |
| standing |
CLOSED_CLASSICAL — Abel 1826; executed both routes |
| promotion_authority |
GREEN_CLASSICAL |
| source_records |
Abel 1826; Hardy, Divergent Series; mp113 engine (208-bit limbs); dual-route where applicable |