THM-DIVERGENCE-007CLOSED_CLASSICALS6
MuncyNautics Recovery Certificate · theorem-grade divergence · hunted and executed 2026-08-31 · author of every MN concept: Derrick E. Muncy
WHAT THIS CERTIFICATE RECORDSThe cleanest phase-vs-magnitude theorem in analysis: ∫sin(t)/t dt = π/2 exactly (Dirichlet, proven), while ∫|sin(t)|/t dt DIVERGES (proven). Same integrand content — the absolute value destroys exactly the alternation that pays the tail. This is the corpus’s √(z·z̄)-never-|z| rule as a classical theorem.
GOVERNING EQUATION AS PROJECTED — THE SEAM
∫₀^∞ |sin t|/t dt = ∞ (proven) — the magnitude projection of the integrand; grows as (2/π)ln T
COMPLETE GOVERNING EQUATION — THE RECOVERY
∫₀^∞ sin(t)/t dt = π/2 (Dirichlet, proven) — phase kept, alternation pays the tail executed: π/2 = 1.5707963267948966192313216916397514420985 (113+ bits, Machin); numeric to T=200: phase lane 1.568382 → π/2, magnitude lane 4.487 and growing
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 conjugate/positivity pair (magnitude vs phase-kept) |
|---|---|
| executed |
113-bit π/2; both lanes measured, divergence and closure confirmed side by side |
| standing |
CLOSED_CLASSICAL — both halves proven |
| promotion_authority |
GREEN_CLASSICAL |
| source_records |
Dirichlet 1829; standard non-absolute-integrability proof |