INET-DIVERGENCE-001EXECUTED_113BITS4
MuncyNautics Corrected Recovery Work Order (Copilot, 2026-08-31) · EXECUTED cold by Claude this date · author of every concept: Derrick E. Muncy
WHAT THIS RECORD ISCopilot’s corrected recovery work order, EXECUTED this date. Rayleigh–Jeans is retained as the low-frequency projection of the repaired Planck carrier; the divergent UV extension is rejected. All three witnesses now computed.
GOVERNING EQUATION AS PROJECTED — THE SEAM
u_RJ(ν,T) = (8πν²/c³)k_B T; U_RJ(T) = ∫₀^∞ u_RJ dν = ∞ (frequency-blind equipartition: the occupancy rank x = hν/k_BT discarded)
COMPLETE GOVERNING EQUATION — THE RECOVERY
<E_ν> = hν/[exp(hν/k_BT) − 1]; u_rec = (8πhν³/c³)/[exp(hν/k_BT) − 1] EXECUTED: ∫₀^∞ x³/(eˣ−1)dx = 6.493939402265942 vs π⁴/15 = 6.493939402266828 (residual −8.9e-13) Witness A (low-ν): <E>/k_BT = 0.999500083 at x=0.001, matching 1−x/2 = 0.9995 — RJ recovered as the limit Witness B (UV): tail beyond x=30 is 2.8e-9 — integrable, catastrophe closed Witness C (total energy): the Stefan–Boltzmann integral verified to 1e-13 relative
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.
| record_id |
INET-DIVERGENCE-001 (work order Copilot 2026-08-31, executed same date) |
|---|---|
| executed_results |
DOUBLE RUN: residual 8.9e-13. 113-BIT RUN (2026-08-31, mp113 engine): the carrier’s own geometric ledger gives ∫x³/(eˣ−1)dx = 6ζ(4) exactly; ζ(4) computed two independent ways — Euler–Maclaurin rational series (N=1024, through B₈) and π⁴/90 with Machin π — agreeing to 39 decimals (≈ 2⁻¹²⁹), the A−B residual matching the dropped B₁₀ term’s predicted size. Integral = 6.49393940226682914909602217924700741664 at 113+ bits. |
| structured_residual |
symbolic: exact as written. numerical: ≤8.9e-13 relative at double precision |
| falsifier_status |
low-ν RJ recovery: PASS · UV integrability: PASS · independent Planck comparison: PASS (π⁴/15) |
| precision |
208-bit limb engine (mp113.js); two independent formulations; double run retained as the second precision — dual-precision rule satisfied, classification stable |
| standing |
EXECUTED_113BIT — all witnesses PASS at both precisions and both formulations |
| promotion_authority |
GREEN — the work order’s promotion conditions (≥113 bits + independent check) met |
| source_records |
2026-08-31; work order authored by Copilot from internet-sourced physics; certificate architecture and every MN concept Derrick E. Muncy’s; execution run cold by Claude in this project |