INET-DIVERGENCE-002EXECUTED_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. The classical 3Nk_B is retained as the high-temperature limit; the mode address ω, phonon census, occupancy and Debye cutoff restored. All three witnesses now computed.
GOVERNING EQUATION AS PROJECTED — THE SEAM
C_V,classical = 3Nk_B for all T (every vibrational lane projected to full occupancy; fails as T → 0)
COMPLETE GOVERNING EQUATION — THE RECOVERY
C_V(T) = 9Nk_B(T/Θ_D)³ ∫₀^{Θ_D/T} x⁴eˣ/(eˣ−1)² dx
EXECUTED: ∫₀^∞ x⁴eˣ/(eˣ−1)²dx = 25.975757609063624 vs 4π⁴/15 (residual −3.7e-12)
Witness A (low-T): coefficient 12π⁴/5 = 233.781818481606 recovered as 233.781818481573 — the T³ law
Witness B (high-T): C_V/(3Nk_B) = 0.987611, 0.998003, 0.999875 at T/Θ = 2, 5, 20 — Dulong–Petit recovered
Witness C: intermediate-T trace computed; monotone between the two laws
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-002 (work order Copilot 2026-08-31, executed same date) |
|---|---|
| executed_results |
DOUBLE RUN: residual 3.7e-12. 113-BIT RUN (2026-08-31, mp113 engine): the mode-lane ledger gives ∫x⁴eˣ/(eˣ−1)²dx = 24ζ(4) exactly; ζ(4) by two independent routes (Euler–Maclaurin vs Machin π⁴/90) agreeing to 39 decimals. Integral = 25.9757576090673165963840887169880296666 at 113+ bits; low-T coefficient 12π⁴/5 exact by the same ledger. |
| structured_residual |
both asymptotic laws recovered numerically; intermediate-T residual bounded by the integral residual |
| falsifier_status |
low-T T³ law: PASS · 3N mode census: PASS · declared-material trace vs data: EXECUTED (2026-08-31, classical Kittel Θ_D values): Cu 23.36 vs 24.44 measured, Al 22.55 vs 24.20, Pb 24.79 vs 26.44, Si 19.95 vs 19.79, diamond 4.07 vs 6.11 (J/mol·K at 298 K) — metals within 4–8%, Si within 1%; the systematic deficit is itself classically attributed (C_p−C_V dilation + electronic term, channels the phonon-only model deliberately excludes); diamond within the published Θ_D-source spread. Lane CLOSED at SUPPORTED |
| precision |
208-bit limb engine (mp113.js); two independent formulations; dual-precision rule satisfied |
| standing |
EXECUTED_113BIT — mathematical witnesses PASS at both precisions; material lane EXECUTED against classical data (5 materials) — no OPEN items remain |
| promotion_authority |
GREEN — all lanes executed; certificate complete |
| 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 |