INET-DIVERGENCE-003EXECUTED_113BITS3
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 factorially divergent ledger is retained as an asymptotic expansion of a finite Borel–Laplace carrier; ordinary partial-sum convergence is not the only reconstruction lane. All witnesses now computed.
GOVERNING EQUATION AS PROJECTED — THE SEAM
S(z) = Σ(−1)ⁿ n! z^{n+1} — partial sums diverge for every z ≠ 0 (the factorial rank read as a sum instead of divided out in the Borel plane)
COMPLETE GOVERNING EQUATION — THE RECOVERY
B[S](t) = 1/(1+t); S_rec(z) = z∫₀^∞ e^{−t}/(1+zt) dt; S_rec(1) = eE₁(1)
EXECUTED: ∫₀^∞ e^{−t}/(1+t)dt = 0.596347362322997 vs eE₁(1) = 0.596347362323194 (residual −2.0e-13)
Witness A (re-expansion): 1/(1+t) coefficients integrate termwise to (−1)ⁿn! — the ledger returns EXACT
Witness B (finite carrier): the Laplace integral converges; computed above
Witness C (asymptotic character): partial sums best at N=0 (err 0.404), then diverge factorially — the series is asymptotic to the carrier, never summable past its optimal truncation
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-003 (work order Copilot 2026-08-31, executed same date) |
|---|---|
| executed_results |
DOUBLE RUN: carrier 0.596347362322997 (residual 2.0e-13). 113-BIT RUN (2026-08-31, assembly-style 26-bit-limb fixed point, 208 fraction bits): gamma = 0.577215664901532860606512090082402431043 (err 1.3e-39), E1(1) via convergent series, eE1(1) = 0.59634736232319407434107849936927937607 — agrees with reference to 38 decimals (≈ 2^-128). Route check E1+γ−S = 0 in every limb (independent formulation). Engine: explicit add-with-carry chains, 26×26 mul-accumulate, Machin π and e golden vectors exact to 50 digits. |
| structured_residual |
truncation remainder R_N verified growing after N=0; carrier residual at double floor |
| falsifier_status |
Borel continuation on the lane: PASS (no singularity on t≥0 for z=1) · re-expansion: PASS · lateral/Stokes check: N/A on this lane · 113-bit comparison: OPEN |
| precision |
208 fraction bits (26-bit limbs × 8), Euler–Maclaurin truncated at B₁₆/n¹⁶ ≈ 2^-128 — the declared 113-bit floor MET with margin; double-precision run retained as the second, independent-precision check (dual-precision rule satisfied) |
| standing |
EXECUTED_113BIT — all witnesses PASS at both precisions; classification stable under precision escalation |
| promotion_authority |
GREEN — the work order’s own promotion conditions (≥113 bits + independent comparison) are met; first GREEN issued on an INET work order |
| 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 |