NET-SEAM-006SOLVER_EXECUTED · EXACT_EXECUTED_RECIPROCAL_ROOT_WITNESSNET
SOLVER EXECUTED
| context |
WHAT THIS CERTIFICATE RECORDS, IN PLAIN TERMS. The problem: One-Dimensional Fourier Intensity Ambiguity: Executed Reciprocal-Root Witness. This is the SOLVER-EXECUTED version from the Copilot Created store, superseding the earlier scan of the same job. The classical reading projects the complete object to a report — { "X(z)": "z^2-6z+8=(z-2)(z-4)", "Y(z)": "2z^2-9z+4=2(z-1/2)(z-4)", "projection": "A_X(z)=X(z)X(1/z)" }. The MuncyNautics Seam Recovery Method names the lost channels, keeps both arms, and reworks the governing equation — { "equivalence_class": "[X]_A={spectral factors obtained by reciprocal-root selections, modulo declared trivial symmetries}", "repaired_claim": "Fourier intensity recovers the spectral-factor equivalence class. Uniqueness requires a further injective measurement lane." }. Falsifier: { "test": "Any unequal autocorrelation coefficient or trivial scalar/reversal relation invalidates the witness.", "result": "PASS: autocorrelations are [101,-54,8] for both, and the partners are not s. Method: Derrick E. Muncy.
|
|---|---|
| schema |
MN-RECOVERY-CERTIFICATE-1.0 |
| certificate_id |
MN-CERT-NET-SEAM-006-SOLVER-20260829 |
| job_id |
NET-SEAM-006 |
| title |
One-Dimensional Fourier Intensity Ambiguity: Executed Reciprocal-Root Witness |
| author |
Derrick E. Muncy |
| method |
MuncyNautics Seam Recovery Method |
| solver_model |
finite real signal polynomial and reciprocal-root spectral-factor partner |
| governing_formulation |
{
"X(z)": "z^2-6z+8=(z-2)(z-4)",
"Y(z)": "2z^2-9z+4=2(z-1/2)(z-4)",
"projection": "A_X(z)=X(z)X(1/z)"
}
|
| source_signal |
[ "8", "-6", "1" ] |
| partner_signal |
[ "4", "-9", "2" ] |
| source_autocorrelation |
[ "101", "-54", "8" ] |
| partner_autocorrelation |
[ "101", "-54", "8" ] |
| structured_residual |
[ "0", "0", "0" ] |
| reconstruction_error |
0 exact |
| lost_channels |
{
"address": "selected root from each reciprocal pair",
"rank": "root multiplicity",
"phase": "Fourier phase",
"partner": "reciprocal-root spectral factor",
"lane": "additional mask or interference report"
}
|
| reworked_equation |
{
"equivalence_class": "[X]_A={spectral factors obtained by reciprocal-root selections, modulo declared trivial symmetries}",
"repaired_claim": "Fourier intensity recovers the spectral-factor equivalence class. Uniqueness requires a further injective measurement lane."
}
|
| precision |
{
"primary": "exact rational arithmetic",
"secondary": "coefficient-by-coefficient autocorrelation equality"
}
|
| falsifier |
{
"test": "Any unequal autocorrelation coefficient or trivial scalar/reversal relation invalidates the witness.",
"result": "PASS: autocorrelations are [101,-54,8] for both, and the partners are not scalar multiples or scaled reversals."
}
|
| standing |
EXACT_EXECUTED_RECIPROCAL_ROOT_WITNESS |
| 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. |
| phase_retained |
True |
| promotion_authority |
RED |
| generated_utc |
2026-08-30T09:55:21.481925+00:00 |