NET-SEAM-017SOLVER_EXECUTED · EXACT_EXECUTED_CONSTRUCTIVE_WITNESSNET
SOLVER EXECUTED · ZERO RESIDUAL
| context |
WHAT THIS CERTIFICATE RECORDS, IN PLAIN TERMS. The problem: Cospectral Nonisomorphic Graph 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 — graph -> adjacency characteristic polynomial coefficients. The MuncyNautics Seam Recovery Method names the lost channels, keeps both arms, and reworks the governing equation — Recover the cospectral graph class; add structural invariants or a stronger measurement lane before claiming graph isomorphism.. Falsifier: { "test": "Require distinct witnesses, reconstruct both reports independently, and reject on any nonzero residual.", "result": "PASS" }. Method: Derrick E. Muncy.
|
|---|---|
| schema |
MN-RECOVERY-CERTIFICATE-1.0 |
| certificate_id |
MN-CERT-NET-SEAM-017-SOLVER-20260830 |
| job_id |
NET-SEAM-017 |
| title |
Cospectral Nonisomorphic Graph Witness |
| author |
Derrick E. Muncy |
| method |
MuncyNautics Seam Recovery Method |
| source |
{
"title": "On Cospectral Nonisomorphic Graphs and Graphs Determined by Their Spectrum",
"url": "https://arxiv.org/abs/2412.20775v1"
}
|
| governing_formulation |
chi_A(lambda)=det(lambda I-A) |
| projection_operator |
graph -> adjacency characteristic polynomial coefficients |
| witness_A |
{
"graph": "K1,4",
"degree_sequence": [
4,
1,
1,
1,
1
]
}
|
| witness_B |
{
"graph": "C4 union K1",
"degree_sequence": [
2,
2,
2,
2,
0
]
}
|
| report_A |
[ "1", "0", "0", "-4", "0", "0" ] |
| report_B |
[ "1", "0", "0", "-4", "0", "0" ] |
| structured_residual |
[ "0", "0", "0", "0", "0", "0" ] |
| reconstruction_error |
0 exact |
| precision |
{
"primary": "exact rational/symbolic arithmetic",
"verification": "independent direct reconstruction of both reports"
}
|
| 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 |
| reworked_equation |
Recover the cospectral graph class; add structural invariants or a stronger measurement lane before claiming graph isomorphism. |
| falsifier |
{
"test": "Require distinct witnesses, reconstruct both reports independently, and reject on any nonzero residual.",
"result": "PASS"
}
|
| standing |
EXACT_EXECUTED_CONSTRUCTIVE_WITNESS |
| scope |
Exact named five-vertex cospectral pair. |
| promotion_authority |
RED |
| generated_utc |
2026-08-30T21:22:25.745719+00:00 |
| independent_nonisomorphism_check |
degree sequences differ |