QM-SEAM-001EXACT_EXECUTEDS4
MuncyNautics Recovery Certificate · run cold 2026-08-30 · method: MN Seam Recovery v1.0 (phase kept, rank paid, both arms)
WHAT THIS CERTIFICATE RECORDSSource document by Derrick E. Muncy (interface stamp 2026-08-28), verified cold this date. The single-basis probability report preserves populations and discards the off-diagonal coherence carrying relative phase — a proven many-to-one projection. The recovery reconstructs the complete density operator from the two quadrature lanes. The Born rule stays correct; the recovery COMPLETES the report. Physics already accepts this recovery under the name tomography; MN names why it works.
GOVERNING EQUATION AS PROJECTED — THE SEAM
P_Z(rho) = (Tr(Pi_0 rho), Tr(Pi_1 rho)) = (p, 1-p) the projection: rho carries four real parameters (p, |c|, Re c, Im c constrained by |c| <= sqrt(p(1-p))); the Z-basis report keeps ONE. Every state with the same p and any relative phase phi gives the identical report -- the vacuous seam, proven by the witness family rho(phi).
COMPLETE GOVERNING EQUATION — THE RECOVERY
rho = [[p, c*],[c, 1-p]], c = sqrt(p(1-p)) e^{i phi}
reconstruction from the two quadrature lanes (restored arguments, not constants):
Re c = P_X(+) - 1/2 (X-basis lane)
Im c = P_Y(+) - 1/2 (Y-basis lane)
phi = atan2(Im c, Re c); purity check Tr(rho^2) = p^2+(1-p)^2+2|c|^2 = 1 (pure)
Executed cold at p=0.36, phi=1.1: |c| residual 5.6e-17, phi residual 0,
purity 1.000000000000. The recovery is EXACT and the lanes physically exist.
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.
| seam_id |
QM-SEAM-001 |
|---|---|
| species |
S4 -- lane projection (two quadrature lanes discarded) |
| witnesses |
witness_A = rho(p=0.36, phi=1.1); witness_B = rho(p=0.36, phi=2.6) P_Z identical (0.36, 0.64); the states are physically distinct (interfere differently). Seam is real, proven in the source document §3. |
| channels_A_rho_phi_Pi_Lambda |
A: basis seat (Z diagonal vs X/Y off-diagonal)
rho: rank 1 (coherence enters linearly in the quadrature reports)
phi: the relative phase phi -- THE recovered channel
Pi: partner = the conjugate coherence c* (rho Hermitian: the pair closes on the diagonal)
Lambda: lanes {Z populations, X quadrature, Y quadrature}
|
| recovered_value |
c = 0.480000000000 e^{i 1.100000000000} at the test point; reconstruction residuals 5.6e-17 and 0
|
| structured_residual |
|c| residual 5.551e-17 (double-precision floor); phase residual 0.0; purity residual 0.0 |
| falsifier |
state tomography on any prepared superposition: the X/Y lane reconstruction must match the prepared phi. This is routinely PASSED in every qubit lab -- the recovery is the operational content of tomography. |
| promotion |
GREEN — stamped by Derrick E. Muncy’s authority, 2026-08-31 (the record was already EXACT; the stamp is the human promotion the railroad rules require) |
| standing |
EXACT -- executed reconstruction, residual at machine floor, lanes physically realized; source document standing confirmed |
| source_records |
Quantum_Measurement_Diagonal_Seam_Recovery_v1_0 (Derrick E. Muncy, 2026-08-28); cold check this registry 2026-08-30 |
| precision |
double (residuals at 1e-16 floor); symbolic identities exact |