NET-SEAM-003 — Dark-Siren Gravitational-Wave Lens Reconstruction: Executed Degeneracy Witness

WHAT THIS CERTIFICATE RECORDS, IN PLAIN TERMS. The problem: Dark-Siren Gravitational-Wave Lens Reconstruction: Executed Degeneracy 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 — { "normalized_images": "x_plus=y+1; x_minus=y-1", "magnifications": "|mu_plus|=1+1/y; |mu_minus|=|1-1/y|", "dimensionless_delay": "Delta_tau=2y", "physical_delay": "Delta_t=D_dt*theta_E^2*Delta_tau", "GW_amplitude_lane": "a_i=sqrt(|mu_i|)/d_L" }. The MuncyNautics Seam Recovery Method names the lost channels, keeps both arms, and reworks the governing equation — { "GW_only_equivalence_class": "[M]_GW={T_s M, MST_lambda M : identical normalized image report, with compensating D_dt and d_L scalings}", "absolute_recovery_condition": "Adjoin EM lens redshift/Einstein radius to separate similarity scale and lens-galaxy velocity dispersion to . Falsifier: { "test": "Find any declared GW-only observable in this model that differs between the constructed partners after compensating transformations.", "result": "PASS: normalized images, physical delay, an. Method: Derrick E. Muncy.

MN-RECOVERY-CERTIFICATE-1.0

MN-CERT-NET-SEAM-003-SOLVER-20260829

NET-SEAM-003

Dark-Siren Gravitational-Wave Lens Reconstruction: Executed Degeneracy Witness

Derrick E. Muncy

MuncyNautics Seam Recovery Method

{
  "title": "Galaxy lens reconstruction based on strongly lensed gravitational waves: similarity transformation degeneracy and mass-sheet degeneracy",
  "url": "https://arxiv.org/abs/2406.06463"
}

dimensionless singular-isothermal-sphere witness with explicit similarity-scale and mass-sheet partner transformations

{
  "normalized_images": "x_plus=y+1; x_minus=y-1",
  "magnifications": "|mu_plus|=1+1/y; |mu_minus|=|1-1/y|",
  "dimensionless_delay": "Delta_tau=2y",
  "physical_delay": "Delta_t=D_dt*theta_E^2*Delta_tau",
  "GW_amplitude_lane": "a_i=sqrt(|mu_i|)/d_L"
}

{
  "y": "0.3",
  "theta_E": "1.7",
  "D_dt": "4200",
  "d_L_GW": "2600",
  "x_plus": "1.3",
  "x_minus": "-0.7",
  "mu_plus": "4.333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333",
  "mu_minus": "2.333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333",
  "Delta_t": "7282.800",
  "a_plus": "0.0008006407690254356674162683488384351873170461510245713215965348628986681026389121154658123220796590496",
  "a_minus": "0.0005875097044815179495625701530420523703826226380471758849496464261419062084035603700774822512171083375"
}

{
  "scale_s": "1.4",
  "theta_E_prime": "2.38",
  "beta_prime": "0.714",
  "D_dt_prime": "2142.857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857143",
  "recovered_identity": "y_prime=y and D_dt_prime*theta_E_prime^2=D_dt*theta_E^2"
}

{
  "lambda": "0.8",
  "beta_prime": "lambda*beta",
  "mu_prime": "mu/lambda^2",
  "D_dt_prime": "5.25e+3",
  "d_L_prime": "3.25e+3",
  "recovered_identity": "Delta_t is preserved by D_dt_prime=D_dt/lambda; GW amplitude is preserved by d_L_prime=d_L/lambda"
}

{
  "address": "lens/source redshift seats",
  "rank": "first independent EM or kinematic lane separating the scale family",
  "phase": "GW arrival phase and time-delay orientation",
  "partner": "similarity-scaled and mass-sheet-transformed families",
  "lane": "GW-only, EM redshift/Einstein-radius, velocity dispersion"
}

{
  "GW_only_equivalence_class": "[M]_GW={T_s M, MST_lambda M : identical normalized image report, with compensating D_dt and d_L scalings}",
  "absolute_recovery_condition": "Adjoin EM lens redshift/Einstein radius to separate similarity scale and lens-galaxy velocity dispersion to separate the H0/mass-sheet branch."
}

{
  "normalized_image_plus_similarity": "0.0",
  "normalized_image_minus_similarity": "0.0",
  "time_delay_similarity": "0e-116",
  "image_plus_mst": "0",
  "image_minus_mst": "0",
  "time_delay_mst": "0.000",
  "gw_amplitude_plus_mst": "2e-123",
  "gw_amplitude_minus_mst": "0e-123"
}

2e-123

3e-173

IDENTICAL at 120 and 170 decimal-digit lanes

0 at both precision lanes for all declared reports

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.

True

{
  "test": "Find any declared GW-only observable in this model that differs between the constructed partners after compensating transformations.",
  "result": "PASS: normalized images, physical delay, and both GW amplitude lanes reconstruct identically."
}

EXACT_EXECUTED_HIGH_PRECISION_CONSTRUCTIVE_WITNESS

This executes and certifies the degeneracy witness for the stated SIS model; it does not select a unique physical lens without independent EM or kinematic data.

RED

2026-08-30T09:49:20.845532+00:00