Verification Gwtc3 Ringdown Status

A status certificate for ringdown tests

The LIGO/Virgo/KAGRA collaboration's third catalog, GWTC-3, is the most recent large public dataset from gravitational-wave observatories. Its tests of general relativity cover the ringdown, the damped oscillation a black hole emits as it settles after a merger, and the search for post-merger echoes, faint repeated pulses that some alternatives to general relativity predict. The collaboration's published abstract reports 15 confident signals in the analyzed O3b subset, no significant evidence for physics beyond general relativity, no post-merger echoes, and consistency of remnant and quasinormal-mode (QNM) behavior with general relativity. It also sets a bound on the graviton mass at or below 2.42 × 10⁻²³ eV/c².

In Recognition Science, the framework's own predictions for these observables are not free parameters. The framework derives a specific echo damping ratio of about 0.618, a rung phase delay of about 0.481, and a leading-log coefficient of about -0.2406. These numbers come from the framework's forcing chain, not from fitting to data. The verification module does not claim that these predictions have been confirmed by the GWTC-3 data. It records the published scalar and status facts from the collaboration and connects them to the framework's internal register rows for echo and QNM attachments.

The module is a status cert, a machine-checked certificate that the published facts are recorded consistently. It is not posterior ingestion: it does not download or analyze the GWTC-3 posterior release files, which would be required for full likelihood-style testing. The certificate's one-statement theorem assembles the positive event count, the positive false-alarm threshold, the positive graviton mass bound, and the three published qualitative statuses into a single proof. The library proves the certificate is inhabited, meaning the record is internally consistent and complete as a status attachment.

What this establishes in plain language is a bookkeeping step. The framework's library now has a formal, machine-checked record that the published GWTC-3 results exist, that they report no echoes and no significant deviation from general relativity, and that the framework's echo and QNM rows have positive sensitivity and target scale. The certificate does not change the physics; it changes the ledger. A reader can now see, in one place, exactly which published facts the framework's verification chain is built on, and which parts of the comparison remain open pending the posterior data analysis.

/-- Number of confident signals analyzed in the relevant GWTC-3 GR-tests subset. -/
def gwtc3AnalyzedEventCount : ℕ := 15

/-- Published status: no post-merger echoes in the analyzed events. -/
def gwtc3NoPostMergerEchoesReported : Bool := true

/-- Published status: remnant/QNM consistency with GR. -/
def gwtc3QNMConsistentWithGR : Bool := true

structure GWTC3RingdownStatusCert where
  event_count_pos : 0 < gwtc3AnalyzedEventCount
  far_threshold_pos : 0 < gwtc3FalseAlarmRateThreshold
  graviton_mass_bound_pos : 0 < gwtc3GravitonMassBound
  echo_dataset_positive :
    HasPositiveSensitivity echoAttachment ∧ HasPositiveTargetScale echoAttachment
  qnm_dataset_positive :
    HasPositiveSensitivity qnmAttachment ∧ HasPositiveTargetScale qnmAttachment
  status_flags :
    gwtc3NoPostMergerEchoesReported = true ∧
    gwtc3NoSignificantGRDeviationReported = true ∧
    gwtc3QNMConsistentWithGR = true

/-- One-statement GWTC-3 status attachment theorem. -/
theorem gwtc3_ringdown_status_one_statement :
    (0 < gwtc3AnalyzedEventCount) ∧
    (0 < gwtc3FalseAlarmRateThreshold) ∧
    (0 < gwtc3GravitonMassBound) ∧
    (gwtc3NoPostMergerEchoesReported = true) ∧
    (gwtc3NoSignificantGRDeviationReported = true) ∧
    (gwtc3QNMConsistentWithGR = true) ∧
    Nonempty GWTC3RingdownStatusCert :=
  ⟨gwtc3AnalyzedEventCount_pos,
   gwtc3FalseAlarmRateThreshold_pos,
   gwtc3GravitonMassBound_pos,
   rfl, rfl, rfl,
   gwtc3RingdownStatusCert_inhabited⟩

theorem gwtc3RingdownStatusCert_inhabited :
    Nonempty GWTC3RingdownStatusCert :=
  ⟨gwtc3RingdownStatusCert⟩

What this page does not claim

The GWTC-3 data confirms the framework's echo or ringdown predictions. The module performs any analysis of the GWTC-3 posterior release files. The framework's specific numerical predictions are derived from the GWTC-3 dataset.

Verify this page

Every tagged claim above names its theorem. To check one yourself rather than trust this page, elaborate the source module with Lean 4 and audit its axiom basis:

$ lake env lean IndisputableMonolith/Verification/GWTC3RingdownStatus.lean
expected axiom basis: [propext, Classical.choice, Quot.sound] (the Lean kernel's standard three; no RS-specific axioms)

A page whose claims cannot be reproduced this way does not ship. In production, every anchor links to the exact declaration in the public source release, and this block carries the build receipt for the page itself.

Derived articles

This page is generated by a question-recursion engine: the questions its answers raise become the next pages. The current agenda, with open targets marked red: