Verification Gwtc3 Ringdown Kerr22010 Mdamping Family

The damping statistic

When two black holes merge, the new black hole rings like a struck bell, emitting gravitational waves that fade in a characteristic way. The rate of that fading is called the ringdown damping time. In the Recognition Science (RS) framework, this damping is not an accident: the framework's forcing chain (a series of theorems leading from a single cost function to physical constants) predicts a specific value for the damping ratio, namely the inverse of the golden ratio, about 0.618.

The module under discussion, verification (a machine-checked comparison of theory against measured data), tests this prediction against real observations. It uses 22 gravitational-wave events from the GWTC-3 catalog, specifically the Kerr 220 quasi-normal mode, and changes the ringdown start time to 10M (ten times the black hole mass in geometric units). This is the second such controlled test; the first used a start time of 128M. The data pool contains 664,154 posterior samples from the event analyses.

The pooled statistics are stark. The mean damping value is 0.3487, with a standard deviation of 0.1039. The median is 0.3202. The 90% confidence interval runs from 0.2333 to 0.5460, and the 68% interval from 0.2487 to 0.4590. The predicted target of 0.618 lies outside both intervals. In fact, 98.14% of all pooled samples fall below the target, and the pooled mean is 2.59 standard deviations away from it. At the level of individual events, none of the 22 member-level 68% intervals contain the target.

These numbers are recorded as formal theorems in the machine-checked library of formal theorems. The library proves, for example, that the 95th percentile of the pooled distribution is strictly less than the target, that the z-score exceeds 2, and that zero members fall within the 68% interval. The module also proves that this family's mean is less than the mean of the previous 128M family, showing the result is not an artifact of one time window. All of this is done with zero unproven assumptions and zero framework-specific axioms.

The plain-language conclusion is that the RS prediction for the ringdown damping does not match the GWTC-3 data. The measured values cluster around 0.35, far from the predicted 0.618, and the discrepancy is statistically significant. This is a controlled-family test only, not a full analysis of all possible astrophysical effects, but it provides a clear empirical check that fails to confirm the framework's prediction.

def kerr22010PooledMean : ℝ := 0.348730205961

def kerr22010PooledStd : ℝ := 0.103850136706

theorem kerr22010_target_above_pooled_95 :
    kerr22010PooledQ95 < kerr22010RSDampingTarget := by
  obtain ⟨hlo, _hhi⟩ := Constants.PhiLadder.phi_inv_bracket_tight
  unfold kerr22010PooledQ95 kerr22010RSDampingTarget
  linarith

theorem kerr22010_target_above_pooled_84 :
    kerr22010PooledQ84 < kerr22010RSDampingTarget := by
  obtain ⟨hlo, _hhi⟩ := Constants.PhiLadder.phi_inv_bracket_tight
  unfold kerr22010PooledQ84 kerr22010RSDampingTarget
  linarith

theorem kerr22010_no_members_inside68 :
    kerr22010MembersInside68Count = 0 := rfl

theorem kerr22010_z_from_mean_gt_two :
    2 < kerr22010PooledZFromMean := by
  unfold kerr22010PooledZFromMean
  norm_num

What this page does not claim

This module does not claim the RS framework is falsified; it records a controlled empirical test that fails to confirm the prediction. The 22 events are not a complete catalog of all gravitational-wave ringdown observations. The pooled statistics do not account for selection effects or detector calibration uncertainties beyond those in the original event analyses.

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/GWTC3RingdownKerr22010MDampingFamily.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

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