Gravity Bhecho Per Event Catalog Predicted Echo Frequency

Predicted echo frequency

Black hole echoes are hypothetical repeating signals that would follow the main gravitational wave burst from a merger, if the new object has a reflective surface just outside its event horizon. The Recognition Science framework's ledger, a discrete record of recognition events, implies such a surface and predicts a specific echo delay and frequency for each event. The declaration predictedEchoFrequency in the machine-checked library of formal theorems defines that frequency for four headline LIGO/Virgo events as the reciprocal of the predicted echo delay: f_echo(N) = 1 / Δt(N).

For each event, the catalog names the source mass M, the recognition rung N (a discrete level chosen from log-mass scaling), the predicted echo delay Δt(N), and the predicted echo frequency f_echo(N). The four events and their rungs are: GW150914 at rung 8, GW170817 at rung 1, GW190521 at rung 10, and GW230529 at rung 2. The delays are expressed in RS-native units, for example 47·log φ for GW150914, where φ is the golden ratio. The framework proves that every predicted delay and frequency is strictly positive, and that the four rungs are strictly ordered by mass, with the two largest events at higher rungs than the two smaller ones.

The catalog is a falsifiable prediction, not a measurement. The framework's library proves the internal consistency of the table, but it does not claim any echo has been observed. The per-event ladder admits falsification by any single high-SNR event whose echo signature does not appear at the predicted rung. The catalog count is exactly four, and the ordering of rungs by mass is part of the certified structure.

/-- Predicted echo frequency per event is `1 / Δt(N)`. -/
def predictedEchoFrequency (e : HeadlineEvent) : ℝ :=
  1 / predictedEchoDelay e

theorem predictedEchoFrequency_pos (e : HeadlineEvent) :
    0 < predictedEchoFrequency e := by
  unfold predictedEchoFrequency
  exact div_pos one_pos (predictedEchoDelay_pos e)

/-- The two largest events (GW190521 and GW150914) sit at higher rungs
than the two smaller (GW170817, GW230529). -/
theorem rung_ordering :
    predictedRung .GW170817 < predictedRung .GW230529 ∧
    predictedRung .GW230529 < predictedRung .GW150914 ∧
    predictedRung .GW150914 < predictedRung .GW190521 := by
  refine ⟨?_, ?_, ?_⟩ <;> decide

What this page does not claim

No observed echo is claimed; the catalog is a prediction, not a detection. The exact numerical value of the echo frequency in physical units (hertz) is not derived here, only the dimensionless RS-native expression. The choice of rung N for each event is a modeling assumption, not a theorem.

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/Gravity/BHEchoPerEventCatalog.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.

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