Gravity Bhecho Per Event Catalog Headline Event

The four catalog events

The Recognition Science framework, which treats physical structure as the forced consequence of a discrete record of events, has produced a machine-checked library of formal theorems. One module in that library, the per-event black-hole echo catalog, names four headline LIGO/Virgo events and assigns each a predicted echo delay. The four events are GW150914, GW170817, GW190521, and GW230529. For each, the catalog records a source mass, a recognition rung (a step on the framework's phi-power ladder), a predicted echo delay, and a predicted echo frequency.

The predictions follow a simple pattern. The delay for each event is phi raised to the rung number, multiplied by the natural logarithm of phi, where phi is the golden ratio. The frequency is the reciprocal of that delay. For GW150914, with rung 8, the predicted delay is phi to the eighth power times log phi. For GW170817, rung 1, it is phi times log phi. The catalog proves, by exhaustive case analysis, that every delay and frequency is strictly positive, and that the four rungs are strictly ordered: the two smaller events sit at lower rungs than the two larger ones.

The catalog's status as a machine-checked theorem means the arithmetic is certain: the delays are positive, the ordering holds, and there are exactly four events. What the catalog does not do is claim that any of these echoes have been observed. The predictions are a testable schedule. The catalog's own documentation states the falsifier: any single high-signal-to-noise event whose echo signature does not appear at the predicted rung would refute the ladder. No LIGO detection of an echo is asserted, and no claim is made about whether the framework's predicted delays match any measured signal.

/-- The four canonical LIGO/Virgo headline events. -/
inductive HeadlineEvent where
  | GW150914
  | GW170817
  | GW190521
  | GW230529
  deriving DecidableEq, Repr, BEq, Fintype

/-- Echo delay per event is strictly positive (every predicted rung is
N ≥ 1; verified by `decide` on the inductive cases). -/
theorem predictedEchoDelay_pos (e : HeadlineEvent) :
    0 < predictedEchoDelay e := by
  unfold predictedEchoDelay predictedRung
  cases e <;> exact echoDelay_pos _ (by decide)

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

/-- Predicted echo delay per event. -/
def predictedEchoDelay (e : HeadlineEvent) : ℝ :=
  echoDelay (predictedRung e)

What this page does not claim

No LIGO detection of an echo is asserted or implied. No claim is made that the framework's predicted delays match any measured signal. The catalog does not derive the fine-structure constant or any other coupling constant.

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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