Gravity Bhecho Per Event Catalog Rung Ordering

The rung ordering

Gravitational-wave observatories like LIGO and Virgo detect ripples in spacetime from colliding black holes and neutron stars. Some models predict that the merged object does not settle quietly but bounces, producing a train of faint "echoes" after the main signal. A machine-checked library of formal theorems, built inside the Recognition Science framework, assigns each of four headline events a predicted echo delay. The declaration rung_ordering proves that these four predicted delays, when sorted by their associated rung number, fall in a strict sequence.

The four events are GW170817, GW230529, GW150914, and GW190521. Their masses range from about 2.7 to 150 solar masses. The framework assigns each event a recognition rung, a positive integer chosen from a log-scale relation to the source mass. The theorem states, in plain terms, that the predicted rungs satisfy: rung(GW170817) < rung(GW230529) < rung(GW150914) < rung(GW190521). The smallest event sits at rung 1, the largest at rung 10. The proof is a direct check of the four assigned values, and the library records zero unproved assumptions in this file.

The ordering matters because the framework's echo-delay formula is monotone in the rung: a higher rung means a longer predicted delay and a lower echo frequency. So the theorem guarantees that the predicted echo signals for these four events do not cross. GW190521, the most massive, should show the latest echo; GW170817, the lightest, the earliest. The rung_ordering declaration is a certificate that the catalog is internally consistent on this point.

What the theorem does not claim is just as important. It does not assert that any echo has been observed. It does not say the rung assignment itself is derived from first principles; the assignment is a definitional choice, a model input. It does not compare the predicted delays to any measured value. The theorem only certifies a consistency property of the catalog's own predictions. Whether those predictions match the sky is an empirical question, and the catalog itself states that a single high-signal event whose echo appears at the wrong rung would falsify the ladder.

/-- 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

/-- 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 recognition rung for each headline event (chosen from
log-mass scaling: rung N ≈ ⌊log_φ(M / M_ref)⌋). -/
def predictedRung : HeadlineEvent → ℕ
  | .GW150914 => 8
  | .GW170817 => 1
  | .GW190521 => 10
  | .GW230529 => 2

What this page does not claim

No observed echo is claimed; the theorem concerns only predicted values. No comparison to measured echo delays is made. The rung numbers themselves are not derived from the framework's axioms.

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)

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