bhEchoCatalogCert
plain-language theorem explainer
The definition assembles the black hole echo catalog certificate by supplying the fixed count of four headline events together with per-event positivity of bounce radii, delays, and frequencies plus the rung ordering among them. Gravitational wave researchers testing Recognition Science predictions would cite this certificate when confronting the phi-ladder forecasts with LIGO/Virgo data. The construction is a direct record that references the decide-based count, the per-event positivity lemmas, and the local rung ordering theorem.
Claim. Let $C$ be the black hole echo catalog certificate. Then $C$ consists of the structure with event count equal to 4, strictly positive predicted bounce radius for every headline event, strictly positive predicted echo delay for every headline event, strictly positive predicted echo frequency for every headline event, and the rung ordering GW170817 rung < GW230529 rung < GW150914 rung < GW190521 rung.
background
The BHEchoCatalogCert structure records the per-event black hole echo predictions inside the Recognition Science gravity module. It demands that the catalog contains exactly four headline events, that bounce radius, echo delay, and echo frequency are each strictly positive at every event, and that the assigned rungs obey the chain GW170817 < GW230529 < GW150914 < GW190521. The module tabulates the predictions in RS-native units using the phi-ladder: GW150914 at rung 8 with delay 47 log phi, GW170817 at rung 1 with delay phi log phi, and similarly for the remaining two events. Upstream results include the rung_ordering theorem from AnimalZComplexityBound establishing a full strict ordering on cognitive rungs and the local event_count theorem fixing the catalog size at 4 by decision.
proof idea
This definition is a direct construction of the BHEchoCatalogCert structure. It assigns event_count from the decide-based theorem, bounce_pos from the per-event bounce radius positivity lemma, delay_pos from the echo delay positivity lemma, freq_pos from the echo frequency positivity lemma, and rung_ordering from the local ordering result.
why it matters
This certificate supplies the concrete per-event predictions that instantiate the generic structural catalog for direct comparison with LIGO data. It completes the per-event tables described in the module documentation and inherits rung ordering from the cognitive complexity bounds. The construction relies on the phi-ladder and positivity at rungs N greater than or equal to 1 from the forcing chain, leaving open the question of explicit data confrontation since no downstream uses are recorded.
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