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Explain the Lean def `fastRadioBurstFromBITCert` in module `IndisputableMonolith.Astrophysics.FastRadioBurstFromBIT`. Write for an educated reader who knows science and programming but may not know Lean. Cover: (1) what the declaration says in plain English, (2) why it matters in Recognition Science, (3) how to read the formal statement, (4) visible dependencies or certificates in the supplied source, and (5) what this declaration does not prove. Cite only declarations present in the supplied Recognition source.

Big AI job. Grok 4.3 reads the canon and writes a Lean-grounded derivation; usually 20 seconds to 2 minutes. Your answer will appear below.
confidence: high in recognition cached

(1) Plain English. The declaration fastRadioBurstFromBITCert is a definition that builds a concrete record (instance) of the FastRadioBurstFromBITCert structure. This record packages eight proved facts: the BIT carrier period equals 1/(5·phi) and lies in (0.12, 0.13) s; the per-rung amplification factor is exactly 360; the FRB period at rung k is BIT_carrier_period · 360^k; adjacent rungs differ by exactly 360; the period is strictly increasing with k; and phi > 1. It is the master certificate for the closed-form FRB period prediction.

(2) Why it matters in Recognition Science. It supplies a theorem-grade, parameter-free structural result that places FRB repeater periods on the phi-ladder using only the recognition cost J and the canonical 8-tick × gap-45 amplification. The module states a sharp falsifier: precision catalogs (CHIME/FRB 2030+) reporting periods off the ladder by more than J(phi) log units would falsify the identification.

(3) How to read the formal statement. In Lean, def fastRadioBurstFromBITCert : FastRadioBurstFromBITCert where constructs the structure by field assignment. Each field receives a previously proved theorem or reflexivity proof from the same module (e.g., BIT_carrier_pos := BIT_carrier_period_pos, FRB_amplification_eq := FRB_amplification_factor_eq, BIT_carrier_period_eq := rfl). The structure type itself lists the eight clauses as fields of type Prop or equality.

(4) Visible dependencies or certificates. The definition directly references and re-exports: BIT_carrier_period_pos, BIT_carrier_period_band, FRB_amplification_factor_eq, FRB_period_at_rung_pos, FRB_period_geometric, FRB_period_strict_increasing, and fast_radio_burst_one_statement. It also uses one_lt_phi (imported via Constants) and the structure FastRadioBurstFromBITCert.

(5) What this declaration does not prove. It establishes only the algebraic and ordering properties of the phi-ladder formula; it does not prove any specific observed FRB period matches a particular rung k, nor does it derive the physical emission mechanism or the value of the single empirical seam tau0_seconds.

cited recognition theorems

outside recognition

Aspects Recognition does not yet address:

  • Empirical match of any specific FRB period to a rung k
  • Physical mechanism producing the radio emission
  • Value or measurement protocol for the single-anchor tau0_seconds seam

recognition modules consulted

The Recognition library is at github.com/jonwashburn/shape-of-logic. The model is restricted to the supplied Lean source and instructed not to invent theorem names. Treat output as a starting point, not a verified proof.