(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.