Explanation of FastRadioBurstFromBITCert

(1) In plain English, the declaration FastRadioBurstFromBITCert defines a Lean structure (a record type that groups related properties) bundling eight facts: the BIT carrier period 1/(5·phi) is positive and lies in (0.12, 0.13) seconds; the per-rung amplification factor equals exactly 360; the FRB period at rung k is positive for every natural number k; adjacent rungs differ by a factor of exactly 360; the period strictly increases with rung count; the explicit formula BIT_carrier_period = 1/(5·phi); and phi > 1.

(2) This matters in Recognition Science because it supplies a theorem-grade certificate for the structural claim that FRB repeater periods sit on the phi-ladder with canonical 8-tick × gap-45 amplification, yielding the closed-form P_FRB(k) = (1/(5 phi)) · 360^k and a sharp falsifier (periods off the ladder by more than J(phi) log units).

(3) To read the formal statement, treat the structure as a typed container whose fields are named propositions or theorems. Each field (e.g., FRB_period_geometric) asserts a specific property that must be proved; the companion definition fastRadioBurstFromBITCert constructs a concrete inhabitant by supplying the corresponding Lean proofs for every field.

(4) Visible dependencies and certificates in the supplied source include the supporting theorems 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 the summary fast_radio_burst_one_statement that packages the core claims into a single conjunction.

(5) This declaration does not prove any empirical match between the predicted periods and specific observed FRB values (e.g., ~157 days or ~16.35 days), nor does it derive the structure from the absolute-floor or full forcing-chain theorems in other modules; those remain outside its scope.