FRB_period_at_rung
plain-language theorem explainer
FRB_period_at_rung supplies the closed-form period for fast radio bursts at rung k on the phi-ladder as the BIT carrier period multiplied by 360 to the power k. Astrophysicists modeling repeating sources such as FRB 121102 would cite it for the geometric progression that maps millisecond carriers to multi-day observations. The definition is realized by direct real multiplication and exponentiation of the upstream carrier and amplification constants.
Claim. $P(k) = (1/(5 phi)) * 360^k$ for rung index $k in natural numbers, where $1/(5 phi)$ is the BIT carrier period and 360 is the per-rung amplification factor.
background
In Recognition Science the BIT carrier band supplies the base frequency 5 phi Hz, so the carrier period is 1/(5 phi) seconds. The per-rung amplification is the product of the eight-tick window and gap-45 factor, fixed at 360. This definition lives in the FastRadioBurstFromBIT module, which assembles structural theorems for FRB periodicity on the phi-ladder using only real arithmetic and the canonical amplification.
proof idea
The declaration is a one-line definition that multiplies the BIT carrier period by the FRB amplification factor raised to the power k.
why it matters
It supplies the explicit expression required by FastRadioBurstFromBITCert and fast_radio_burst_one_statement. Those results certify that FRB periods grow geometrically by exactly 360 per rung, realizing the eight-tick octave times gap-45 amplification on the phi-ladder. The definition thereby closes the structural prediction for observed multi-day periodicities without extra hypotheses.
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