period
plain-language theorem explainer
The definition assigns to each natural-number rung k the real value phi^k, supplying the base scaling for periods on the phi-ladder across the five canonical pulsar emission regimes. Astrophysicists deriving regime periods or fast-radio-burst amplification factors in the Recognition Science framework cite it when converting rung indices into dimensionless times. It is introduced as a direct one-line definition with no lemmas or proof obligations.
Claim. The period at rung $k$ is $phi^k$, where $phi$ denotes the golden-ratio fixed point of the Recognition Science forcing chain.
background
The Pulsar Emission Regimes from RS module defines five canonical emission regimes (normal pulsar, millisecond pulsar, magnetar, rotating radio transient, fast radio burst source) that correspond to configDim D=5. Period scaling on the phi-ladder requires that the ratio between adjacent regimes equals phi, with the supplied definition providing the explicit base function period(k).
proof idea
One-line definition that directly sets period(k) := phi^k with no lemmas or tactics.
why it matters
This definition supplies the fundamental rung-to-period map for the phi-ladder, feeding parent results such as fast_radio_burst_one_statement (which states FRB periods as (1/(5 phi)) * 360^k) and ruleOfThirds_lattice_period in aesthetics. It realizes T6 (phi forced as self-similar fixed point) and T7 (eight-tick octave) from the UnifiedForcingChain, enabling the D=3 spatial dimensions to appear in astrophysical periods and closing the B12 astrophysical MHD depth scaffolding.
Switch to Lean above to see the machine-checked source, dependencies, and usage graph.