PulsarRegime
plain-language theorem explainer
Recognition Science classifies pulsar sources into five emission regimes whose periods scale by successive factors of phi on the ladder. Astrophysicists modeling population statistics or emission mechanisms would cite the enumeration when enforcing the configDim D = 5 constraint and the adjacent-regime ratio. The declaration is a direct inductive type equipped with Fintype derivation, allowing immediate cardinality and decidability results.
Claim. The set of pulsar emission regimes consists of five elements: normal, millisecond, magnetar, rotating radio transient, and fast radio burst source, with the property that the period ratio between adjacent regimes equals phi.
background
The module introduces five canonical pulsar emission regimes under the Recognition Science treatment of astrophysical MHD, where the number of regimes equals configDim D = 5. Periods are required to lie on the phi-ladder so that the ratio between successive regimes is exactly phi, consistent with the self-similar fixed point forced in the T0-T8 chain. The inductive definition supplies the finite type whose cardinality is later certified to be five.
proof idea
The declaration is a direct inductive definition enumerating the five constructors normal, millisecond, magnetar, rrat, and frbSource. Derivation of Fintype, DecidableEq, Repr, and BEq is automatic and supplies the decidable equality and finite cardinality needed by downstream statements.
why it matters
PulsarRegime supplies the carrier type for the structure PulsarEmissionCert, which records the exact count of five regimes together with the phi-ratio and positivity conditions. It realizes the configDim D = 5 requirement for pulsar populations and connects the phi-ladder scaling to the eight-tick octave and the Recognition Composition Law. No open scaffolding remains; the definition is complete and zero-sorry.
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