pith. sign in
inductive

BViolationChannel

definition
show as:
module
IndisputableMonolith.Cosmology.BaryogenesisTrajectoryFromPhiLadder
domain
Cosmology
line
50 · github
papers citing
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plain-language theorem explainer

Canonical B-violation channels in the Recognition Science framework consist of sphaleron transitions, electroweak processes, QCD effects, leptogenesis, and neutrino mass contributions. Cosmologists modeling the eta_B asymmetry growth along the phi-ladder cite this enumeration to confirm exactly five mechanisms operate. The inductive definition directly lists these five cases and derives the necessary typeclass instances for counting and equality.

Claim. The inductive type enumerating the five canonical B-violation channels consists of the constructors sphaleron, electroweak, QCD, leptogenesis, and neutrino-mass.

background

The module establishes the baryogenesis trajectory as a phi-ladder on the temperature axis, with T_k = T_GUT · phi^(-k) and eta_B(T_k) = phi^(k-44). The asymmetry reaches its observed late-time value at rung k=44, growing by exactly phi per rung as the universe cools. This enumeration supplies the five B-violation channels required for asymmetry generation, with the neutrino-mass channel drawing on the upstream definition neutrinoMass(k) := phi^k.

proof idea

The declaration is a direct inductive definition with five constructors. It derives DecidableEq, Repr, BEq, and Fintype instances automatically. No lemmas or tactics are applied beyond the primitive inductive formation.

why it matters

This supplies the five_channels field in BaryogenesisCert, which also requires the rung ratio etaB(k+1)/etaB(k) = phi, completeness at rung 44, and positivity for all k. It anchors the count of violation mechanisms in the phi-ladder model, consistent with the Recognition Science forcing chain through T8 (D=3) and the Recognition Composition Law. The definition closes the enumeration needed for dynamical closure from GUT to late-time scales.

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