Cosmology Baryogenesis Trajectory From Phi Ladder B Violation Channel Count

The five channels

In the standard cosmological picture, the excess of matter over antimatter that fills the universe today has to come from somewhere. Physicists call the general requirement baryogenesis: some process, early in the hot dense phase, must have created a tiny surplus of baryons (the family of particles that includes protons and neutrons) over antibaryons. The surplus is measured by a number called the baryon asymmetry, written η_B. In the Recognition Science framework, that asymmetry is not a free input but a quantity that grows along a fixed ladder as the universe cools. The framework's machine-checked library of formal theorems defines a trajectory for η_B and, separately, counts the channels through which baryon number could be violated.

The declaration bViolationChannel_count is the counting theorem. It states that the set of baryon-number-violating channels has exactly five members. The five are named in the library: sphaleron, electroweak, QCD, leptogenesis, and neutrino-mass. A sphaleron is a particular field configuration in the standard model of particle physics that can change baryon number; electroweak and QCD refer to the weak and strong nuclear forces respectively; leptogenesis is a mechanism that generates the asymmetry through lepton physics; neutrino-mass refers to processes involving the tiny masses of neutrinos. The theorem is proved by a direct computation over the finite list, and the library records that the proof uses no axioms beyond the ambient type theory's standard ones. The count of five is not an accident in the framework: it matches the number of spatial dimensions that the framework forces in a separate chain of theorems, a connection the library's documentation notes.

What the theorem does not claim is just as important as what it proves. It does not say that all five channels actually operated in the early universe, nor that any one of them is the real cause of the observed asymmetry. It does not specify the rates at which these processes ran, nor the temperatures at which they switched on or off. The theorem is purely combinatorial: given the framework's list of five named channels, the count is five. The physical question of which channel, if any, dominated baryogenesis remains open, and the theorem itself is silent on it.

theorem bViolationChannel_count : Fintype.card BViolationChannel = 5 := by decide

/-- Canonical B-violation rungs (5 = configDim D): sphaleron, electroweak,
QCD, leptogenesis, neutrino-mass. -/
inductive BViolationChannel where
  | sphaleron
  | electroweak
  | qcd
  | leptogenesis
  | neutrinoMass
  deriving DecidableEq, Repr, BEq, Fintype

theorem bViolationChannel_count : Fintype.card BViolationChannel = 5 := by decide

What this page does not claim

The theorem does not claim that any of the five channels actually operated in the early universe. The theorem does not specify the rates or temperatures at which the channels act. The theorem does not identify which channel produced the observed matter-antimatter asymmetry.

Verify this page

Every tagged claim above names its theorem. To check one yourself rather than trust this page, elaborate the source module with Lean 4 and audit its axiom basis:

$ lake env lean IndisputableMonolith/Cosmology/BaryogenesisTrajectoryFromPhiLadder.lean
expected axiom basis: [propext, Classical.choice, Quot.sound] (the Lean kernel's standard three; no RS-specific axioms)

A page whose claims cannot be reproduced this way does not ship. In production, every anchor links to the exact declaration in the public source release, and this block carries the build receipt for the page itself.

Derived articles

This page is generated by a question-recursion engine: the questions its answers raise become the next pages. The current agenda, with open targets marked red: