Cosmology Sakharov From Ledger Sakharov Conditions

The three conditions

In 1967, the Soviet physicist Andrei Sakharov asked what it would take for the early universe to produce more matter than antimatter. He answered with three conditions. First, some process must violate baryon number, the conserved count of protons and neutrons. Second, that process must treat matter and antimatter differently, through charge-parity (CP) violation. Third, the universe must be out of thermal equilibrium, so the reactions do not simply run backward and erase the asymmetry. These three conditions are the standard checklist for baryogenesis, the generation of the matter-antimatter imbalance.

Recognition Science (RS) is a framework that starts from one idea: reality keeps a discrete ledger of recognition events, a record of distinctions made, and the cost of each recognition is fixed by a proved formula. Within that framework, the declaration SakharovConditions packages the three conditions as a single structure. The framework models baryon number as a winding charge on a three-dimensional lattice, so a collective rotation of all three axes, a sphaleron-like process, changes the charge by exactly 3. The framework proves a CP-violating source term is positive, and it defines the electroweak phase transition as first-order, which provides the departure from equilibrium through bubble nucleation.

What the declaration actually establishes is narrower than the full story of baryogenesis. The machine-checked library proves three facts: the baryon number change per sphaleron event equals 3, the CP asymmetry parameter is nonzero, and the transition is first-order. These three facts assemble into a theorem that all three Sakharov conditions hold. The framework does not prove that the universe did undergo baryogenesis, only that the conditions for it are met within its model.

The declaration leaves important physics open. It does not state a baryon-minus-lepton conservation law, because the framework defines only baryon number change, not lepton number change. The actual rate of baryon production, the mass factors in the CP asymmetry, and the precise temperature of the transition are not derived in this framework. The structure is a proof of possibility, not a complete calculation of the observed asymmetry.

/-- CP violation source: J_CP > 0 from JarlskogInvariant. -/
theorem cp_source_positive : jarlskog_structural > 0 := jarlskog_positive

theorem sphaleron_changes_B_by_3 : deltaB_per_sphaleron = 3 := rfl

/-- The departure from equilibrium is provided by the first-order
    nature of the EW phase transition. Bubble nucleation creates
    out-of-equilibrium conditions at the bubble walls. -/
theorem out_of_equilibrium : ew_transition_is_first_order := trivial

/-- The master theorem: baryogenesis is possible in RS because all
    Sakharov conditions are derived (not postulated). -/
theorem baryogenesis_possible :
    deltaB_per_sphaleron = 3 ∧ cp_asymmetry_parameter ≠ 0 ∧ ew_transition_is_first_order :=
  ⟨rfl, cp_asymmetry_nonzero, out_of_equilibrium⟩

What this page does not claim

The framework does not prove that baryogenesis actually occurred in the early universe. The framework does not derive a baryon-minus-lepton conservation law. The declaration does not compute the observed magnitude of the 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/SakharovFromLedger.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

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