Cosmology Sakharov From Ledger Cp Asymmetry Nonzero

The CP asymmetry source

In particle physics, the dominance of matter over antimatter in the visible universe is a stubborn fact with a standard explanation. In 1967 Andrei Sakharov listed three conditions a process must meet to generate that imbalance: baryon number must not be conserved, charge-parity (CP) symmetry must be violated, and the universe must have been out of thermal equilibrium. The second condition matters because CP symmetry links matter and antimatter; if it held exactly, any process creating matter would create antimatter at the same rate, and the net asymmetry would stay zero.

The Recognition Science framework, which derives physical structure from a discrete record of recognition events, takes up Sakharov's second condition in its machine-checked library of formal theorems. The library defines a quantity called the CP asymmetry parameter, a real number meant to represent the strength of CP violation available for baryogenesis. The theorem cp_asymmetry_nonzero proves that this parameter is not zero. The proof is direct: the framework has already established that a structural quantity called the Jarlskog invariant is positive, and the asymmetry parameter is defined to equal that invariant, so the parameter inherits the positivity. The chain of definitions and proofs is checked by the library's kernel, so the nonzero conclusion is a theorem in the framework, not a postulate.

What the theorem does not claim is just as important as what it proves. It does not say how large the asymmetry is, only that it is nonzero. It does not identify the measured value of CP violation in the Standard Model, nor does it predict the observed baryon-to-photon ratio of the universe. The parameter is defined as the Jarlskog invariant itself, with no mass factors or other multiplicative terms attached, so it is a structural marker of CP violation rather than a complete physical rate. The library's own notes state that the full baryon production rate would involve mass factors from the framework's mass hierarchy, and those factors are not part of this declaration.

The declaration also does not, by itself, establish that baryogenesis actually occurred. It is one of three Sakharov conditions assembled in the library; the framework packages all three together in a separate structure, and only that assembled result claims that baryogenesis is possible within the framework. A nonzero CP asymmetry is necessary for the matter-antimatter imbalance, but it is not sufficient on its own. The theorem secures one link in a longer chain, and the chain's other links carry their own conditions and their own open questions.

theorem cp_asymmetry_nonzero : cp_asymmetry_parameter ≠ 0 :=
  ne_of_gt jarlskog_positive

/-- The CP asymmetry parameter ε is proportional to J_CP. -/
noncomputable def cp_asymmetry_parameter : ℝ := jarlskog_structural

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

/-- The CP asymmetry parameter ε is proportional to J_CP. -/
noncomputable def cp_asymmetry_parameter : ℝ := jarlskog_structural

What this page does not claim

The theorem does not state the magnitude of the CP asymmetry, only that it is nonzero. The theorem does not predict the observed baryon-to-photon ratio of the universe. The theorem does not by itself establish baryogenesis; it is one of three Sakharov conditions.

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)

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Derived articles

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