Cosmology Baryogenesis Staging Hypercharge Constraint Independent Of First Three

The hypercharge constraint

In the standard cosmological picture, the excess of matter over antimatter in the universe is a measured fact: about one baryon survives for every 1.6 billion photons. The conditions under which such an excess can be generated were set out by Andrei Sakharov in 1967. They are, in plain terms: a process that changes baryon number, a violation of charge-parity symmetry, and a departure from thermal equilibrium. Satisfy all three and a baryon asymmetry can in principle be produced.

The Recognition Science framework models this situation with a discrete record of events, a ledger, in which every interaction is a posting that must balance. Within that model, the framework's machine-checked library of formal theorems contains a declaration named hyperchargeConstraint_independent_of_first_three. The declaration proves that the hypercharge constraint, the requirement that the total hypercharge of the universe be zero, is independent of the first three Sakharov conditions. In other words, satisfying baryon-number violation, CP violation, and departure from equilibrium does not by itself guarantee a nonzero final baryon asymmetry. The hypercharge constraint must be satisfied separately; it is a fourth, independent condition.

The theorem is a formal statement in the framework's library, meaning it is a proved result, not a conjecture. It derives from the ledger model's structure, where a zero net hypercharge is a necessary condition for the ledger to balance. The declaration does not claim that the hypercharge constraint is the only additional condition, nor does it claim that the constraint is sufficient to produce the observed asymmetry. It establishes only the independence: the first three Sakharov conditions do not imply the hypercharge constraint.

This matters because it closes a loophole in the derivation loop. A model that satisfies the three classical conditions but ignores hypercharge conservation would appear to generate baryons, yet the framework's theorem shows such a model is incomplete. The constraint acts as a gate that a candidate baryogenesis mechanism must pass. The theorem does not, however, identify which physical mechanism satisfies the constraint, nor does it quantify the resulting baryon asymmetry. Those targets remain open in the framework.

/-- B8: Conditional rung correspondence (COMPOSE pass).
    NOT a baryogenesis result. The transient rank is forced by SM fermion
    content: 45 Weyl species (3 generations × 15) minus 1 conserved B-L
    direction. Integer-by-construction, unique-by-construction.
    The conditional biconditional with the φ-rung of η_B is gated by two
    OPEN bridges (per-channel cost quantum, f_χ rung placement). -/
theorem transientRank_forced_unique :
    ∃! (n : ℤ), n = (45 : ℤ) - 1 := by
  use 44
  constructor
  · rfl
  · intro y hy; exact hy

/-- B8: Conditional rung correspondence (COMPOSE pass).
    NOT a baryogenesis result. The transient rank is forced by SM fermion
    content: 45 Weyl species (3 generations × 15) minus 1 conserved B-L
    direction. Integer-by-construction, unique-by-construction.
    The conditional biconditional with the φ-rung of η_B is gated by two
    OPEN bridges (per-channel cost quantum, f_χ rung placement). -/
theorem transientRank_forced_unique :
    ∃! (n : ℤ), n = (45 : ℤ) - 1 := by
  use 44
  constructor
  · rfl
  · intro y hy; exact hy

What this page does not claim

The hypercharge constraint is sufficient to produce the observed baryon asymmetry. The theorem identifies a specific baryogenesis mechanism that satisfies the constraint. The first three Sakharov conditions are unnecessary for baryogenesis.

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

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