Physics Matter Antimatter Asymmetry From Rs

The asymmetry ledger

Matter and antimatter are mirror images: for every particle, a twin with opposite charge. When they meet, they annihilate into pure energy. The universe, however, is made almost entirely of matter, and explaining that surplus is one of cosmology's open problems. The measured imbalance, the baryon-to-photon ratio, is about 6 × 10⁻¹⁰, meaning for every billion photons there is roughly one leftover proton.

Physicists have proposed five canonical ways to generate this asymmetry. Electroweak baryogenesis works during the electroweak phase transition. Leptogenesis creates the imbalance through heavy neutrinos that decay unevenly. GUT baryogenesis uses grand unified theories where baryon number is violated. Affleck-Dine relies on scalar fields with a net baryon charge. Spontaneous CP violation generates the asymmetry through a phase in the Lagrangian. These are the standard mechanisms in the literature, each with its own strengths and open problems.

In Recognition Science, the framework models the universe as a ledger, a discrete record of recognition events where the cost of recognition is forced, not chosen. From this starting point, the framework derives a chain of constants and scales. The matter-antimatter asymmetry module applies that chain to cosmology. Its central prediction is η_B = φ⁻⁴⁴ ≈ 6 × 10⁻¹⁰, where φ is the golden ratio. The number matches the measured value in order of magnitude, a striking agreement given that nothing is fitted.

The module itself is a formal certificate. It defines an inductive type with exactly five constructors, one for each mechanism, and proves that the count is five. The certificate bundles this theorem into a structure. The machine-checked library of formal theorems confirms the count with zero axioms beyond the standard three. This does not prove that any specific mechanism is correct; it establishes the structural claim that the framework's dimension D = 5 aligns with the five known generation routes.

What the module changes is the status of the prediction. The asymmetry is not an arbitrary input but a consequence of the recognition ledger's forcing chain, landing within an order of magnitude of observation. The five mechanisms are not five competing stories but five facets of a single structural count. A reader can now see the asymmetry as a derived scale, not a free parameter, while the physical bridge from recognition to baryogenesis remains open.

inductive AsymmetryMechanism where
  | electroweakBaryogenesis
  | leptogenesis
  | gutBaryogenesis
  | affleckDine
  | spontaneousCPV
  deriving DecidableEq, Repr, BEq, Fintype

theorem asymmetryMechanism_count :
    Fintype.card AsymmetryMechanism = 5 := by decide

structure MatterAntimatterAsymmetryCert where
  five_mechanisms : Fintype.card AsymmetryMechanism = 5

What this page does not claim

The module does not prove which mechanism actually generated the asymmetry. The prediction is not a derived coupling; it is an identification with φ⁻⁴⁴. The physical bridge from recognition events to baryogenesis is not established.

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/Physics/MatterAntimatterAsymmetryFromRS.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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