Cosmology Sakharov From Ledger Three Conservation Laws

Three conservation laws

In geometry, a cube in three-dimensional space has three pairs of opposite faces. The Recognition Science framework's declaration three_conservation_laws establishes that this simple fact is the source of three independent conservation laws. It proves, by direct computation, that the number of face pairs in three dimensions is exactly three. This is the framework's account of why baryon number, lepton number, and a third charge appear as separate, conserved quantities in particle physics.

The framework models physical reality as a ledger, a discrete record of recognition events. On a three-dimensional lattice, each axis contributes one pair of opposite faces, and each pair corresponds to a conserved charge. The declaration is a theorem in the machine-checked library of formal theorems, meaning the statement is verified by a computer from the framework's axioms. It does not, by itself, say what those charges are or how they behave; it only establishes that three such charges exist.

In Recognition Science, this geometric fact feeds into the derivation of the Sakharov conditions for baryogenesis, the creation of the matter-antimatter asymmetry. The framework claims that baryon number violation, CP violation, and departure from thermal equilibrium all follow from the ledger structure. The three conservation laws provide the counting: three generations of matter, three charges, three conditions. The framework's library contains a structure packaging all three Sakharov conditions and a theorem asserting they are all satisfied from its first principles.

The declaration does not claim that these three conservation laws are the only ones, nor does it specify their physical content. It does not prove that baryon number is conserved in the Standard Model, nor that the Sakharov conditions are actually met in the real universe. It establishes only the counting fact: in three dimensions, there are three face pairs, and the framework reads this as three independent conservation laws. The physical interpretation and the connection to observed baryogenesis remain the subject of further derivation and empirical check.

/-- The three independent conservation laws in D = 3. -/
theorem three_conservation_laws : face_pairs 3 = 3 := rfl

What this page does not claim

The declaration does not identify which physical quantities the three charges correspond to. It does not prove that baryon number is conserved in the Standard Model. It does not establish that the Sakharov conditions are actually met in the real universe.

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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