Masses Baseline Derivation Quark Baseline Matches Anchor Down

The quark baseline anchor

In the Recognition Science framework, particle masses are organized on a ladder of integer baselines. The declaration quark_baseline_matches_anchor_down is a machine-checked theorem stating that the quark baseline, defined as the number of edges per face of a cube, equals 4, and that this value matches the framework's down-anchor integer for quarks. The proof is a direct computation: the definition of quark_baseline unfolds to edges_per_face at dimension 3, which evaluates to 2^(3-1) = 4, and the anchor value is defined to be the same integer.

The significance is that a quantity previously assumed as a boundary condition, the quark baseline, is now derived from the geometry of the 3-cube. The cube has 6 faces, each with 4 edges, so the number of edges per face is 4. This integer is not fitted to experimental data; it emerges from the combinatorial structure of the cube. The theorem quark_baseline_matches_anchor_down confirms that this derived value is consistent with the framework's internal anchor for the down quark, labeled "d". A companion theorem, quark_baseline_matches_anchor_up, establishes the same match for the up quark anchor "u".

The framework does not claim that this integer 4 is a measured mass or a prediction of a specific quark mass in kilograms or electronvolts. The baseline is a structural index, not a physical mass value. The framework's particle masses sit on a phi-power ladder, and the scaling law is proved separately; the comparison against measured PDG values is an empirical check, not a theorem. The theorem here only establishes an internal consistency: the derived baseline equals the anchor. It does not assert that the down quark has a mass of 4 in any physical unit, nor does it derive the fine-structure constant or any other coupling.

theorem quark_baseline_eq : quark_baseline = 4 := by
  unfold quark_baseline
  exact edges_per_face_at_D3

/-- At D = 3: edges per face = 4. -/
theorem edges_per_face_at_D3 : edges_per_face D = 4 := by native_decide

theorem quark_baseline_matches_anchor_down :
    (quark_baseline : ℤ) = Integers.r_down "d" := by
  simp [quark_baseline, edges_per_face, D, Integers.r_down]

What this page does not claim

The theorem does not claim that the down quark has a mass of 4 in any physical unit. The theorem does not derive the fine-structure constant or any coupling constant. The theorem does not claim the baseline is measured from experiment; it is derived from cube geometry.

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

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