Constants Consistency Tau0 Si Pos

The SI tick

The Recognition Science framework builds its physics from a discrete ledger of events, and its native unit of time is the tick: one step in that record. In the framework's own units, the tick duration τ₀ is set to 1 by definition. The declaration tau0_SI_pos is a machine-checked theorem that the same duration, when expressed in seconds using SI-calibrated constants, is a positive real number.

The proof is short and direct. The module defines tau0_SI as √(ħG/(πc³))/c, using CODATA values for the reduced Planck constant ħ, the gravitational constant G, and the speed of light c. A companion theorem, tau0_SI_eq_derivation, shows this SI expression equals the framework's own derived tau0. The positivity lemma then follows from the already-proved positivity of that derived value. In plain terms: the framework's fundamental time step, however you calibrate it, is not zero and not negative; it is a genuine, positive duration.

This is a consistency check, not a new physical prediction. The declaration does not assign a numerical value to the tick in seconds; it only proves that the value is positive. It does not claim that the SI expression is the correct measured duration of anything in the laboratory. The SI-calibrated value exists for external calibration, to compare the framework's internal scale against experiment, and the positivity lemma is a guardrail ensuring that comparison starts from a physically sensible quantity.

/-- τ₀_SI is positive. -/
lemma tau0_SI_pos : 0 < tau0_SI := by
  rw [tau0_SI_eq_derivation]
  exact Derivation.tau0_pos

/-- The τ₀_SI matches Derivation.tau0. -/
theorem tau0_SI_eq_derivation : tau0_SI = Derivation.tau0 := by
  unfold tau0_SI Derivation.tau0
  rfl

What this page does not claim

The declaration does not assign a specific numerical value to the tick in seconds. The declaration does not claim the SI expression is a measured laboratory duration. The declaration does not establish that the framework's derived constants match experimental values.

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/Constants/Consistency.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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