Constants Consistency Tau0 Si

The tick in seconds

A tick is the framework's base unit of time, the discrete step in its record of recognition events. In the framework's own native units, one tick is simply 1, by definition, and the speed of light is 1 voxel per tick. That is a clean internal convention, but it says nothing about how long a tick is in seconds. The declaration tau0_SI supplies that missing link: it defines the tick duration in SI seconds, using the standard CODATA values for the reduced Planck constant, the gravitational constant, and the speed of light.

The formula is √(ħG/(πc³))/c, evaluated with those CODATA numbers. The declaration does not invent a new constant; it converts the framework's derived constants into familiar units. A companion theorem, tau0_SI_eq_derivation, proves that this SI value equals the framework's own derived tick duration, and another lemma proves the result is positive. The framework's library of formal theorems checks both statements mechanically. The practical payoff is that a theorist can take the framework's predictions and compare them directly against laboratory measurements, which are always reported in seconds, not ticks.

What the declaration does not claim is important. It does not assert that this computed value has been measured. It is a definition, a number produced from a formula, not a measurement with a receipt. The library's own summary calls SI values "for external calibration only." The declaration also does not claim that the framework's derived constants are correct; it only claims that the conversion is consistent. If future experiments disagree with the resulting number, that would test the framework's derivations, not this conversion step.

noncomputable def tau0_SI : ℝ :=
  sqrt ((Derivation.hbar_codata) * (Derivation.G_codata) /
        (Real.pi * (Derivation.c_codata) ^ 3)) / Derivation.c_codata

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

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

What this page does not claim

The declaration does not claim the tick duration has been measured. The declaration does not claim the framework's derived constants are correct, only that the unit conversion is consistent. The declaration does not claim the SI value is a fundamental constant of nature.

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)

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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