tauZero_exists
The declaration establishes existence of a positive real calibration scalar τ₀ for the Recognition Science time unit. Researchers deriving cortical resonance frequencies at 5φ/τ₀ or Schumann alignments would cite this to fix the scale. Proof proceeds by exhibiting the witness 1 and invoking the standard positivity fact for one.
claimThere exists a positive real number τ₀ such that τ₀ > 0.
background
The module sets τ₀ as the single calibration scalar fixing the RS time unit, from which all Hz-scale predictions such as the 5φ cortical resonance and Schumann alignments follow. tauZeroDefinition is the proposition asserting existence of a positive real number for this scalar. The upstream definition states exactly that τ₀ is a positive calibration scalar.
proof idea
The proof is a direct witness construction supplying the number 1 together with the standard lemma that one is positive.
why it matters in Recognition Science
This existence result supplies the required premise for the TauZeroCert definition, which bundles the cortical resonance band and fifth mode band. It anchors the RS time calibration for deriving frequency predictions from the phi ladder and eight-tick octave structure.
scope and limits
- Does not fix any numerical value for the calibration scalar.
- Does not derive the femtosecond scale estimate.
- Does not prove uniqueness of the scalar.
formal statement (Lean)
49theorem tauZero_exists : tauZeroDefinition := ⟨1, one_pos⟩
proof body
50