tauZeroDefinition
plain-language theorem explainer
The declaration asserts the existence of a positive real number serving as the fundamental time calibration scalar in Recognition Science. Physicists calibrating RS predictions for cortical resonances and plasma frequencies would cite this when fixing the base time unit. It is introduced directly as the positive existence proposition without further constraints or derivations.
Claim. There exists a positive real number $τ_0 > 0$ that serves as the single calibration scalar setting the Recognition Science time unit.
background
The module presents $τ_0$ as the single calibration scalar that fixes the RS time unit, with an approximate value of $7.3 × 10^{-15}$ s on the femtosecond scale. This scalar supports derivations such as the $5φ$ Hz cortical resonance expressed as $5φ/τ_0$ and Schumann alignments at integer multiples of $φ$ Hz, with numerical checks confirming $5φ$ lies in the cortical alpha interval (8.05, 8.10) Hz and the fifth-mode band (7.5, 8.1) Hz. The setting stresses that uniqueness of this scalar allows all Hz-scale predictions to follow from $τ_0$ alone.
proof idea
The declaration is a direct definition of the existence proposition. No lemmas or tactics are applied; it encodes only the requirement that the calibration scalar be positive.
why it matters
This definition supplies the tau0_exists field inside the TauZeroCert structure, which also records the cortical band and fifth-mode band conditions. It anchors the calibration step that enables cortical resonance and plasma-control predictions at $5φ$ Hz, consistent with the phi-ladder and eight-tick octave landmarks. The module notes the calibration uniqueness from which all frequency results derive.
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