tau_0_pos
plain-language theorem explainer
The base time quantum expressed in femtoseconds is strictly positive. Researchers tracing the Recognition Science constant chain from the golden ratio through coherent energy would cite this to keep all subsequent time scales well-defined and ordered. The proof is a one-line numerical normalization that directly evaluates the explicit definition of the femtosecond-scale time quantum.
Claim. $0 < t_0$ where $t_0$ is the fundamental time quantum of the Recognition Science framework expressed in femtoseconds.
background
The RRF Foundation module derives all physical constants from the golden ratio via a fixed sequence of gate identities. The chain runs φ to coherent energy E_coh to the base time τ₀ to c, ℏ, G and finally α⁻¹. Key relations include the IR gate ℏ = E_coh · τ₀ and the K-gates that tie recurrence times and lengths to 2π/(8 ln φ).
proof idea
The proof is a term-mode one-liner that invokes the norm_num tactic on the definition of the femtosecond time quantum, reducing the inequality to an immediate numerical check.
why it matters
Positivity of the base time unit closes the initial segment of the constant derivation chain and supports the eight-tick octave structure required for spatial dimension emergence. It supplies a consistency anchor for any later use of the IR gate or Planck gate identities even though the current dependency graph shows no direct downstream citations.
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