tau_0_fs
plain-language theorem explainer
tau_0_fs assigns the numerical value 7.3 to the fundamental tick τ₀ in RS units. Researchers deriving physical constants from the Recognition Science chain cite this when calibrating time scales from coherence energy. The definition is a direct assignment obtained via the IR gate identity relating ℏ to E_coh and τ₀, producing the SI approximation of 7.3 fs.
Claim. $τ_0 = 7.3$ in RS units, where $τ_0$ is the fundamental tick derived from the coherence energy $E_{coh} = φ^{-5}$ through the IR gate identity $ℏ = E_{coh} · τ_0$.
background
The RRF Foundation module derives all constants from φ via gate identities. The coherence energy is defined as $E_{coh} = φ^{-5}$ (approximately 0.09 eV in RS units). The overall chain is φ → E_coh → τ₀ → c → ℏ → G → α^{-1}, with the IR gate stated as ℏ = E_coh · τ₀ and K-gates relating recurrence times to 2π/(8 ln φ).
proof idea
The definition is a direct numerical assignment of 7.3. It is calibrated from the IR gate identity and the upstream value of E_coh. No lemmas or tactics are invoked beyond the constant declaration itself.
why it matters
This supplies the time scale τ₀ that feeds the positivity result tau_0_pos and the subsequent derivations of c, ℏ, G, and α^{-1}. It occupies the τ₀ slot in the derivation chain from φ to physical constants. The value supports the eight-tick octave and the framework's T7 period of 2^3.
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