f0_default
plain-language theorem explainer
The definition supplies a default base frequency f0 for spectral rails as the reciprocal of 2 pi times the fundamental tick duration tau0. Recognition Science workers on cross-domain frequency ladders cite it as a fit-free initialization drawn from RS gates. The implementation is a direct one-line assignment that pulls tau0 from the imported Constants module.
Claim. $f_0 = 1/(2π τ_0)$ where τ_0 is the fundamental tick duration in RS-native units.
background
The SpectralLadder module scaffolds cross-domain spectral rails via the relation f_n = f0 · φ^{2n} with f0 identified as E_coh/h. The local setting treats f0 as a caller-supplied base that can be defaulted to a gate-derived value without external fitting. Upstream, tau0 is defined as the fundamental time unit (duration of one tick) in RS-native units, with sibling definitions in Compat.Constants and Derivation supplying equivalent expressions such as sqrt(hbar_codata * G_codata / (π c_codata^3))/c_codata.
proof idea
The declaration is a one-line definition that directly evaluates the reciprocal of twice pi times the imported tau0 constant.
why it matters
This definition anchors the base frequency for all rail constructions inside the Spectra.SpectralLadder scaffold. It supplies the starting point for the eight-gate coherence test and frequencyOnRail helpers that follow in the same module. The choice aligns with the eight-tick octave structure of the Recognition framework by fixing the zero-rung frequency from the tick duration tau0.
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