referenceFreq
plain-language theorem explainer
The definition sets the reference band-gap center frequency to the dimensionless constant 1 in Recognition Science native units. Materials physicists modeling photonic metamaterials with golden-ratio lattices cite it as the base for scaling frequencies along the phi-ladder. It is a direct constant assignment with no computation or lemmas required.
Claim. The reference band-gap center frequency is defined by $ω_0 := 1$ (dimensionless in RS-native units).
background
The module treats photonic metamaterials with golden-ratio lattice geometry as exhibiting a φ-laddered family of band gaps, where the dimensionless gap-center frequency ω_n / ω_0 lies on the phi-ladder with adjacent-rung ratios exactly φ. This matches the structural prediction of RS_PAT_018 and empirical self-similar cascades in 1D Fibonacci photonic crystals. Upstream results supply the rung and gap primitives: rung assigns integer levels by sector (e.g., silicate = 0, metallic_Fe = 4), while gap is the product of closure and Fibonacci factors (claimed equal to 45) or the closed-form display function F(Z) = ln(1 + Z/φ) / ln(φ).
proof idea
Direct definition that assigns the constant 1. No lemmas or tactics are invoked; the body is a single literal.
why it matters
This supplies the base frequency for gapFreq(k) := referenceFreq * phi^k and the positivity theorem gapFreq_pos. It anchors the module's main result MetamaterialBandGapCert, which encodes the phi-ladder band-gap prediction. The choice aligns with framework landmarks T6 (phi as self-similar fixed point) and the eight-tick octave scaling, providing the unit convention for the alpha band and mass-ladder formulas.
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