emSpectrumCert
plain-language theorem explainer
The emSpectrumCert definition assembles a certificate for the electromagnetic spectrum organized into five phi-scaled bands with a cortical carrier frequency in (8,9) Hz. Physicists modeling spectral structure via Recognition Science would cite it to confirm the five-band phi-ladder configuration. It is assembled as a direct structure instance that supplies the band count, ratio property, and carrier bounds from three upstream theorems.
Claim. The electromagnetic spectrum admits a certificate $C$ such that the number of bands satisfies $|B|=5$, consecutive band frequencies obey $ν_{k+1}/ν_k=φ$ for all $k$, and the cortical carrier frequency lies in the open interval $(8,9)$ Hz.
background
The module organizes the electromagnetic spectrum into five canonical bands (radio through gamma) where each band spans one phi-decade, so $ν_k=ν_0 φ^k$. The structure EMSpectrumCert requires exactly five bands, the uniform ratio property, and a carrier frequency in (8,9) Hz tied to biological resonances. Upstream, emBandCount enumerates the five bands by decidable finiteness, bandRatio proves the ratio equals phi by algebraic simplification of the frequency definition, and corticalCarrier_band supplies the numerical bounds via phi inequalities.
proof idea
The definition constructs the EMSpectrumCert instance by direct field assignment: five_bands is supplied by emBandCount, phi_ratio by bandRatio, and carrier_band by corticalCarrier_band.
why it matters
This definition supplies the concrete certificate that realizes the phi-ladder description of the electromagnetic spectrum inside the Recognition Science framework. It closes the local construction in the ElectromagneticSpectrumFromPhiLadder module and aligns with the self-similar fixed point that forces phi as the scaling constant. No downstream theorems yet reference it, so its integration into larger derivations such as the eight-tick octave or mass ladder remains open.
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