FalsificationCriteria
plain-language theorem explainer
The FalsificationCriteria structure records the explicit test conditions for the zero-parameter Schumann formula f(n)=(4n-1)φ+3 forced by the Recognition Composition Law. Researchers auditing RS predictions against cavity and EEG data would cite it to state when the Earth-brain resonance claim survives or fails. The definition is a direct record of five string fields that separate the unfalsifiable mathematical core from the empirical falsifiers.
Claim. The falsification criteria consist of the structural statement that $f(n)=(4n-1)φ+3$ is a mathematical theorem, the claim that all five Schumann harmonics lie within 0.06 Hz of the RS prediction, the deviation threshold >0.5 Hz that falsifies the formula, the overlap of harmonics with theta/beta/gamma EEG bands, and the neurochemical-artifact condition that would falsify cavity coupling.
background
The module derives the Schumann spectrum from the Recognition Composition Law. T6 forces φ as the unique self-similar fixed point satisfying x²=x+1. T8 forces D=3 as the spatial dimension arising from linking and synchronization. The formula is written f(n)=(4n-1)φ+3 with zero free parameters; its fundamental equals 3φ²=φ⁴+1 and its spacing equals 4φ. The EarthBrainResonanceCert structure packages the forced equalities together with the empirical match statements. Upstream results supply the J-cost factorization, the phi-ladder tiers, and the stable-state arithmetic used to derive the octave structure.
proof idea
The declaration is a direct definition of a structure whose five fields are string literals. No lemmas are applied; the body simply assigns the descriptive texts that separate the mathematical theorem from the two empirical falsifiers.
why it matters
It supplies the falsification interface for the earthBrainResonance_forced certificate that appears immediately above it in the same module. The criteria close the empirical loop required by the master theorem: the RCL forces φ and D=3, the resulting ladder matches the five measured Schumann lines within 0.06 Hz, and the structure states the precise observations that would refute the cavity-brain coupling. It touches the open question of whether EEG band boundaries are purely neurochemical or contain a geometric component.
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