eegPredictions
The definition supplies an explicit list of six predicted EEG frequency peaks located at successive integer powers of the golden ratio phi, each equipped with bandwidth, minimum amplitude, and confidence parameters. Researchers designing EEG experiments to test the Recognition Science voxel model would reference this list when searching for phi-scaled oscillations in meditative states. The definition is realized by direct enumeration of the phi-ladder entries without additional computation or lemmas.
claimThe set of predicted EEG peaks consists of six records, one for each integer mode index n from -2 to 3, with central frequency phi^n Hz (setting phi^0 = 1), bandwidth 0.2 Hz, minimum amplitude 0.5 or 1.0 mu V^2/Hz, and detection confidence 0.95.
background
The module formalizes testable predictions from voxel theory, listing EEG phi-frequencies as peaks at phi^n Hz during meditation together with mode ratios, healing mechanisms, and explicit falsification criteria for each hypothesis. All entries remain hypotheses rather than theorems. The EEGPrediction structure records a predicted peak by its mode index n (corresponding to frequency phi^n), central frequency, bandwidth (default 0.2 Hz), minimum amplitude, and confidence level. This definition draws on the phi emergence axioms and simplicial ledger geometry to ground the listed frequencies.
proof idea
The definition constructs the list by direct enumeration of the six phi-powered frequencies together with their fixed bandwidth, amplitude, and confidence values. No lemmas are invoked; the list is written out explicitly using the phi constant imported from the emergence axioms.
why it matters in Recognition Science
This definition supplies the concrete EEG predictions checked by the theoryConfirmed predicate, which returns true only when none of the five falsification flags (including the EEG flag) are raised. It implements the first core prediction in the experimental protocols module: peaks at phi^n Hz during meditation. Within the Recognition Science framework it makes the phi self-similar fixed point (T6) and the eight-tick octave (T7) directly observable in brain wave data.
scope and limits
- Does not establish that the listed frequencies will appear in actual EEG recordings.
- Does not define the procedure for detecting peaks or computing statistics.
- Does not extend to frequencies beyond the theta band.
- Does not apply to non-meditation or pathological brain states.
formal statement (Lean)
62noncomputable def eegPredictions : List EEGPrediction :=
proof body
Definition body.
63 [⟨-2, φ^(-2 : ℤ), 0.2, 0.5, 0.95⟩, -- ~0.38 Hz (infra-slow)
64 ⟨-1, φ^(-1 : ℤ), 0.2, 0.5, 0.95⟩, -- ~0.62 Hz (delta-low)
65 ⟨0, 1, 0.2, 1.0, 0.95⟩, -- 1.00 Hz (delta-high)
66 ⟨1, φ, 0.2, 1.0, 0.95⟩, -- ~1.62 Hz (delta-theta)
67 ⟨2, φ^(2 : ℤ), 0.2, 0.8, 0.95⟩, -- ~2.62 Hz (theta-low)
68 ⟨3, φ^(3 : ℤ), 0.2, 0.5, 0.95⟩] -- ~4.24 Hz (theta)
69
70/-- FALSIFICATION: The EEG prediction is falsified if no φ-peaks found -/