pith. machine review for the scientific record. sign in

Explain the Lean def `matchesPhiPeak` in module `IndisputableMonolith.Experiments.Protocols`. Write for an educated reader who knows science and programming but may not know Lean. Cover: (1) what the declaration says in plain English, (2) why it matters in Recognition Science, (3) how to read the formal statement, (4) visible dependencies or certificates in the supplied source, and (5) what this declaration does not prove. Cite only declarations present in the supplied Recognition source.

permalink: https://pith.science/recognition/ask/explain-the-lean-def-matchesphipeak-in-module-indisputablemo-b9876dec · first asked 2026-05-10 · browse all asks

Big AI job. Grok 4.3 reads the canon and writes a Lean-grounded derivation; usually 20 seconds to 2 minutes. The page will refresh to your answer when it’s ready.
confidence: high in recognition cached

Explanation of matchesPhiPeak

(1) In plain English: matchesPhiPeak returns true if a measured frequency f lies within the given tolerance of any of six predicted EEG peak locations: φ raised to the powers -2, -1, 0, 1, 2, or 3 (approximately 0.38 Hz, 0.62 Hz, 1 Hz, 1.62 Hz, 2.62 Hz, 4.24 Hz).

(2) Why it matters in Recognition Science: It supplies the concrete matching test used by the EEG falsification protocol. Recognition Science predicts that coherent brain states produce spectral peaks at golden-ratio multiples of a base frequency; this definition lets experimental data be checked against that hypothesis in a machine-readable way.

(3) How to read the formal statement: The declaration is a noncomputable definition returning Bool. It takes two real-number arguments f and tolerance, computes the absolute difference of f from each of the six φ-powers, tests whether each difference is strictly less than tolerance, and returns the disjunction of those six Boolean results. All operations are standard real arithmetic.

(4) Visible dependencies or certificates in the supplied source: The definition appears verbatim in IndisputableMonolith.Experiments.Protocols. It references the module-local φ and is invoked inside isEEGFalsified to count matching peaks. It is also used by the list eegPredictions. The module contains only definitions and structures; no theorems or certificates are present.

(5) What this declaration does not prove: It does not establish that any φ-peaks exist in real EEG recordings, nor that the Recognition Science predictions are empirically correct. It is a pure computational predicate with no soundness or completeness proof attached. The surrounding module likewise supplies protocol scaffolding but no empirical data, statistical theorems, or derivations of the underlying φ-forcing results.

cited recognition theorems

outside recognition

Aspects Recognition does not yet address:

  • Empirical EEG datasets or statistical tests confirming φ-peaks
  • Proofs of the φ-forcing theorems (located in other modules)
  • Any guarantee that the tolerance values or min_matches thresholds are optimal

recognition modules consulted

The Recognition library is at github.com/jonwashburn/shape-of-logic. The model is restricted to the supplied Lean source and instructed not to invent theorem names. Treat output as a starting point, not a verified proof.