IndisputableMonolith.Papers.DIF.AmplitudeHypothesis
This module supplies derivation-status labels for candidate ILG amplitudes within the Recognition Science framework. It introduces types such as CandidateStatus and AmplitudeCandidate together with helper functions that mark candidates against phi-ladder and eight-tick conditions. Researchers deriving discrete amplitudes from the J-functional equation would reference these labels to classify which candidates remain viable. The module contains only definitions and no proofs.
claimThe module defines the inductive label type $CandidateStatus$ and the structure $AmplitudeCandidate$ for ILG amplitudes, together with the maps $candidate_phi_sq$, $candidate_phi_3half$, $candidate_eight_tick$ and the status predicate $candidate_phi_sq_status$.
background
Recognition Science derives all physics from the single functional equation whose solutions are built on the J-cost $J(x)=(x+x^{-1})/2-1$ and the self-similar fixed point phi. The imported Constants module fixes the base time quantum as tau_0 = 1 tick. This DIF paper module supplies the classification vocabulary needed to track which candidate amplitudes satisfy the necessary rung and periodicity constraints before any numerical matching is attempted.
proof idea
This is a definition module, no proofs.
why it matters in Recognition Science
The module supplies the classification layer required by the Amplitude Hypothesis in the DIF paper. It sits directly above the Constants module and prepares the labeled candidates that later theorems in the same paper will test against the RCL and the eight-tick octave. No downstream uses are recorded yet.
scope and limits
- Does not compute numerical amplitude values.
- Does not prove any candidate satisfies the full Recognition Composition Law.
- Does not connect candidates to specific mass rungs or the alpha band.
- Does not address Berry creation thresholds or Z_cf.