IndisputableMonolith.Physics.PhiVsUniformPulseSpacingCert
This module certifies that pulse intervals spaced by the golden ratio φ incur lower J-cost than uniform spacing in RS-native units. Researchers modeling discrete event timing or quantum pulse trains would cite the certification when comparing recognition costs. The module proceeds by introducing auxiliary interval definitions and verifying cost inequalities through direct comparison to uniform_step_cost.
claimThe module introduces the φ-spaced interval with successive ratios φ and certifies that its total J-cost is strictly less than that of uniform spacing over the same number of steps, where J(x) = (x + x^{-1})/2 - 1 and τ₀ = 1 tick.
background
Recognition Science quantizes time in fundamental ticks τ₀ = 1 from the Constants module. The Cost module supplies the J-cost function used to measure recognition effort. This module works in that setting to compare φ-spaced pulse sequences against uniform ones, using the self-similar fixed point φ from the forcing chain.
proof idea
This is a definition module that introduces phiSpacedInterval, phiSpaced_ratio and uniform_step_cost, then establishes the cost inequality phi_beats_2 and the prediction experiment_a_prediction_holds by algebraic reduction of the J expressions.
why it matters in Recognition Science
The module supplies the concrete comparison needed for ExperimentAPrediction and PhiVsUniformCert. It supports the claim that φ spacing aligns with the eight-tick octave and the phi-ladder mass formula by showing lower defect cost than uniform alternatives.
scope and limits
- Does not address continuous-time limits or non-periodic patterns.
- Does not claim global optimality beyond the two-interval comparison.
- Does not incorporate higher-dimensional or multi-particle effects.