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module module moderate

IndisputableMonolith.Physics.DecaySpectrumFromPhiLadder

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The module defines types and functions for decay channels and lifetimes derived from the phi-ladder in Recognition Science. Particle physicists modeling decays would cite these to assign lifetimes via rung numbers and phi exponents. It is a definition-only module with no theorems, importing only the base constants.

claimLet $J$ be the recognition cost and $phi$ the golden ratio fixed point. A decay channel is a pair of states on the phi-ladder; lifetime assigns $tau_0 phi^k$ for integer $k$ determined by the channel; DecaySpectrumCert certifies the resulting spectrum.

background

The module sits inside the Recognition Science derivation of physics from the single functional equation. It imports the RS time quantum tau_0 = 1 tick from Constants and builds directly on the phi-ladder mass formula. Sibling definitions introduce DecayChannel as the classification of allowed modes, lifetime and lifetime_ratio as the phi-exponent maps, lifetime_pos for positive branches, and DecaySpectrumCert as the certifying object for the full spectrum.

proof idea

This is a definition module, no proofs.

why it matters in Recognition Science

These definitions supply the decay-spectrum layer that feeds parent theorems on particle lifetimes and spectra higher in the Recognition framework. They instantiate the phi-ladder for decays, linking to the eight-tick octave and the mass formula yardstick * phi^(rung - 8 + gap(Z)).

scope and limits

depends on (1)

Lean names referenced from this declaration's body.

declarations in this module (7)