ml_from_phase_ratio
plain-language theorem explainer
The declaration establishes that the mass-to-light phase ratio equals exactly 5/3 from the fixed tick counts in one recognition cycle. Researchers deriving cosmological M/L values from ledger topology rather than external observations would cite this when grounding the ratio in the eight-tick partition. The proof reduces immediately to numerical normalization of the two phase constants.
Claim. The ratio of mass-accumulation ticks to light-emission ticks satisfies $m/l = 5/3$, where $m$ counts the mass-bearing events and $l$ the photon-emitting events in one cycle.
background
The module derives the mass-to-light ratio from the recognition ledger by partitioning the eight-tick cycle into mass-accumulation and light-emission phases. massPhase is defined as the integer 5 counting mass-bearing ticks; lightPhase is defined as the integer 3 counting light-emitting ticks. The phase ratio is fixed by ledger topology, so the resulting M/L inherits algebraic structure from the cycle rather than from external data.
proof idea
One-line wrapper that applies norm_num to the constants massPhase and lightPhase, unfolding their definitions and confirming the numerical equality 5/3.
why it matters
This theorem supplies the phase-fraction step in the Gap 10 derivation, showing M/L emerges directly from the 5:3 partition of the eight-tick octave rather than as an empirical input. It supports the module claim that M/L inherits the φ structure from phase ratios and closes one route from ledger topology to observed galaxy-cluster ratios.
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