tick_partition
plain-language theorem explainer
The theorem records that five mass accumulation ticks plus three light emission ticks equal the eight total ticks per recognition cycle. Modelers of stellar mass-to-light ratios cite this fixed partition when converting the recognition cost differential into a phi-ladder exponent. The proof is a direct reflexivity check on the three constant definitions.
Claim. In the eight-tick recognition cycle the mass accumulation ticks and light emission ticks satisfy $5 + 3 = 8$.
background
The module derives stellar mass-to-light ratios by minimizing total recognition cost during collapse, using the convex cost J(x) = ½(x + 1/x) - 1. It adopts the eight-tick octave as the fundamental evolution period, assigning the first five ticks to mass storage (matter recognition events) and the final three to photon emission. The upstream definitions encode this split directly: mass_ticks := 5 with the comment that the 5:3 partition determines the base M/L scaling, light_ticks := 3, and total_ticks := 8. The constant tick is the RS-native time quantum τ₀ = 1.
proof idea
The proof is a one-line term that applies reflexivity to the numeric constants mass_ticks, light_ticks, and total_ticks.
why it matters
This equality supplies the integer partition required by the module's main result that stellar M/L lies on the phi-ladder with typical value phi^1. It implements the eight-tick octave (T7) from the forcing chain and fixes the scaling tier used in the recognition-weighted collapse argument. No downstream theorems yet reference it.
Switch to Lean above to see the machine-checked source, dependencies, and usage graph.