ticksToOctaves
plain-language theorem explainer
The definition converts a natural number of discrete time steps into the integer number of eight-tick cycles by division. Physicists modeling ledger-based time evolution would reference it to normalize durations across the fundamental period. The implementation consists of a single integer division operation that directly encodes the octave length fixed by the dimension count.
Claim. The function sending a natural number $t$ of ticks to the natural number $t/8$ of octaves.
background
The RS-native system takes the tick as the base time quantum and the voxel as the base length, with light speed unity. Derived units include the coherence quantum equal to phi to the minus five. The eight-tick octave arises as the period 2 raised to the spatial dimension count, which equals eight when there are three dimensions.
proof idea
The declaration is a direct definition performing integer division of the tick input by eight.
why it matters
It implements the conversion needed for the eight-tick octave in the unified forcing chain. The result feeds into models of musical scales, harmonic modes, and coherence exponents that rely on the periodic structure. It closes the gap between raw tick counts and the octave units used throughout the Recognition framework.
Switch to Lean above to see the machine-checked source, dependencies, and usage graph.