tick
plain-language theorem explainer
The tick sets the fundamental RS time quantum to 1 in native units. Researchers modeling 8-tick cycles for photobiomodulation patterns or FRB carrier bands cite it to anchor all dimensionless periods and masses. It is introduced by direct definition with no reduction steps or lemmas.
Claim. The fundamental RS time quantum satisfies $τ_0 = 1$ in native units, where $τ_0$ is the base tick for all periods and the eight-tick octave.
background
The Constants module fixes base quantities in RS-native units with $c=1$. Tick supplies the time scale for the octave, defined as 8 times tick, which realizes the eight-tick evolution period. Upstream results include the MusicalScale octave as the ratio 2 and the statement that one octave equals 8 ticks as the fundamental evolution period.
proof idea
This is a direct definition that assigns the real number 1. No lemmas or tactics are invoked; the declaration serves as the base case for subsequent simp reductions in dependent calculations.
why it matters
The definition anchors the Recognition framework by fixing the time base for the T7 eight-tick octave landmark and supplies the unit for downstream results including the rs_pattern_window_neutral theorem and FRB period bands. It closes the unit convention inside the self-reference structure and enables all phi-ladder scalings for masses and frequencies.
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