modal_period
plain-language theorem explainer
Modal period defines the fundamental period of modal evolution as the natural number 8. Researchers modeling possibility spaces in Recognition Science cite it when deriving discrete sampling bounds. The assignment follows directly from the upstream octave definition of eight ticks with no additional lemmas required.
Claim. The fundamental period of modal evolution is $8$.
background
Recognition Science fixes the time quantum as the tick τ₀ = 1 in RS-native units. The Constants module defines octave as 8 * tick, while MusicalScale sets the octave ratio to 2 and notes φ^5 ≈ 11.09. ModalGeometry imports these to treat modal evolution as periodic with this eight-tick interval, matching the T7 step of the unified forcing chain.
proof idea
Direct constant definition that assigns the value 8, inheriting the octave length from Constants without tactic steps or lemmas.
why it matters
The definition supplies the period used by the downstream modal_nyquist_limit, which states the finest modal resolution is one tick and the bandwidth is 4 ticks per octave. It realizes the eight-tick octave from T7 and grounds the Nyquist analogy for modal equivalence in possibility spaces.
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