breathCycle
The breathCycle definition fixes a time interval of 1024 ticks in the RS-native system. Researchers modeling discrete evolution periods or octave multiples in Recognition Science reference it for scaled time quanta. The definition is a direct multiplication of the imported base tick by the integer 1024, which the comment equates to eight times 128.
claimThe breath cycle duration equals $1024 tau_0$, where $tau_0$ is the fundamental time quantum (one tick).
background
The RSNativeUnits module defines a native measurement system with tick as the base time quantum, the discrete ledger posting interval. Time is an abbreviation for the reals, and all scales sit on the phi-ladder with c equal to 1 in voxel per tick units. Upstream, the Constants module states that one octave equals eight ticks as the fundamental evolution period, while the tick itself is defined as the constant 1.
proof idea
The definition is a one-line wrapper that multiplies the integer 1024 by the tick constant imported from the base Constants module.
why it matters in Recognition Science
This supplies a concrete scaled time interval in the RS-native units, extending the eight-tick octave from the forcing chain T7. It supports period calculations in musical scale and coherence contexts even though no immediate downstream theorems list it as a dependency. The definition fills a gap in the phi-ladder time quanta without invoking the Recognition Composition Law.
scope and limits
- Does not derive the factor 1024 from any upstream theorem.
- Does not include an SI conversion factor.
- Does not specify a physical process that realizes the breath cycle.
- Does not interact with the golden ratio phi or the J-cost function.
formal statement (Lean)
186@[simp] def breathCycle : Time := 1024 * tick
proof body
Definition body.
187
188/-- Convert tick count to octave count (integer division). -/