supervisoryTicks
plain-language theorem explainer
supervisoryTicks defines the supervisory horizon as the 360-tick consciousness barrier. Control theorists working on recognition bandwidth and load-ratio stability cite this constant to fix the integration window for persistence checks. The definition is a direct alias to the upstream barrierTicks value, which equals lcm(8,45).
Claim. Let $T_s$ denote the supervisory horizon. Then $T_s = 360$, where 360 equals the least common multiple of the 8-tick pulse period and the 45-octave barrier period.
background
The Critical Recognition Loading module introduces the load ratio rho = R_dem / R_max as the central control variable for bounded recognition regions. Healthy operation is claimed to lie in the narrow band rho_min < rho < 1, with the actuator on the native 8-tick cadence while stability is judged over the 360-tick supervisory horizon forced by lcm(8,45). This horizon supplies the minimum integration time for consciousness checks.
proof idea
This is a one-line definition that directly aliases barrierTicks. No tactics or lemmas are applied beyond the alias.
why it matters
The definition supplies the fixed 360-tick window required by the critical recognition loading certificates. It is referenced in criticalRecognitionLoading_certificate and forcedCriticalRecognitionLoading_certificate, which conclude subcritical operation together with bounds on attention and z. The period realizes the eight-tick octave extended across 45 repetitions, consistent with the T7 landmark in the forcing chain.
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