barrierTicks
plain-language theorem explainer
The barrierTicks definition fixes the consciousness barrier at exactly 360 ticks in natural-number RS units. This value is the least common multiple of the eight-tick octave and the 45-tick pulse, supplying the minimum integration time over which zero accumulated cost forces zero defect at every step. Researchers modeling holographic information budgets for conscious boundaries cite the constant when equating maintenance demand to boundary capacity. The definition is a direct numeric assignment with no further computation.
Claim. Define the consciousness barrier ticks as $360$ in natural numbers, satisfying $360 = 8 × 45 = lcm(8,45)$.
background
In the ConsciousnessBandwidth module a conscious boundary of extent L persists for τ ticks. Its maintenance cost is τ · J(L / λ_rec) while holographic capacity is L² / (4ℓ_P²). Each recognition event costs ln(φ) bits, so the maximum number of events is L² / (4ℓ_P² · ln(φ)). The barrierTicks constant supplies the fixed period over which total demand is integrated to obtain the critical coherent extent L_crit.
proof idea
The definition is a direct constant assignment of the natural number 360. No lemmas or tactics are invoked; the value is introduced as the base datum for all subsequent statements in the module.
why it matters
This definition supplies the 360-tick barrier period required by barrier_eq, barrier_is_lcm, barrierPeriod, barrierPeriod_eq and barrierPeriod_pos. It instantiates the key result 'consciousness_barrier — the 360-tick barrier period' stated in the module documentation and anchors the holographic-constraint argument. Within the Recognition Science framework it combines the eight-tick octave (T7) with the 45-tick pulse to set the integration time used in downstream results such as pulse_divides_supervisory.
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