barrierPeriod
plain-language theorem explainer
The declaration defines the consciousness barrier period in RS time units as 360 times the base tick duration τ₀. Researchers bounding conscious extent via holographic information budgets cite this scaling when integrating J-cost over the minimum zero-defect window. It is obtained by casting the natural-number barrierTicks definition to reals and multiplying by τ₀.
Claim. The barrier period is defined by $τ_b := 360 τ_0$, where $τ_0$ is the fundamental recognition time unit and 360 equals the length of the consciousness barrier in ticks.
background
In the Consciousness Bandwidth module a conscious boundary persists for a fixed number of ticks given by the least common multiple of the eight-tick octave and 45, producing the 360-tick consciousness barrier. The upstream definition barrierTicks states: 'The consciousness barrier: lcm(8, 45) = 360 ticks. Over this period, zero accumulated cost forces zero defect at every step. This is the minimum integration time for consciousness.' The module compares the integrated J-cost of boundary maintenance against the holographic capacity $L^2/(4ℓ_P^2)$ of the boundary area to obtain a maximum coherent extent.
proof idea
The definition is a direct one-line scaling that casts barrierTicks to ℝ and multiplies by the constant τ₀. No lemmas or tactics are invoked beyond the casting and multiplication.
why it matters
This definition supplies the integration window for the holographic maintenance budget. It is used by barrierPeriod_eq to prove equality with 360, by barrierPeriod_pos to confirm positivity, and by maintenanceDemand to form the recognition cost 360 · J(L). The 360-tick length originates in the eight-tick octave (T7) combined with the 45-fold structure, closing the minimum integration time for zero-defect consciousness and supporting the viability of the identity scale L = 1.
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