barrier_eq
plain-language theorem explainer
The equality establishes that the consciousness barrier period equals 360 ticks as 8 times 45, spanning exactly 45 octaves of the eight-tick structure. Researchers deriving holographic bounds on conscious extent from information budgets cite this when setting the minimum integration interval for zero-defect maintenance. The proof reduces directly to numerical normalization of the barrierTicks definition.
Claim. The consciousness barrier period equals $8 times 45$ ticks.
background
The ConsciousnessBandwidth module imposes holographic constraints on the maximum spatial extent of a conscious boundary (ConsciousnessH). Maintenance cost over τ ticks is τ · J(L / λ_rec), where J is the Recognition Science J-cost; holographic capacity is L² / (4ℓ_P²) with each event costing ln(φ) bits. The barrierTicks definition supplies the integration period over which demand must not exceed this budget.
proof idea
The proof is a one-line wrapper that applies norm_num to the definition of barrierTicks, confirming the numerical identity 360 = 8 * 45.
why it matters
This anchors the 360-tick barrier used in consciousness_barrier and critical_extent_exists to compute L_crit. It instantiates the eight-tick octave (T7) from the forcing chain as the temporal unit, with 45 octaves fixing the minimum zero-defect window for holographic accounting. No downstream uses are recorded yet.
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