barrierPeriod_eq
plain-language theorem explainer
The equality fixes the consciousness barrier period at exactly 360 ticks, or 45 octaves, in Recognition Science units. Researchers deriving holographic bounds on conscious extent L_crit from boundary maintenance cost versus information capacity would cite this when setting the integration window for N_events. The proof is a direct term-mode unfolding of barrierPeriod, τ₀, tick, and barrierTicks followed by norm_num evaluation.
Claim. The consciousness barrier period equals 360 fundamental time quanta, where the period is the integration window over which boundary maintenance demand is compared to the holographic information budget $S_{holo} = L^2 / (4ℓ_P^2)$.
background
The Consciousness Bandwidth module derives a maximum coherent extent for a conscious boundary by equating total maintenance demand over a fixed period to the holographic capacity of its surface area. The fundamental time quantum is the tick, with τ₀ defined as 1 in RS-native units; one octave comprises 8 ticks per the forcing chain. BarrierPeriod is constructed as 360 ticks (45 octaves) to set the window for N_demand ∝ 360 · J(L / λ_rec) against the budget N_events = L² / (4ℓ_P² · ln(φ)). Upstream, Constants.tick supplies the definition τ₀ := 1 and the octave relation, while NucleosynthesisTiers.of and LedgerFactorization.of calibrate the J-cost and defect accounting used in the demand integral.
proof idea
The term proof unfolds the definitions of barrierPeriod, τ₀, tick, and barrierTicks, then applies norm_num to reduce the resulting numerical expression directly to 360.
why it matters
This equality anchors the 360-tick window required for the holographic constraint argument in the module, directly supporting the key result consciousness_barrier and the subsequent existence of L_crit. It aligns with the eight-tick octave (T7) and D = 3 from the UnifiedForcingChain, ensuring the maintenance budget scales consistently with the phi-ladder and Recognition Composition Law. The fixed period closes the definitional step before bandwidth_constrains_extent and z_complexity_reduces_extent are proved.
Switch to Lean above to see the machine-checked source, dependencies, and usage graph.