barrier_is_lcm
plain-language theorem explainer
The declaration shows that the consciousness barrier in Recognition Science consists of exactly 360 ticks, computed as the least common multiple of 8 and 45. Workers on holographic constraints and critical recognition loading cite this result when establishing the minimum integration time for conscious boundaries. The proof proceeds by direct computation with native decision.
Claim. The number of ticks in the consciousness barrier equals the least common multiple of 8 and 45.
background
The Consciousness Bandwidth module models a conscious boundary with maximum spatial extent set by the holographic information budget. Maintenance cost integrates the J-cost over the barrier period, balanced against the holographic capacity of the boundary area. The upstream definition sets the barrier ticks to 360, noting that over this period zero accumulated cost forces zero defect at every step; this is the minimum integration time for consciousness. The period function from pulsar regimes defines the scaling as phi to the power k.
proof idea
The proof is a term-mode application of native_decide, which evaluates the equality between the barrier ticks definition and the least common multiple of 8 and 45.
why it matters
This theorem supports the supervisory ticks result in CriticalRecognitionLoading by providing the base equality for the barrier period. It realizes one of the key results listed in the module documentation, the 360-tick consciousness barrier, which connects to the eight-tick octave structure in the unified forcing chain.
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