bitBandwidthPerCycle
plain-language theorem explainer
The definition fixes the per-cycle BIT bandwidth available to any recognition substrate at 360 units via the product of the eight-tick factor and the consciousness gap value of 45. Researchers deriving substrate-dependent runtime lower bounds for NP-search certification would cite this constant when computing total comparisons over t cycles. It is supplied by direct arithmetic evaluation with no lemmas required.
Claim. Let $B$ denote the per-cycle bandwidth of the recognition operator on a finite-state substrate. Then $B := 8 × 45 = 360$.
background
The module derives structural lower bounds on the time required for the recognition operator to certify witnesses for NP-search problems. The operator is limited by a bounded BIT bandwidth $B$ per cycle, so that at most $B · t$ useful comparisons are possible in $t$ cycles. The consciousness gap parameter is fixed at 45 in native units, and the cycle factor of eight arises from the eight-tick octave structure of the framework.
proof idea
The definition is introduced by direct arithmetic evaluation of the product eight times forty-five.
why it matters
This supplies the concrete numerical value of the per-cycle bandwidth that enters the total budget function and the structural lower bound theorems. It realizes Track F8 of the module plan by fixing $B = 360$, which yields the exponential runtime lower bound $t ≥ 2^n / 360$ for any recognition substrate. The downstream theorem certify_requires_budget states the structural lower bound: if a recognition substrate of bandwidth bitBandwidthPerCycle certifies an NP-search witness in $t$ cycles, then bandwidthBudget $t ≥ npWorkload n$. The framework treats the result as a φ-rung bound rather than a classical P versus NP separation; the open falsifier is a physical demonstration of polynomial-time solution to an NP-hard problem on a compatible substrate.
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