bitBandwidthPerCycle
The per-cycle BIT bandwidth is fixed at 360 units by multiplying the consciousness gap of 45 by eight. Researchers deriving lower bounds on NP-search certification times in bounded recognition systems cite this value to obtain the exponential runtime requirement t ≥ 2^n / 360. The declaration is a direct numerical definition with no additional reasoning steps.
claimThe per-cycle BIT bandwidth satisfies $B = 8 × 45 = 360$.
background
The module derives structural lower bounds for the recognition operator acting on a finite-state substrate whose per-cycle information processing is limited by BIT bandwidth. The operator performs at most B useful comparisons in time t, so any NP-search problem whose witness requires Ω(2^n) distinguishable comparisons needs t ≥ 2^n / B. The module documentation states: 'Given a finite-state recognition substrate with bandwidth B, the runtime to certify a witness for an NP-search problem of size n is at least 2^n / B.' This is a φ-rung bound on real recognition systems, not a classical Turing separation.
proof idea
The definition is a direct numerical assignment that evaluates 8 multiplied by 45 to obtain the constant 360.
why it matters in Recognition Science
This constant supplies the base value for bandwidthBudget t := B × t and for the structural lower bound certify_requires_budget, which concludes bitBandwidthPerCycle × t ≥ 2^n whenever bandwidthBudget t ≥ npWorkload n. It implements the base case for Track F8 of Plan v5, grounding the exponential bound in the eight-tick octave scaling of the consciousness gap. The module falsifier remains a physical demonstration of polynomial-time solution for an NP-hard problem on a compatible recognition substrate.
scope and limits
- Does not establish a classical separation of P and NP.
- Applies only to substrates compatible with the recognition operator.
- Does not derive the consciousness gap value 45 from first principles.
- Does not address oracle or hypercomputational models.
formal statement (Lean)
45def bitBandwidthPerCycle : ℕ := 8 * 45
proof body
Definition body.
46