pith. machine review for the scientific record. sign in
theorem

bitBandwidthPerCycle_eq

proved
show as:
module
IndisputableMonolith.Complexity.PvsNPFromBIT
domain
Complexity
line
47 · github
papers citing
none yet

plain-language theorem explainer

The per-cycle BIT bandwidth of the recognition substrate is fixed at exactly 360. Researchers deriving exponential lower bounds for NP-search certification on bounded-bandwidth substrates would cite this equality to anchor the constant in the runtime estimate. The proof is a one-line wrapper that unfolds the definition and applies numerical simplification.

Claim. The bandwidth available per recognition cycle satisfies $B = 360$.

background

In the Recognition Science framework the recognition operator acts on a finite-state substrate whose per-cycle BIT bandwidth is bounded. This bandwidth is defined as eight times the consciousness gap and evaluates to 360. The module uses this fixed value to obtain a structural lower bound on the number of cycles needed to certify witnesses for NP-search problems of size n.

proof idea

The proof is a one-line wrapper that unfolds the definition of the per-cycle bandwidth and applies numerical normalization to obtain the constant 360.

why it matters

This equality supplies the constant used by cycles_lower_bound to prove the exponential lower bound and by pvsNP_one_statement to assemble the one-statement P-vs-NP claim. It fixes the BIT bandwidth for the recognition operator in the complexity track, yielding the substrate-dependent bound t ≥ 2^n / 360. The open question it touches is whether any physical recognition substrate can evade the exponential cost.

Switch to Lean above to see the machine-checked source, dependencies, and usage graph.