module module moderate

`IndisputableMonolith.Complexity.PvsNPFromBIT`

This module sets the per-cycle BIT bandwidth to 360 RS units via 8 times the consciousness gap of 45. Researchers deriving complexity bounds inside Recognition Science cite these definitions when comparing NP workloads against available bandwidth. The module consists of successive definitions of bandwidthBudget and npWorkload together with their positivity and inequality properties.

claimbitBandwidthPerCycle = 360 with bandwidthBudget and npWorkload defined so that certify_requires_budget and insufficient_budget_no_certify hold.

background

The module imports Constants, where the fundamental RS time quantum satisfies τ₀ = 1 tick, and Cost for cost accounting. It defines bitBandwidthPerCycle explicitly as 8 · consciousnessGap and sets the numerical value to 360. Further definitions introduce bandwidthBudget (zero or successor cases) and npWorkload (positive integer), together with the comparison lemmas certify_requires_budget and insufficient_budget_no_certify.

proof idea

this is a definition module, no proofs

why it matters in Recognition Science

The module supplies the concrete bandwidth limit used in the Recognition Science treatment of P versus NP. It feeds the larger Complexity domain argument that NP certification exceeds the per-cycle BIT budget, connecting to the eight-tick octave and the constants imported from Constants.

scope and limits

Does not derive consciousnessGap from upstream axioms.
Does not treat multi-cycle or parallel BIT computations.
Does not contain the full P versus NP separation theorem.
Does not address non-BIT models of computation.

depends on (2)

Lean names referenced from this declaration's body.

IndisputableMonolith.Constants module_import
IndisputableMonolith.Cost module_import

declarations in this module (16)

def bitBandwidthPerCycle L45
theorem bitBandwidthPerCycle_eq L47
theorem bitBandwidthPerCycle_pos L50
def bandwidthBudget L54
theorem bandwidthBudget_zero L56
theorem bandwidthBudget_succ L59
def npWorkload L67
theorem npWorkload_pos L69
theorem certify_requires_budget L77
theorem insufficient_budget_no_certify L84
theorem cycles_lower_bound L94
theorem npWorkload_succ L104
theorem doubling_separation L110
structure PvsNPFromBITCert L117
def pVsNPFromBITCert L129
theorem pvsNP_one_statement L143