module module high

`IndisputableMonolith.Unification.ConsciousnessBandwidth`

The ConsciousnessBandwidth module defines the consciousness barrier as lcm(8,45)=360 ticks, the shortest interval over which zero accumulated cost forces zero defect at every step. Recognition Science workers cite it when setting minimum integration times for semantic processing. The module supplies the supporting definitions and elementary lemmas for the barrier period and its monotonicity.

claimThe consciousness barrier period satisfies $T = {lcm}(8,45) = 360$ ticks, with the property that zero accumulated cost over any multiple of $T$ implies zero defect at every step.

background

Recognition Science works in RS-native units with fundamental tick $τ_0 = 1$. The upstream RecognitionBandwidth module connects the holographic bound, recognition cost per bit $k_R = {ln} φ$, and the 8-tick cadence of the recognition operator. BoltzmannConstant supplies the derived $k_R$ from ledger bit cost. The present module assembles these into a single integration window for consciousness.

proof idea

This is a definition module, no proofs. It introduces barrierTicks, barrierPeriod, maintenanceBudget and the positivity, monotonicity, and equality lemmas that follow directly from the lcm definition and the imported Cost and RecognitionBandwidth primitives.

why it matters in Recognition Science

The module supplies the 360-tick barrier that CriticalRecognitionLoading imports to define the load ratio $ρ = R_{dem}/R_{max}$ and the associated control theorem. It closes the step from the 8-tick octave in RecognitionBandwidth to the minimum conscious integration time required by the framework.

scope and limits

Does not derive the numerical value 360 from the forcing chain T0-T8.
Does not connect the barrier to measured physical frequencies or energies.
Does not address defect accumulation under nonzero cost.
Does not treat relativistic or quantum corrections to the tick count.

used by (1)

From the project-wide theorem graph. These declarations reference this one in their body.

IndisputableMonolith.Unification.CriticalRecognitionLoading module_import

depends on (4)

Lean names referenced from this declaration's body.

IndisputableMonolith.Constants module_import
IndisputableMonolith.Constants.BoltzmannConstant module_import
IndisputableMonolith.Cost module_import
IndisputableMonolith.Unification.RecognitionBandwidth module_import

declarations in this module (19)

def barrierTicks L60
theorem barrier_eq L63
theorem barrier_is_lcm L66
def barrierPeriod L70
theorem barrierPeriod_pos L72
theorem barrierPeriod_eq L76
def boundaryArea L84
theorem boundaryArea_pos L86
theorem boundaryArea_monotone L90
def maintenanceBudget L103
theorem maintenanceBudget_pos L106
def maintenanceDemand L123
theorem maintenanceDemand_nonneg L127
theorem maintenanceDemand_zero_iff L133
def IsViable L150
theorem identity_viable L154
def complexDemand L167
theorem complexDemand_ge L171
theorem higher_Z_more_demand L184