module module high

`IndisputableMonolith.Unification.ConsciousnessBandwidth`

This module defines the consciousness barrier as the period lcm(8,45) equaling 360 ticks, over which zero accumulated cost forces zero defect at every step. It supplies the minimum integration timescale for consciousness in the Recognition Science unification. Researchers modeling semantic condensation or cognitive timescales would cite it when linking recognition bandwidth to temporal structure. The module consists of definitions and elementary lemmas on positivity and monotonicity.

claimThe consciousness barrier period is the time interval $T = 360$ ticks satisfying $T = 360 = 8k = 45m$ for integers $k,m$, such that zero total cost accumulated over one full period implies zero defect at every individual tick.

background

Recognition Science sets the base time quantum to one tick via the Constants module. The upstream RecognitionBandwidth module connects the holographic information bound to the per-bit recognition cost $k_R = ln(phi)$ and the eight-tick cadence of the recognition operator. This module extends that setting by adjoining a 45-tick parameter to produce the least-common-multiple barrier. The BoltzmannConstant and Cost imports supply the energy-temperature ledger used to define accumulated cost.

proof idea

This is a definition module, no proofs.

why it matters in Recognition Science

The module supplies the integration timescale required by the downstream CriticalRecognitionLoading module to define the load ratio rho = R_dem / R_max and sketch its control theorem. It operationalizes the minimum period for zero-defect semantic integration within the recognition bandwidth framework that already incorporates the eight-tick octave and holographic bound.

scope and limits

Does not derive the 45-tick parameter from the phi-ladder or forcing chain.
Does not prove that 360 ticks is the unique global minimum for consciousness.
Does not model concrete physical realizations such as neural or quantum substrates.
Does not address relativistic or higher-dimensional extensions of the barrier.
Does not supply numerical simulations or empirical falsification criteria.

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