module module high

`IndisputableMonolith.Unification.CriticalRecognitionLoading`

The CriticalRecognitionLoading module defines the native actuation period and loading predicates for recognition systems in the unification framework. It introduces pulseTicks as the base cycle, supervisoryTicks as their LCM, loadRatio as rho, and predicates classifying states as underloaded, subcritical, overloaded or in the critical band with rhoCriticalMin. Researchers analyzing holographic bounds and consciousness extent cite these when determining system criticality thresholds. The module consists of definitions and equality lemmas on tick

claimLet $τ_0$ be the fundamental RS time quantum. Define pulseTicks as the native actuation period, supervisoryTicks as the least common multiple of pulses satisfying the equality and LCM properties, loadRatio as $ρ$, and the predicates IsUnderloaded, IsSubcritical, IsOverloaded, InCriticalBand together with the minimum critical density $ρ_{crit,min}$ obeying the defining equality.

background

The module resides in the Unification domain and imports Constants where $τ_0 = 1$ tick is the RS-native time quantum. It draws the 8-tick cadence from RecognitionBandwidth, where the recognition operator completes one cycle per $8τ_0$, together with the holographic information budget and maintenance cost from ConsciousnessBandwidth. RecognitionBandGeometry supplies the band geometry. These imports set the stage for timing structures that classify recognition loading relative to critical density.

proof idea

this is a definition module, no proofs

why it matters in Recognition Science

This module supplies the actuation timing and criticality predicates that feed the unification of recognition bandwidth with consciousness constraints. It connects the eight-tick octave (T7) to holographic boundary analysis and closes the timing layer needed for critical loading statements in the broader framework.

scope and limits

Does not derive the numerical value of pulseTicks from microscopic events.
Does not prove dynamical stability inside the critical band.
Does not treat non-native actuation periods or external driving.
Does not link loadRatio to specific physical constants beyond the imported modules.

depends on (4)

Lean names referenced from this declaration's body.

IndisputableMonolith.Constants module_import
IndisputableMonolith.Unification.ConsciousnessBandwidth module_import
IndisputableMonolith.Unification.RecognitionBandGeometry module_import
IndisputableMonolith.Unification.RecognitionBandwidth module_import

declarations in this module (29)

def pulseTicks L44
def supervisoryTicks L47
theorem supervisoryTicks_eq L49
theorem supervisoryTicks_is_lcm L52
theorem pulse_divides_supervisory L56
def loadRatio L64
def IsUnderloaded L68
def IsSubcritical L72
def IsOverloaded L76
def InCriticalBand L80
abbrev rhoCriticalMin L84
theorem rhoCriticalMin_eq L86
def InForcedCriticalBand L90
theorem loadRatio_pos L93
theorem criticalBand_implies_subcritical L98
theorem criticalBand_not_overloaded L109
def semanticFreeEnergy L121
theorem higher_entropy_lowers_freeEnergy L125
theorem higher_berry_lowers_freeEnergy L135
def SemanticCondensationGate L146
theorem semanticGate_implies_attention_cap L154
theorem semanticGate_implies_gap_ready L161
structure ControllerState L171
def IsCriticalRecognitionLoading L185
def IsForcedCriticalRecognitionLoading L192
def loadPenalty L196
theorem loadPenalty_zero_of_critical L199
theorem criticalRecognitionLoading_certificate L211
theorem forcedCriticalRecognitionLoading_certificate L226