module module moderate

`IndisputableMonolith.Unification.CriticalRecognitionLoading`

This module defines the native actuation period together with pulseTicks, supervisoryTicks, loadRatio, and the predicates IsUnderloaded, IsSubcritical, IsOverloaded, InCriticalBand, and rhoCriticalMin. Researchers working on holographic bounds and 8-tick recognition cycles cite it to locate critical loading regimes. The module is a collection of definitions and short lemmas that relate the basic tick to its supervisory multiple via lcm and establish the critical-band threshold.

claimLet τ₀ = 1 be the RS time quantum. Define pulseTicks as the base actuation interval, supervisoryTicks as its least common multiple with the 8-tick octave, loadRatio = pulseTicks / supervisoryTicks, and the predicates IsUnderloaded, IsSubcritical, IsOverloaded, InCriticalBand together with the threshold ρ_crit^min such that a boundary lies in the critical band precisely when its recognition load satisfies ρ_crit^min ≤ loadRatio < 1.

background

Constants supplies the fundamental time quantum τ₀ = 1 tick. RecognitionBandwidth records the 8-tick cadence of the recognition operator, the holographic information bound, and the per-bit cost ln(φ). ConsciousnessBandwidth states that a conscious boundary of extent L persisting for τ ticks incurs a maintenance cost bounded by the holographic budget. RecognitionBandGeometry supplies the geometric setting in which these costs are compared across recognition bands. The present module assembles these elements into explicit loading predicates.

proof idea

this is a definition module, no proofs

why it matters in Recognition Science

The definitions supply the critical-band conditions required by the unification of recognition and consciousness bandwidths. They close the gap between the 8-tick octave (T7) and the holographic constraint on conscious extent, preparing the ground for any later theorem that derives stability or phase-transition behavior inside the critical band.

scope and limits

Does not derive ρ_crit^min from the holographic bound.
Does not prove that any physical system actually reaches the critical band.
Does not address time evolution or stability inside the band.
Does not connect loadRatio to measurable observables beyond the RS-native units.

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