IndisputableMonolith.Unification.RecognitionBandwidth
The RecognitionBandwidth module fixes the recognition cycle at eight ticks and defines bandwidth as the ratio of holographic bits to per-cycle cost. Unification researchers working on information limits in gravity or consciousness cite these definitions when bounding throughput. The module consists of definitions plus elementary lemmas establishing positivity, monotonicity, and linearity.
claimOne full recognition cycle has period $8τ_0$. Bandwidth is $B = N_{bits}/C_{cycle}$ where $N_{bits}$ is the holographic information capacity and $C_{cycle}$ is the ledger cost per cycle; $B$ is positive, monotone, and linear in the cost denominator.
background
The module imports the RS time quantum $τ_0 = 1$ tick from Constants, the Boltzmann constant $k_R$ derived from ledger bit cost, the ILG framework, the Cost ledger, and the holographic bound stating that information in a region is bounded by boundary area. It introduces the eight-tick cadence as the minimum duration of one complete recognition operator cycle R̂. The holographic bound supplies the information budget while cost tracks bit expenditure per event.
proof idea
This is a definition module, no proofs.
why it matters in Recognition Science
The definitions feed BandwidthSaturation (ILG gravity from recognition throughput limits), BlackHoleBandwidth (maximal saturation case), ConsciousnessBandwidth (holographic extent constraint), and CriticalRecognitionLoading (load ratio ρ). It quantifies the T7 eight-tick octave by setting the minimum time for a complete recognition event.
scope and limits
- Does not derive the numerical value of bandwidth for concrete physical systems.
- Does not prove the eight-tick period from lower axioms.
- Does not incorporate relativistic corrections to tick counting.
- Does not extend to non-holographic information measures.
used by (4)
depends on (5)
declarations in this module (20)
-
def
eightTickCadence -
theorem
eightTickCadence_pos -
theorem
eightTickCadence_eq -
def
bandwidth -
theorem
planckArea_pos -
theorem
bandwidth_denom_pos -
theorem
bandwidth_pos -
theorem
bandwidth_pos' -
theorem
bandwidth_monotone -
theorem
bandwidth_linear -
def
holographicBits -
theorem
bandwidth_eq_bits_over_cost -
theorem
bandwidth_times_cost_eq_rate -
theorem
Clag_eq_phi_neg5 -
theorem
alpha_locked_in_unit -
def
demandedRate -
theorem
demandedRate_pos -
def
IsSaturated -
def
IsSubSaturated -
theorem
saturated_or_sub