IndisputableMonolith.Unification.RecognitionBandwidth
RecognitionBandwidth fixes one complete recognition cycle to eight fundamental ticks as the minimal processing interval. It supplies the temporal granularity and bandwidth function used in saturation, black-hole, and consciousness models. The module consists of definitions for the eight-tick cadence together with positivity, monotonicity, and linearity lemmas on the bandwidth derived from holographic bits over cost.
claimOne full recognition cycle satisfies $T=8$ ticks. Bandwidth is $B=N_h/C$ where $N_h$ is the holographic bit count from the boundary area and $C$ is the recognition cost per cycle.
background
The module rests on the fundamental tick $τ_0=1$ from Constants and the holographic bound derived from ledger projection, which limits information content to boundary area rather than volume. It introduces the eight-tick cadence as the period of a complete recognition event and defines bandwidth via the ratio of holographic bits to cost, consistent with the Boltzmann analog obtained from ledger bit cost.
proof idea
This is a definition module, no proofs. It states the eight-tick cadence, proves positivity and monotonicity of bandwidth, and records the equality bandwidth equals holographic bits over cost.
why it matters in Recognition Science
This module supplies the bandwidth primitive required by BandwidthSaturation to derive ILG gravity from recognition throughput limits, by BlackHoleBandwidth for the maximal saturation case, by ConsciousnessBandwidth for the holographic constraint on conscious extent, and by CriticalRecognitionLoading for the load-ratio control variable.
scope and limits
- Does not derive the numerical value of the Boltzmann constant.
- Does not compute bandwidth for concrete physical systems.
- Does not incorporate multi-cycle batching or time kernels.
- Does not address temperature-energy relations beyond basic cost.
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