IndisputableMonolith.Unification.RecognitionBandwidth
RecognitionBandwidth fixes the recognition cycle at eight ticks as the base period for one complete event in the ledger. Unification researchers cite it when bounding throughput in holographic or gravitational settings. The module collects the cadence definition together with positivity, monotonicity, and equivalence lemmas that relate bandwidth to cost and bit count.
claimA full recognition cycle has period $8\tau_0$ where $\tau_0$ is the fundamental tick; bandwidth is the reciprocal of this period scaled by the recognition cost function, satisfying $B = \frac{1}{8\tau_0} \cdot \frac{1}{C}$ with $C$ the per-event cost.
background
The module imports the RS time quantum $\tau_0 = 1$ tick from Constants, the Boltzmann constant derivation from ledger bit cost, the ILG framework, the Cost ledger, and the holographic bound on information. It introduces the eight-tick cadence as the minimum duration for one complete recognition event, aligning with the eight-tick octave of the forcing chain. Sibling definitions establish positivity of the cadence, its equality to eight ticks, and the bandwidth function together with its monotonicity and linear scaling properties.
proof idea
This is a definition module whose structure proceeds by declaring the eight-tick cadence, proving its positivity and equality lemmas, then defining bandwidth and deriving its positivity, monotonicity, and equivalence to bits over cost via the imported holographic and cost results.
why it matters in Recognition Science
The module supplies the eight-tick period that downstream modules BandwidthSaturation, BlackHoleBandwidth, ConsciousnessBandwidth, and CriticalRecognitionLoading use to set recognition throughput limits. It realizes the T7 eight-tick octave step of the forcing chain and supplies the base period required for holographic bit-count and ILG gravity derivations.
scope and limits
- Does not derive the integer 8 from the forcing chain axioms.
- Does not compute numerical values of bandwidth for specific systems.
- Does not treat variable or adaptive cycle lengths.
- Does not address multi-cycle batching or saturation regimes.
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