maintenanceDemand
maintenanceDemand defines the recognition cost of sustaining a boundary of spatial extent L across the 360-tick consciousness barrier. Researchers bounding conscious extent by holographic information budget cite it when deriving viability constraints. The definition is a direct product of the barrier period and the J-cost function in RS-native units.
claimThe maintenance demand for a boundary of extent $L$ is $360 · J(L)$, where $J$ is the J-cost function and 360 is the consciousness barrier period in ticks.
background
In the ConsciousnessBandwidth module a conscious boundary persists for the fixed barrier period of 360 ticks, obtained as 45 times the eight-tick octave. The J-cost function, imported from the Recognition module, supplies the per-unit recognition cost; Cost.Jcost is the canonical cost measure from RSNative.Core. The module sets demand equal to barrierPeriod multiplied by J(L) under the convention λ_rec = ℓ_P = 1.
proof idea
One-line definition that multiplies barrierPeriod by Cost.Jcost L, implementing the BoundaryCost formula stated in the module documentation.
why it matters in Recognition Science
This definition supplies the core demand quantity used by IsViable to enforce the holographic viability constraint and by complexDemand to incorporate Z-complexity scaling. It fills the maintenance-demand step in the argument that bandwidth constrains conscious extent, linking directly to the eight-tick octave via the 360-tick period. It touches the open question of the maximum coherent extent L_crit.
scope and limits
- Does not incorporate Z-complexity scaling.
- Does not compare demand against the holographic budget.
- Does not compute the critical extent L_crit.
- Does not introduce empirical constants outside RS-native units.
Lean usage
theorem identity_viable : IsViable 1 := by unfold IsViable maintenanceDemand maintenanceBudget; rw [Cost.Jcost_unit0, mul_zero]; exact le_of_lt (maintenanceBudget_pos (by norm_num))formal statement (Lean)
123noncomputable def maintenanceDemand (L : ℝ) : ℝ :=
proof body
Definition body.
124 barrierPeriod * Cost.Jcost L
125
126/-- Maintenance demand is nonneg for positive extent. -/