IndisputableMonolith.Information.LocalCache
This module defines total access cost without cache as the weighted sum of frequencies times distances, plus cached variants and local cache benefit using J-cost. Researchers modeling information hierarchies cite these primitives to analyze cache optimization. The module supplies only definitions, importing J-cost from Cost and the time quantum from Constants.
claimTotal access cost is defined as $C = f_i d_i$ (summed), with cachedAccessCost and local_cache_benefit obtained by subtracting J-cost savings at the cache boundary.
background
Recognition Science models information flow via J-cost, the functional J(x) = (x + x^{-1})/2 - 1 drawn from the Cost module. Constants supplies the RS time quantum τ₀ = 1 tick. This module introduces local cache structures to quantify access penalties in hierarchies of positive reals.
proof idea
This is a definition module, no proofs.
why it matters in Recognition Science
The definitions feed IndisputableMonolith.Information.PhiHierarchyGrowth, whose doc-comment states that J-cost gradient descent on cache hierarchies necessarily converges to the Fibonacci/φ partition. The module supplies the cost functions required for that convergence argument.
scope and limits
- Does not prove any convergence or optimality result.
- Does not specify concrete frequency or distance values.
- Does not connect costs to physical units beyond imported constants.
- Does not simulate or numerically evaluate hierarchies.
used by (1)
depends on (2)
declarations in this module (16)
-
def
totalAccessCost -
def
cachedAccessCost -
theorem
local_cache_benefit -
def
fibonacci_recurrence -
def
constant_ratio -
theorem
fibonacci_ratio_forces_golden -
theorem
fibonacci_partition_forces_phi -
theorem
Jcost_symmetry_forces_geometric_boundary -
def
synapse_cost -
theorem
Jcost_pos_away_from_one -
theorem
hebbian_sign_structure -
theorem
Jcost_min_at_one -
theorem
Jcost_pos_of_ne_one -
def
working_memory_capacity -
theorem
working_memory_approx -
def
localCacheStatus