module module high

`IndisputableMonolith.Information.LocalCache`

The LocalCache module supplies cost accounting for uncached and cached access in information hierarchies. It defines totalAccessCost as the weighted sum of frequencies times distances, plus cachedAccessCost and local_cache_benefit, together with lemmas on Fibonacci recurrence, constant ratio, and J-cost symmetry. Researchers analyzing cache optimization under Recognition Science cite these when deriving self-similar partitions. The module contains only definitions and supporting calculations with no proofs.

claimtotalAccessCost = $\sum_i f_i d_i$ (weighted sum of access frequencies $f_i$ and distances $d_i$); cachedAccessCost is the corresponding reduced sum after local storage; local_cache_benefit is their difference. Supporting results include the Fibonacci recurrence $F_n = F_{n-1} + F_{n-2}$, constant_ratio forcing the golden ratio, and J-cost symmetry forcing geometric boundaries.

background

This module belongs to the Information domain. It imports the RS time quantum $\tau_0 = 1$ tick from Constants and the J-cost framework from Cost. The supplied doc-comment states that totalAccessCost is the weighted sum of access frequencies times distances. Sibling definitions cover cachedAccessCost, local_cache_benefit, fibonacci_recurrence, constant_ratio, fibonacci_ratio_forces_golden, fibonacci_partition_forces_phi, Jcost_symmetry_forces_geometric_boundary, synapse_cost, Jcost_pos_away_from_one, hebbian_sign_structure, and Jcost_min_at_one.

proof idea

This is a definition module, no proofs.

why it matters in Recognition Science

The definitions feed directly into the PhiHierarchyGrowth module, whose doc-comment states that J-cost gradient descent on cache hierarchies necessarily converges to the Fibonacci/φ partition. The module therefore supplies the cost model required for the argument that self-similar hierarchies arise from gradient flow on J-cost.

scope and limits

Does not prove convergence of any hierarchy to a fixed point.
Does not define the full space of cache hierarchies.
Does not connect definitions to the T0-T8 forcing chain.
Does not compute numerical values inside the alpha band.
Does not address mass formulas or Berry thresholds.

used by (1)

From the project-wide theorem graph. These declarations reference this one in their body.

IndisputableMonolith.Information.PhiHierarchyGrowth module_import

depends on (2)

Lean names referenced from this declaration's body.

IndisputableMonolith.Constants module_import
IndisputableMonolith.Cost module_import

declarations in this module (16)

def totalAccessCost L26
def cachedAccessCost L31
theorem local_cache_benefit L46
def fibonacci_recurrence L63
def constant_ratio L67
theorem fibonacci_ratio_forces_golden L73
theorem fibonacci_partition_forces_phi L108
theorem Jcost_symmetry_forces_geometric_boundary L138
def synapse_cost L183
theorem Jcost_pos_away_from_one L192
theorem hebbian_sign_structure L210
theorem Jcost_min_at_one L228
theorem Jcost_pos_of_ne_one L231
def working_memory_capacity L245
theorem working_memory_approx L247
def localCacheStatus L264