IndisputableMonolith.Economics.SupplyChainFromRS
This module defines supply chain structures in Recognition Science where optimality requires the J-cost to vanish. Economists deriving efficient logistics from the phi-ladder would cite it for tier counts and zero-defect certificates. It consists entirely of type and function definitions imported from the Cost module, with no theorems or proofs.
claimSupplyChainTier denotes discrete levels in a logistics network; optimal_chain is the configuration satisfying $J=0$ where $J(x)=(x+x^{-1})/2-1$; SupplyChainCert certifies that a tier count achieves this minimum.
background
The module builds directly on the J-cost defined in IndisputableMonolith.Cost, which quantifies deviation from self-similarity via the Recognition Composition Law. It introduces SupplyChainTier as an inductive type for successive stages, supplyChainTierCount as a natural-number measure of depth, and optimal_chain together with SupplyChainCert as the predicate and witness that J vanishes on the chosen structure. The local setting is the application of RS-native units and the phi-ladder to economic flows, treating supply tiers as rungs whose scaling must satisfy the fixed-point condition.
proof idea
This is a definition module, no proofs.
why it matters in Recognition Science
It extends the J-cost formalism from the Cost module to economics, supplying the basic objects needed to embed supply-chain optimization inside the broader Recognition framework. No downstream theorems are recorded yet, but the construction aligns with the forcing chain steps that force phi as the self-similar fixed point and the eight-tick octave periodicity.
scope and limits
- Does not derive explicit numerical tier counts or rung values.
- Does not connect optimality to physical constants such as alpha or G.
- Does not address time-dependent or stochastic supply networks.
- Does not prove existence of finite optimal chains beyond the definitional predicate.