IndisputableMonolith.Foundation.MultiChannelJCost
The MultiChannelJCost module defines multi-channel J-cost as the sum of individual per-channel J-costs. Experimental validation teams cite it when aggregating costs across independent substrates. The module supplies the Jcost_n family of definitions and basic lemmas.
claim$J_n(\{x_i\}_{i=1}^n) = \sum_{i=1}^n J(x_i)$ where $J$ denotes the single-channel J-cost.
background
The module imports IndisputableMonolith.Cost, which supplies the base J-cost function obeying the Recognition Composition Law. Multi-channel J-cost extends this by summation to handle independent channels or substrates.
Sibling definitions cover Jcost_n together with non-negativity, the zero condition, and symmetry. These rest on the single-channel properties already established in the Cost module.
proof idea
This is a definition module, no proofs.
why it matters in Recognition Science
Definitions here are imported by ThreeSubstrateValidationCert, which certifies J-cost behavior across language-model, photonic-qubit, and magnetized-plasma substrates. The module supplies the aggregation step required for the RS Exp B summary.
scope and limits
- Does not derive the base J-cost function.
- Does not prove non-negativity or symmetry (handled by siblings).
- Does not link to forcing-chain steps or physical constants.
- Does not contain experimental data or numerical checks.