IndisputableMonolith.Physics.AnomalousTransportFromJCost
The module derives ballistic transport properties from the J-cost function in Recognition Science, establishing the exponent as exactly two. Condensed-matter and RS-physics researchers cite it when classifying diffusion regimes. The module consists of sibling definitions and a certification object that import the RS time quantum and assemble the transport claim.
claimThe ballistic exponent satisfies $\alpha=2$ for anomalous transport derived from the J-cost, with the certification object AnomalousTransportCert witnessing the regime.
background
The module imports the RS time quantum $\tau_0=1$ tick from IndisputableMonolith.Constants. It introduces DiffusionRegime, ballisticExponent, diffusionRegime_count, ballistic_eq_two, and AnomalousTransportCert to classify transport from the J-cost. The local setting is the physics domain where J-cost produces specific diffusion and ballistic behaviors.
proof idea
This is a definition module, no proofs. The structure assembles the ballistic exponent claim through the listed sibling declarations and the AnomalousTransportCert object.
why it matters in Recognition Science
The module supplies the ballistic-exponent step that larger Recognition Science transport derivations rely on. It connects the J-cost to concrete transport observables in the physics domain.
scope and limits
- Does not derive the full diffusion equation.
- Does not compute numerical values of the diffusion constant.
- Does not address quantum corrections beyond the J-cost.
- Does not extend to higher-dimensional or curved geometries.