IndisputableMonolith.Foundation.SimplicialLedger.EdgeLengthFromPsi

This module defines the log-potential assignment ε_i = ln ψ(σ_i) on vertices of the simplicial 3-complex. It supplies the discrete object that ContinuumBridge.laplacian_action and downstream Regge reductions rely on. Researchers closing the discrete-to-continuum gap in Recognition Science cite these definitions when moving from J-cost stationarity to the Einstein equations. The module consists entirely of supporting definitions and no top-level theorems.

claimThe log-potential is the map $\varepsilon : \mathrm{Fin}\, n \to \mathbb{R}$ given by $\varepsilon_i = \ln \psi(\sigma_i)$ on the vertices of the simplicial ledger; the associated edge-length field is obtained by the conformal ansatz $\ell_{ij} = \ell_0 \exp((\varepsilon_i + \varepsilon_j)/2)$.