IndisputableMonolith.RRF.Core.Strain
The Strain module defines a strain functional that maps states to non-negative reals, vanishing exactly at balanced equilibria. RRF core developers cite it to anchor cost-based ordering before scaling or categorical constructions. It is a pure definition module with class constraints and no proofs.
claimA strain functional is a map $J : X → ℝ$ satisfying $J(x) ≥ 0$ for every state $x$, with $J(x) = 0$ if and only if $x$ is balanced.
background
This module introduces the strain functional as the basic cost object in the Reality Recognition Framework. It equips an arbitrary state space with a non-negative real-valued map whose kernel marks equilibrium, using a type-class constraint for nonnegativity. Sibling definitions cover predicates for balance, equilibria, minimizers, and ordering relations such as strictlyBetter and weaklyBetter.
proof idea
this is a definition module, no proofs
why it matters in Recognition Science
The module supplies the core strain concept to the RRF.Core umbrella, Glossary, Octave, VantageCategory, and OrderPreservation theorems. It supplies the definitional base for cost ordering that later modules extend to scaling and categorical equivalence.
scope and limits
- Does not introduce physical constants or numerical scales.
- Does not prove existence or uniqueness of equilibria.
- Does not specify the concrete form of the state space X.
- Does not connect to phi-ladder or J-uniqueness from upstream forcing chain.