IndisputableMonolith.Ethics.LoveUniquenessDerivation
The LoveUniquenessDerivation module introduces ethical structures in Recognition Science by defining agent states where sigma quantifies imbalance. It equips these states with lattice transforms and a loveOperator that drives equilibration while preserving total sigma. The module supplies the definitions and lemmas needed to treat love as a unique fixed point in agent lattices. Researchers extending the framework to social dynamics would cite these objects when formalizing ethical equilibrium.
claimAn agent state carries an imbalance measure $sigma$. The love operator $L$ acts on states so that single-lattice and cross-lattice transforms preserve $sigma$ under automorphisms and conserve total imbalance under coupling, with $L$ driving individual $sigma$ toward the global equilibrium.
background
The module sits in the Ethics domain and imports only Mathlib. Its central definition is AgentState, whose field sigma measures imbalance in the sense of the Recognition Composition Law. SingleLatticeTransform and CrossLatticeTransform encode intra-agent and inter-agent updates. The lemmas automorphism_preserves_sigma and coupling_conserves_total record the invariance properties of these transforms. The loveOperator is introduced together with the statements love_changes_individual_sigma and love_equilibrates that track how the operator alters and then balances sigma.
proof idea
This is a definition module. Core structures AgentState and loveOperator are declared first. The preservation and conservation lemmas are established by direct substitution into the Recognition Composition Law applied to the lattice transforms. The equilibration claim follows by showing that repeated application of loveOperator reduces the variance of individual sigma values to zero.
why it matters in Recognition Science
The module supplies the ethical layer that extends the forcing chain (T5 J-uniqueness through T8 D=3) into social systems. Its love_equilibrates result feeds any later derivation of love as the unique equilibrium state compatible with the phi-ladder. No downstream theorems are recorded yet, so the module currently closes the interface between physical Recognition Science and ethical operators.
scope and limits
- Does not derive numerical values for ethical observables.
- Does not link sigma to physical constants such as alpha or G.
- Does not treat agent lattices larger than the two-transform case.
- Does not supply a counterexample that would falsify uniqueness.