LatticeState
plain-language theorem explainer
LatticeState encodes a recognition lattice configuration with strictly positive average cost J-bar, spectral gap, and energy. Virtue effect modelers cite it when simulating how love lowers collective cost or courage permits high-gradient transitions. The definition assembles three positivity constraints drawn directly from upstream energy and gap theorems.
Claim. A lattice state is a record $(j, Δ, E)$ of real numbers satisfying $j > 0$, $Δ > 0$, $E > 0$, where $j$ is average recognition cost, $Δ$ is spectral gap, and $E$ is total energy.
background
The Virtue Lattice Effect module studies how the fourteen DREAM virtues modify lattice parameters. J-bar stands for average recognition cost, the spectral gap is the minimum nonzero cost on the phi-ladder, and energy is the total resolution energy. The spectral gap theorem states that for every nonzero integer rung n, J(φ^n) ≥ J(φ) > 0. Energy positivity is supplied by the energy_level and energyPerResolution results, each obtained by multiplying positive factors involving phi.
proof idea
Direct structure definition. The three positivity fields are required by the signature and are justified by the referenced energy_pos theorems from oscillatory dynamics and recognition bounds together with gap_pos and the spectral_gap theorem.
why it matters
LatticeState supplies the common input type for applyLove, applyCourage, applyWisdom and the derived results love_reduces_collective_jbar, love_widens_gap, and courage_enables_high_gradient_action. It anchors the ethics layer in the Recognition framework by importing the spectral gap theorem and energy positivity constraints. No open questions are resolved here; the structure simply closes the interface between physical lattice data and virtue transformations.
Switch to Lean above to see the machine-checked source, dependencies, and usage graph.