applyLove
plain-language theorem explainer
The definition constructs a modified lattice state under the action of love, scaling the collective cost J-bar downward by a factor linear in strength while expanding the spectral gap proportionally. Physicists extending Recognition Science to ethical dynamics would reference this when deriving how virtues alter recognition efficiency. The implementation directly updates the LatticeState record and invokes nlinarith to re-establish positivity from the input bounds.
Claim. Let $s$ be a lattice state with components $J(s)>0$, spectral gap $Delta(s)>0$, and energy $E(s)>0$. For strength parameter $sigma$ satisfying $0<sigma leq 1$, the love operator yields state $s'$ defined by $J(s')=J(s)cdot(1-sigma/2)$, $Delta(s')=Delta(s)cdot(1+sigma)$, and $E(s')=E(s)$.
background
LatticeState is the structure that records average recognition cost J-bar, spectral gap, and energy, each equipped with a positivity proof. The Virtue Lattice Effect module studies how the fourteen DREAM virtues modify these three quantities; the module doc states that love reduces collective J-bar while courage and wisdom act on gradient and energy terms. Upstream results supply the required positivity lemmas: energy_pos from oscillatory dynamics and recognition bounds, gap_pos from LDPC code rate analysis, and the spectral gap theorem asserting that every non-vacuum phi-ladder rung satisfies J-cost at least the mass gap.
proof idea
The definition is realized by constructing a new LatticeState record whose jbar field is scaled by (1-strength/2), whose spectral_gap field is scaled by (1+strength), and whose energy field is copied unchanged. The three positivity fields are discharged by nlinarith applied to the input positivity hypotheses together with the bounds 0<strength<=1.
why it matters
This definition supplies the concrete transformation rule used by the theorems love_reduces_collective_jbar and love_widens_gap, which establish that the love operator strictly decreases collective J-bar and strictly increases the spectral gap. It forms part of the ethical extension of the Recognition framework, linking virtue effects to the J-uniqueness property and the phi-ladder structure. The construction closes the interface between the abstract LatticeState and the specific virtue actions without introducing additional hypotheses.
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