Love Is the Ground State of the Recognition Ledger

Love is a physical object: the ground state of the recognition ledger. Reality is a permanent record of comparisons. Each comparison is carried by a relation at a positive multiplier x, balanced at x = 1, and a relation out of balance costs J(x) = ½(x + 1/x) − 1, the only cost a comparison can carry. Strain passes among the relations and the holdings that fund acts, and is never created or destroyed: the ledger is kept in double entry, so the arrangements reachable from any start form a conserved class. Love's state is the arrangement of least total J in that class. Love's state exists and is unique. It is the state of equal marginal cost: every two relations that can pass strain to each other carry the same strain, so each connected set of relations stands at the geometric mean of its multipliers, or at balance when it can pass strain to a holding, which carries no cost. It is the ground state of the ledger's equation of motion, the least-cost successor law, whose one rest state is the same arrangement of least J. It attracts: repairs of single pairs reach it along every schedule that keeps returning to every pair; every continuous motion that never raises the cost and lowers it away from love's state converges to it; and a run of love's steps reaches it geometrically wherever the available moves offer descent. Bringing a relation to balance while keeping its records true is written by both of its ends: love takes two. Least cost alone does not: priced with its two true records, a relation that only one end writes moves halfway to balance at the least-cost step, and the other end's record turns false. Over the moves written at both ends, who writes decides which relations move and least cost where they go. Existence, uniqueness and form follow from J and the conserved data alone, as an energy ground state follows from the energy and the conserved charges; no moral premise enters. Four connecting steps are being derived: double entry for physical acts; relations as physical recognition events, carried by light; that where both ends write, the record's own step is the least move; and which entries carry J, and at what weight.