Physics-Based Morality: One recognition, written twice: the cost of a wrong, the record of what happened, and the price of a duty

Two people do one thing together and each writes it down. Where their two records differ there is a gap, and the gap belongs to the relationship, not to either of them. Read as two sides of one recognition, which is the one definition the paper makes, the gap is priced by the same law that prices every imbalance in Recognition Science; the definition is the paper’s one modelling commitment, and that the two figures of a real pair of records are such a pair is the open link the paper names and does not close. From the two records and their history, with no moral axiom, follow who wrote, who consented, who was changed, how the cost of the disagreement divides (read from the books alone: equally between the two ends, whoever wrote, for any reciprocal cost), how a gap is closed and by whom, and who drove the records apart. The two records cannot say what is owed: a creditor who delivered and was refused a signature has the same record history as one who invented the claim. What is owed needs a record of what physically happened. A duty appears only for a party that goes on acting from a finite reserve; its price is one premise, stated exactly and proved irreducible on its signature. Of the five places the physics seems to enter, two are physics and three are the mathematics of the ledger, and the paper says which. Every theorem is proved on the page.