Ability Theory

Ability theory is a pre-physical framework: it begins before fields, before space, before time, with the only thing that can exist without prerequisites — distinguishability. Something differs from something else, or there is nothing to discuss. From that floor the theory develops by two moves and one demand. The first move is relation: distinguishables can stand in relations, and a relation can create what neither partner had alone — a new ability. The opening inventory is therefore combinatorial: the abilities available to a set of first distinguishables are a counting problem, and the count is factorial. The second move is coupling: abilities relate to abilities, generating further abilities — but not freely. When two motions or capacities couple, the parallel part of their relation is redundant, the anti-parallel part annihilates, and the only irreducible novelty is the orthogonal residue: new abilities are born at right angles, one at a time, with limited freedom. The demand is conservation, and it is not imposed but inherited: if everything ultimately comes from nothing, the total must remain nothing, so every generation must balance and every interaction must hand on exactly what it received. Conservation is the receipt of origin, and it acts as the selector: of everything generation produces, only what can keep its books persists. Persistence is definitional — a thing continues by maintaining the relations that constitute it, and what cannot maintain them was never a thing but an event. Two structural laws follow. Inheritance: abilities carry upward, so each level of structure contains every ability minted below it and adds its own, which is why low-level phenomena are universal and high-level phenomena are selective. The difference law: like cannot mint with like — self-similarity carries no novelty — with a single exception at the floor, where difference itself is what gets minted. Executed faithfully, this grammar generates a graded tower of persisting structure whose mathematical skeleton turns out to be already proven — the four normed division algebras of Hurwitz and Adams, dimensions 1, 2, 4, 8, and no others — and whose physical reading is developed in the companion work on Ability Generation through Conservative Selection and the Persistence Tower. This document presents the theory itself: the floor, the moves, the demand, and the laws, stated so that the reader can check each step by asking only what a relation could create and what a ledger could allow.