The Necessity of Mass: Formation, Inertia, and the Cost of Coherence

Paper C of the gravity-sector trilogy (A: Constitution; B: Realisation; C: Necessity of Mass). This paper takes the substrate ontology and the standing/evental register reading as established in Paper A (The Constitution of Curvature), and develops three things the constitution leaves open: how mass forms, why inertial and gravitational mass are one quantity, and why there must be occupied mass-energy at all. Abstract Inertia is, across standard physics, left structurally unexplained. Newton takes inertial mass as primitive and states the first law as a fact of resistance without saying what the resistance is. Mach holds that inertia must be relational, a relation to all other matter, and general relativity honours this only in part, since inertia survives in empty Minkowski space. The Higgs mechanism explains how some particles acquire rest-mass, but does not say what inertia is, and supplies in any case only about one per cent of the mass of ordinary matter. The equality of inertial and gravitational mass, tested to better than one part in ten to the fifteen, is in general relativity adopted as a postulate, not derived. This paper grounds that equality at the moment mass forms. When unoccupied fabric, already carrying the global admissibility-structure designated R(Whole), undergoes the participation-actualisation of applied energy and converts to occupied fabric held as C-coherence under a local binding constraint designated R-local, a definite quantity of energy is locked into the occupied configuration. Inertial mass and gravitational mass are that one quantity read in two directions: read statically, as the energy gradient the holding sources; read dynamically, as the cost of re-establishing the holding in a new motion-frame under acceleration. They are equal not by coincidence and not by postulate, but because there is only one locked-in quantity to read. The equivalence principle becomes a structural consequence of the C–R interface holding without exception. The argument ascends from particles to ontology. It begins from the established physics of mass formation and the mass budget of ordinary matter, develops the register reading of the formation event, derives the identity of inertial and gravitational mass, and arrives at a necessity claim: that there must be occupied mass-energy at all, because energy with no occupant cannot participate, and existence that does not participate is excluded by ItoE. The reaction physics throughout is established and is cited as such; the register reading of it is the framework's interpretation, and is falsifiable exactly where the framework is. Dependency and Scope Note This paper is downstream of The Primitive Principle (ItoE, CAB, the three co-primitive registers C, R, P), The Photonic Fabric (the photonic fabric as the physical instantiation of TEF; the P-baseline; operational null-equivalence as a registrability criterion), Whole-Level Roles (R(Whole), and time as the ordering of P-actualisation), and Paper A, The Constitution of Curvature (energy-weighted occupation as substrate; admissibility-maintenance as the constraint reading; the two-floor pairing of Λ and G; and the standing/evental register reading fixed at Paper A §3.6.5, which this paper inherits without re-arguing). It is independent of Paper B; the local realisation of the holding (the phase and standing-wave mechanisms) is Paper B's subject and is not assumed here. The argument is presented in ascending order, from particles to ontology. This is the order of exposition, not the order of grounding. The framework's direction of explanation remains, as throughout the programme, ontology to constraint to structure to physics; the ascent of this paper reveals at its summit the ground on which the particles of its opening already stood. Nothing in the exposition reverses the explanatory dependency. Scope tiers. The claims of this paper sort into four kinds, and are flagged in place. Empirical (established, cited). The reactions of mass formation and annihilation (electron–positron annihilation to photons; the Breit–Wheeler conversion of photons to a particle pair, Breit and Wheeler 1934); energy and momentum conservation across them; the mass budget of the proton (the Higgs-given current-quark rest-mass at roughly one per cent, the remainder being the energy of the confined configuration); the cosmological signature of electron–positron annihilation in the photon-to-neutrino temperature ratio; and the measured equality of inertial and gravitational mass to better than one part in ten to the fifteen. These are not the framework's claims; the framework reads them. Delivered (structural). The formation event as a mode-transition of one fabric; the locking-in of a single quantity of held coherence; the identity of inertial and gravitational mass grounded at formation; and the necessity chain of Part VI. Conjectured (flagged). The identification of the photonic fabric with the instantiation of TEF (inherited from The Photonic Fabric as that paper's load-bearing conjecture); the register reading of the formation event; and the registrability premise on which the necessity argument turns. Inherited. The standing/evental register reading of Paper A §3.6.5: that C and R are the two standing registers and P the evental register, that the binder is the R-constraint and not the participation-exchange, and that the three registers are co-primitive and mutually constituting.