From Objective Collapse to Emergent Mass A Stochastic Rupture Proposal: Inertia, Gravity, and the Equivalence Principle from Branch Pruning Working document conceptual proposal, with derivations

Within the Stochastic Rupture (SR) framework an objective-collapse proposal in which physical facts are produced by the local, irreversible pruning of quantum branches we ask what mass is. We argue that mass is not a substance but a dual manifestation of pruning: gravitationally, as the curvature sourced by the information that pruning records; inertially, as the cost of reorganizing the underlying sheet pattern when a localized excitation is displaced. We derive Newton's second law F = ma from a Lagrangian for that reorganization cost, with inertial mass min = Rf′2 du, and show by a soliton boost that the inertial and gravitational masses are exactly equal, min = mgrav = E0/c2 , so that the equivalence principle becomes a consequence rather than a postulate. We then confront the central diculty: the SR master equation is a reactiondiusion law and carries a preferred frame, so Lorentz invariance cannot be assumed. We develop a candidate route in which the vacuum is a polycrystalline, coordination-three eggbox lattice: each ordered domain supplies a local Dirac cone (giving an emergent light speed), while disordered domain orientations restore spatial isotropy by averaging, the two eects living at separate scales. This route makes a falsiable prediction a residual anisotropy scaling as (D/L) 3/2 with a discriminating exponent and it identies, rather than hides, serious open problems (that pruning must produce the ordered lattice it does not freely generate, the grainsize mechanism, the veried Dirac touching, and the full 3 + 1 gluing). The genuinely novel claim is conceptual: the bridge from objective collapse to emergent spacetime. We restrict the present article to the static stage the spatial vacuum structure and defer the temporal (boost) sector to companion work, with physical justication. The document is oered as a proposal, to invite examination and independent review.