Particles as Localized Persistence Classes

Realized Physics Arc — Paper VII Particles as Localized Persistence Classes The Minimal Object Role of Particle Identity under Field-Carrier Mediation By Amos Jay Maley This manuscript is the seventh paper in the Realized Physics Arc, deriving the minimal persistence-class role underlying particle identity from the previously established framework of realized persistence, standing-localization, continuation-neighborhood domains, quotient comparison carriers, bounded perturbation transport, and field-carrier mediation. The paper proves that particle identity cannot be grounded by: primitive objecthood, point occupancy, trajectory labels, field labels, hidden cores, measurement records, or bookkeeping names alone. A particle instead emerges as a stable localized persistence class of carrier-mediated configurations preserved under admissible continuation. The central result is the Particle Persistence-Class Theorem: (ΦD,  BoundTransD,  CD,  LCDD)∧StableLocD∧IdRetD⇒∃ΠD(\Phi_D,\; \mathrm{BoundTrans}_D,\; C_D,\; \mathrm{LCD}_D) \wedge \mathrm{StableLoc}_D \wedge \mathrm{IdRet}_D \Rightarrow \exists \Pi_D(ΦD,BoundTransD,CD,LCDD)∧StableLocD∧IdRetD⇒∃ΠD equivalently, ParticleRoleD≡ΠD=[κU]≡Π\mathrm{ParticleRole}_D \equiv \Pi_D = [\kappa_U]_{\equiv \Pi}ParticleRoleD≡ΠD=[κU]≡Π where particle-role equivalence preserves: standing signature, boundary/classification witness, transport/restoration profile, quotient comparison class, identity-memory, boundary trace, and transport role. The manuscript develops: localized carrier configurations, standing signatures, boundary/classification witnesses, transport/restoration profiles, particle-role equivalence, stable localization, and persistence-class identity. A central structural claim of the paper is that particle identity first enters physics not as primitive substance or point occupancy, but as the stable equivalence class of localized carrier-mediated persistence under admissible transport, restoration, and comparison. The induced localized carrier configuration is: κU=(U,  ΦD(U),  σU,  χU,  βU)\kappa_U = (U,\; \Phi_D(U),\; \sigma_U,\; \chi_U,\; \beta_U)κU=(U,ΦD(U),σU,χU,βU) where: UUU is a local continuation domain, ΦD(U)\Phi_D(U)ΦD(U) is the carrier profile, σU\sigma_UσU is the standing signature, χU\chi_UχU is the boundary/classification witness, and βU\beta_UβU is the transport/restoration profile. The manuscript proves that: primitive object identity fails, point occupancy collapses, trajectory labels are only skin, field labels are insufficient, hidden cores violate admissibility discipline, and record-only identity is downstream rather than foundational. The analysis further establishes: stable localization requirements, persistence-class equivalence structure, transport-stable identity preservation, localized multiplicity conditions, and interaction-sensitive class preservation. A major consequence of the paper is that later particle formalisms — including: Standard Model particle species, gauge representations, quantum states, Fock-space excitations, scattering descriptions, and detector records — are interpreted as later formal enrichments of a more primitive persistence-class role already forced by field-carrier mediation and bounded perturbation transport. The manuscript remains fully compatible with: quantum field theory, Standard Model classification, gauge theory, algebraic quantum field theory, nonclassical entanglement structure, and quantum particle descriptions, while explicitly rejecting reduction of particle identity to Bell-local hidden variables, primitive corpuscles, or path-only ontology. As the seventh theorem in the Realized Physics Arc, the paper establishes the earliest admissible particle-facing structure from which later reconstructions of gauge classification, quantum statistics, scattering theory, particle species, and detector phenomenology can proceed: particles first enter realized physics as stable localized persistence classes within the field-carrier regime rather than as primitive objects or labels. This paper is downstream of: Minimal Conditions for Admissible Construction  The Structure of Admissibility