Realized Physics Arc — Paper X Vacuum as Minimal Concrete Persistence RegimeThe Non-Null Baseline Role of Field-Carrier Structure By Amos Jay Maley This manuscript is the tenth paper in the Realized Physics Arc, deriving the minimal vacuum role from the previously established framework of field-carrier mediation, particle persistence classes, gauge structure, mass/inertia response, bounded perturbation transport, and quotient comparison structure. The paper proves that removing localized particle-class excitations does not collapse physical reality into nullity, empty spacetime, field absence, trace-only bookkeeping, or arbitrary ground-state convention. A physical vacuum must instead preserve the minimal non-null carrier, boundary, transport, comparison, gauge, restoration, and deformation-response structures required for concrete realized persistence. The central result is the Vacuum-Role Induction Theorem: (ΦD, BoundTransD, CD, ΠD, GD, MD)∧MinPersistD∧NoPartExcD⇒VacRoleD(\Phi_D,\; \mathrm{BoundTrans}_D,\; C_D,\; \Pi_D,\; G_D,\; M_D) \wedge \mathrm{MinPersist}_D \wedge \mathrm{NoPartExc}_D \Rightarrow \mathrm{VacRole}_D(ΦD,BoundTransD,CD,ΠD,GD,MD)∧MinPersistD∧NoPartExcD⇒VacRoleD with induced vacuum profile: ΩD(U)=(ΦU0, ∂U0, TU0, QU0, GU0, μU0, RU0)\Omega_D(U) = (\Phi_U^0,\; \partial_U^0,\; T_U^0,\; Q_U^0,\; G_U^0,\; \mu_U^0,\; R_U^0)ΩD(U)=(ΦU0,∂U0,TU0,QU0,GU0,μU0,RU0) establishing the vacuum as the minimal concrete persistence baseline relative to which localized particle excitations become meaningful. The manuscript develops: field-carrier baselines, particle-class excitations, no-particle conditions, minimal concrete persistence regimes, vacuum profiles, and vacuum-role structure. A central structural claim of the paper is that vacuum first enters realized physics not as: empty spacetime, field absence, zero-point bookkeeping, primitive ground-state selection, or nullity, but as the minimal non-null persistence regime remaining after localized particle persistence classes are absent. The induced vacuum profile preserves: baseline field-carrier mediation, boundary-trace interfaces, transport possibility structure, quotient comparison baselines, gauge-compatible presentation structure, deformation-response baselines, and restoration capacity. The paper proves that: null vacua are impossible, no-particle conditions do not imply nullity, empty-container vacua fail, field-absence vacua collapse, trace-only vacuum descriptions are insufficient, and primitive vacuum-energy assignments are inadmissible prior to role fixation. The manuscript further establishes: gauge-compatible vacuum baselines, deformation-response vacuum structure, vacuum neutrality without nullity, hidden-vacuum-reservoir exclusion, and vacuum-role route exhaustion. A major consequence of the paper is that later vacuum constructions — including: Fock vacua, Hamiltonian ground states, zero-point energy structures, Higgs vacuum expectation values, condensates, cosmological constants, dark-energy models, and quantum field-theoretic vacuum sectors — are interpreted as later specializations of a more primitive non-null persistence baseline already forced by realized persistence and field-carrier structure. The manuscript remains fully compatible with: quantum field theory, symmetry-breaking vacua, vacuum-sector physics, cosmological vacuum models, and dark-energy frameworks, while rejecting reduction of vacuum to primitive emptiness, nullity, arbitrary scalar vacuum-energy assignments, or hidden inaccessible substrates. As the tenth theorem in the Realized Physics Arc, the paper establishes the earliest admissible vacuum-facing structure from which later reconstructions of zero-point structure, condensates, Higgs sectors, vacuum energy, cosmological terms, and quantum vacuum dynamics can proceed: vacuum first enters realized physics as the minimal non-null concrete persistence regime supporting carrier, transport, gauge, comparison, restoration, and deformation structure rather than as empty space or physical nothingness. This paper is downstream of: Minimal Conditions for Admissible Construction The Structure of Admissibility