The Realized Physical Interior

Overview This paper presents a flagship synthesis of the realized physical interior under the Admissibility And Standing Constraint (AASC) mathematical necessity-constraint formalism. Its central claim is that physical theories become about a realized physical regime only when their formal structures occupy a standing-bearing role architecture: one in which physical content can persist, be referenced, survive lawful redescription, and undergo irreversible continuation without same-act repair. The paper does not propose a hidden substrate, a replacement Lagrangian, or a constructive model from which physics is generated. Its method is eliminative and rigidity-theoretic. Once the target class of realized physical persistence is fixed, AASC determines which roles cannot be absent without collapsing the target, changing scope, importing hidden structure, or reintroducing the same role under another presentation. Main Contribution The first half of the paper synthesizes and proves the realized physical interior theorem at the role-architecture level. Beginning from the AASC kernel [ K_D=(\mathrm{Adm}_D,\mathrm{Stand}_D,\mathrm{Ref}_D,\mathrm{Irr}_D), ] the physical arc derives the interdependent interior architecture [ I_D=(\mathrm{NonVacRec}D,[B_D]{\equiv B},\mathrm{Adj}_D,N_D,\mathrm{LCDD},\mathrm{Cmp}_D,\mathrm{BoundTrans}_D,\Phi_D,\Pi_D,G_D,M_D,\Omega_D,T_D,\mathrm{Cau}_D). ] This structure records the minimal role conditions required for realized physical persistence: non-vacuous realization, bounded standing-localization, local continuation domains, quotient-stable comparison, bounded perturbation transport, fields as persistence carriers, particles as localized persistence classes, gauge structure as boundary-fixed presentation equivalence, mass and inertia as deformation-response roles, vacuum as a non-null no-particle baseline, time as irreversible continuation ordering, and causality as witness-dependent dependence. The resulting physical interior is not a list of familiar physical objects. It is a closed role architecture satisfying coherence, closure, and operational minimality. Each major role family is deletion-tested: removing it breaks the same target of standing-bearing realized physical persistence. Standard-Physics Projection Stack The second half of the paper develops controlled projections and specializations into the standard physics stack. Standard physics is not ignored, but neither is it allowed to backflow into the role ladder that licenses it. The downstream stack includes: AER quotient/constraint architecture: coisotropic standing, characteristic redescription, first-class closure, and multiplier-type Hamiltonian form. AASC gravity: the GR-type constraint role of the admissible physical interior. Einstein metric projection: the minimal first-response Lorentzian metric normal form [ G_{\mu\nu}+\Lambda g_{\mu\nu}=\kappa T^{\mathrm{closed}}_{\mu\nu}. ] Quantum predictive structure: Hilbert/Schrödinger predictive geometry, Bell witness typing, and measurement-record quotient closure. Local Yang-Mills QFT: a local gauge-invariant pure Yang-Mills theorem object in the declared scope. Zero-point vacuum-energy discipline: renormalization-quotient invariance as AASC standing preservation in the homogeneous vacuum sector. Standard Model structural tuple: a downstream structural specialization including gauge product, representation-response skeleton, Higgs/bridge carrier, Yukawa-realizability ledger, charge lattice, anomaly-neutral ledger, vacuum compatibility, mass-response slots, and mixing/phase slots. These projections are typed and scope-guarded. They do not function as primitive foundations for the realized physical interior; they are downstream theorem objects, projections, or specializations of the role architecture. Predictive and Claim-Status Discipline AASC is not prediction-free, but its mature predictive force is primarily structural and classificatory. The paper distinguishes: mature structural predictions, including forced role order, primitive-substitute exclusion, and standard-physics projection typing; mature classificatory predictions, including anchor/tensor/skin typing and zero-point vacuum-energy non-predictivity; restricted quotient-level numerical outputs, including charged-lepton mass-shape extraction and Standard Model charge-lattice extraction; conditional sectoral readouts, including a neutrino splitting-ratio standing-admission window; open downstream parameter targets, including the full Standard Model empirical parameter table. The paper explicitly does not claim closure of all QFT, all gravitational physics, all cosmology, quantum gravity, or the full numerical Standard Model parameter table. Numerical constants require separate scale, calibration, exactness, and sector-specific witness ledgers. Methodological Status The paper should be read as a mathematical role-exhaustion and structural-rigidity theorem internal to AASC. It differs from constructive model-building physics, analytic PDE existence theory, and Lagrangian-first derivation. The central question is not which primitive physical object generates the rest of physics. The central question is which roles are mathematically unavoidable once standing-bearing construction and realized physical persistence are fixed. The conclusion is that the realized physical interior is the minimal admissible role architecture through which standard physical theories become theories of a realized physical regime rather than merely formal presentations. Keywords AASC; Admissibility And Standing Constraint; realized physical interior; mathematical necessity-constraint formalism; physical persistence; admissibility; standing; reference; irreversibility; AMetric boundary; admissible equivalence; anchor/tensor/skin; no-backflow; role architecture; structural rigidity; constraint exhaustion; quotient identity; physical locality; metric role; fields; particles; gauge structure; mass; inertia; vacuum; time; causality; AER quotient architecture; AASC gravity; Einstein metric projection; quantum predictive structure; Bell witnesses; measurement records; Yang-Mills QFT; zero-point vacuum energy; renormalization standing; Standard Model structure; charged-lepton mass shape; neutrino splitting ratio; mathematical physics; foundations of physics This paper is downstream of: Non-Degenerate Construction and the Kernel of Admissibility  The Structure of Admissibility