Spacetime Symmetry as Domain Anchor

SYM 02 of Symmetry ARC Poincaré, Lorentz, Translation, and CPT Kernel-Faithful, Constructor-Saturated, Semantically Causal, Projection-Recompositional, Apex-Closed Normal-Form Closure This paper develops a fixed-target normal-form theorem for spacetime symmetry, separating structures that are often conflated under a single symmetry label. The analysis distinguishes the relativistic domain itself, active transformations of states and observables, passive coordinate and frame redescriptions, projective state representations, finite-dimensional field covariance, particle-sector response, infinitesimal generators, Noether currents and charges, Ward identities, and the premise, theorem, and implementation loci of CPT. The principal target is one integrated Minkowski/Wightman/state/sector/Noether/CPT certificate. Its physical and mathematical content is classified through an authoritative constructor grammar, isolated role and candidate-construction processes, validated presentation witnesses, typed projections, recomposition maps, and transport relations. The central finite certificate contains: 128 typed target leaves; 18 executed bridge obligations; 27 standing burdens; 13 canonical target roles; 15 role-blind parent objects; 39 physical facets and target edges; 30 witnessed presentation residues; 390 classified role–residue pairs; 15 positive eligibility edges; 2 complete pointwise-eligible preassignments; 1 compatible complete assignment; 1 lawful assignment orbit. The paper proves that the candidate universe is the fixed point of the registered physical-constructor grammar. Every registered finite-interface refinement is rebuilt from typed executable projections and verified recomposition maps, with all 64 registered architectures transporting to the canonical orbit. Conservative certificate enrichments preserve the orbit, while target-defining or standing-bearing enrichments reopen the closure problem. The resulting normal form separates physical action from representative-level skin. Passive coordinate, frame, spin-frame, ray-phase, current-improvement, and CPT-convention changes are classified as skin where validated witnesses preserve the complete physical tuple. Active translations, rotations, boosts, and CPT remain physical actions. Mass, spin, helicity, causal structure, representation class, generators, and charges remain target-internal content. The theorem also distinguishes the role of the Minkowski projection as a domain anchor from downstream Poincaré actions and their representations. Translation and Lorentz generators, particle-sector response, Noether currents, charges, boundary conditions, projective states, local fields, and CPT are treated as distinct but connected target loci rather than collapsed into one undifferentiated symmetry object. Because the fixed local physical construction is non-degenerate and determinate, the Admissibility–Standing–Reference–Irreversibility kernel is instantiated by necessity. The finite certificate establishes one lawful local assignment orbit. A separately registered downstream apex interface then supplies the imported consequence that, once the kernel, fixed domain, boundary package, and local singleton are in place, one admissible interior is forced and a second same-domain standing classifier or discrete plurality of admissible regimes is excluded. The result is complete for the frozen SYM-2 target and its role-realization-complete certificate. It does not claim uniqueness for all relativistic quantum field theories, all possible spacetime regimes, or every alternative algebraic or Lagrangian formulation. Such formulations remain distinct certificate targets unless connected by an explicitly validated bridge. Principal contributions A fixed-domain Poincaré–CPT normal-form theorem. A distinction between domain anchor, physical action, representation, generator, diagnostic, and redescription. Constructor-saturated candidate generation with a fixed-point criterion. Independent role and physical-object construction. A witnessed presentation groupoid and canonical presentation residue. Complete eligibility and relational compatibility analysis. Full-certificate and live automorphism-group computation. A unique lawful local assignment orbit. A locus-sensitive distinction between physical action and representational skin. Projection-recompositional closure across 64 registered finite-interface architectures. A downstream apex consequence interface with explicit dependency and falsification boundaries. An executable audit supplement covering completeness, reconstruction, independence, determinism, and destructive mutations.