Fields as Persistence Carriers

Realized Physics Arc — Paper VI Fields as Persistence Carriers The Minimal Carrier Role of Physical Field Structure under Bounded Perturbation Transport By Amos Jay Maley This manuscript is the sixth paper in the Realized Physics Arc, deriving the minimal carrier role underlying physical field structure from the previously established framework of realized persistence, standing-localization, continuation-neighborhood domains, quotient comparison carriers, and bounded perturbation transport. The paper proves that localized persistence under bounded perturbation transport cannot be carried by: isolated points, path labels, global undifferentiated substrates, hidden reservoirs, trace-only descriptions, or bookkeeping overlays. Standing-bearing persistence instead requires a distributed carrier assignment over local continuation domains that mediates perturbation transport itself. The central result is the Field-Carrier Role Theorem: (LCDD,  CD,  BoundTransD)∧LocalPersistD∧CarrierReqD⇒FieldRoleD(\mathrm{LCD}_D,\; C_D,\; \mathrm{BoundTrans}_D) \wedge \mathrm{LocalPersist}_D \wedge \mathrm{CarrierReq}_D \Rightarrow \mathrm{FieldRole}_D(LCDD,CD,BoundTransD)∧LocalPersistD∧CarrierReqD⇒FieldRoleD equivalently, FieldRoleD≡∃ΦD:Dom(ΦD)⊆LCDD→CarProfD\mathrm{FieldRole}_D \equiv \exists \Phi_D : \mathrm{Dom}(\Phi_D) \subseteq \mathrm{LCD}_D \to \mathrm{CarProf}_DFieldRoleD≡∃ΦD:Dom(ΦD)⊆LCDD→CarProfD establishing that bounded perturbation transport induces a coherent distributed field-role assignment over local continuation domains. The manuscript develops: persistence carriers, carrier profiles, carrier mediation, carrier coherence, carrier restriction, transport compatibility, boundary coherence, and distributed field-role assignments. The paper argues that physical field structure first enters not as: spacetime-supported field values, gauge bundles, operator algebras, field equations, or particle excitations, but as the distributed carrier role required for localized persistence to retain standing-bearing consequence under bounded perturbation transport. The induced carrier profile for a local continuation domain UUU is: CarProfD(U)=(BU,  SU,  IU,  RU,  PU,  QU,  ∂U,  TU)\mathrm{CarProf}_D(U) = (B_U,\; S_U,\; I_U,\; R_U,\; P_U,\; Q_U,\; \partial_U,\; T_U)CarProfD(U)=(BU,SU,IU,RU,PU,QU,∂U,TU) where the profile preserves: bounded support, standing status, identity-memory, restoration structure, perturbation burden, quotient comparison class, boundary-trace interface, and transport interface. A major structural result of the paper is the distinction between: bookkeeping assignments, which merely record transport, and field-role assignments, which mediate transport. A structure counts as field-role only when admissible modification of its carrier profile changes the regime’s standing-bearing transport organization itself. The manuscript proves that: point-only carriers fail, path-only carriers collapse into syntax, global substrates erase localization, hidden reservoirs become realization-inert, trace-only structures fail mediation, and identity-reset carriers destroy persistence continuity. The analysis further develops: restriction compatibility, carrier transport compatibility, boundary coherence, and carrier-route exhaustion. The resulting field-role structure is explicitly prior to: scalar/vector/tensor field formalisms, gauge structure, quantum field theory, manifold-valued fields, field equations, stress-energy structure, particle ontology, and quantization procedures. The paper remains fully compatible with: classical field theory, gauge theory, algebraic quantum field theory, quantum operator fields, and geometric field formulations, while arguing that these later frameworks occupy a more primitive carrier role already forced by localized persistence under bounded perturbation transport. As the sixth theorem in the Realized Physics Arc, the paper establishes the earliest admissible field-facing structure from which later reconstructions of gauge structure, field equations, particles, quantization, and spacetime-supported physical fields can proceed: physical fields first enter as distributed persistence carriers mediating standing-bearing transport rather than as primitive substances, values, or equations. This paper is downstream of: Minimal Conditions for Admissible Construction  The Structure of Admissibility