Time and Causality from Irreversible Continuation Ordering

Realized Physics Arc — Paper XI Time and Causality from Irreversible Continuation Ordering The Temporal and Causal Roles of Standing-Preserving Physical Persistence By Amos Jay Maley This manuscript is the eleventh paper in the Realized Physics Arc, deriving the minimal temporal and causal roles from the previously established framework of realized persistence, field-carrier mediation, particle persistence classes, gauge structure, mass/inertia response, bounded perturbation transport, and vacuum baseline structure. The paper proves that physical time and causality first enter realized physics not as primitive coordinates, universal temporal parameters, spacetime lines, or hidden influence mechanisms, but as roles induced by irreversible standing-bearing continuation and witness-dependent persistence preservation. The central result is the Temporal-Causal Role Induction Theorem: (ΩD,  ΦD,  ΠD,  GD,  MD,  BoundTransD,  CD)∧IrrevContD∧RecordFixD∧IdRetD⇒(TD,  CD)(\Omega_D,\; \Phi_D,\; \Pi_D,\; G_D,\; M_D,\; \mathrm{BoundTrans}_D,\; C_D) \wedge \mathrm{IrrevCont}_D \wedge \mathrm{RecordFix}_D \wedge \mathrm{IdRet}_D \Rightarrow (T_D,\; C_D)(ΩD,ΦD,ΠD,GD,MD,BoundTransD,CD)∧IrrevContD∧RecordFixD∧IdRetD⇒(TD,CD) with induced structures: TD=(ED,  ≺D)T_D = (E_D,\; \prec_D)TD=(ED,≺D) and CD=(ED,  ⇝D)C_D = (E_D,\; \rightsquigarrow_D)CD=(ED,⇝D) where ≺D\prec_D≺D is irreversible continuation ordering and ⇝D\rightsquigarrow_D⇝D is witness-dependent causal dependence. The manuscript develops: continuation stages, standing-bearing continuation, irreversible continuation, temporal ordering, causal dependence, record fixation, and witness-dependent persistence structure. A central structural claim of the paper is that time first appears as irreversible continuation order: ei≺Deje_i \prec_D e_jei≺Dej meaning that a later standing-bearing configuration retains non-dischargeable consequence from an earlier configuration whose removal would require: identity reset, record erasure, boundary-trace loss, transport incompatibility, gauge-role break, or standing failure. Causality then appears as the stricter role: ei⇝Deje_i \rightsquigarrow_D e_jei⇝Dej where the later stage depends on a fixed continuation witness from the earlier stage. Temporal order alone is insufficient; causality requires witness-dependent standing preservation. The paper proves that: primitive temporal parameters fail, reversible continuation collapses temporal role, simultaneity-by-default collapses persistence asymmetry, pathless causal influence is inadmissible, and metric-time imports presuppose the ordering role they attempt to explain. The manuscript further establishes: local partiality of temporal order, record-fixed continuation retention, witness-dependent causal induction, no pathless causal dependence, and exclusion of closed reversal of standing-bearing consequence. A major consequence of the paper is that later temporal and causal frameworks — including: clock time, relativistic causal cones, proper time, thermodynamic arrows, causal-set structures, field-theoretic causality, and spacetime temporal geometry — are interpreted as later mathematical and physical specializations of a more primitive irreversible continuation role already forced by standing-bearing persistence. The manuscript remains fully compatible with: relativistic spacetime theory, thermodynamic time asymmetry, quantum measurement frameworks, causal-set approaches, and quantum field-theoretic causal structure, while explicitly rejecting reduction of time or causality to primitive coordinate assignments, observer chronology, reversible co-description, or pathless hidden influence. As the eleventh theorem in the Realized Physics Arc, the paper establishes the earliest admissible temporal-facing and causal-facing structures from which later reconstructions of relativistic time, causal geometry, thermodynamic irreversibility, field dynamics, and spacetime ordering can proceed: physical time first enters realized physics as irreversible continuation ordering, and physical causality as witness-dependent standing-preserving dependence across that order, rather than as primitive coordinates or external temporal background structure. This paper is downstream of: Minimal Conditions for Admissible Construction  The Structure of Admissibility