Conditional Reconstruction Closure F; Conditional Reconstruction of Classical Field Equations: Hypothesis Independence and Discriminative Certificates

This paper presents the final main theorem of the conditional reconstruction ofclassical field equations together with its complete supporting structure. The eightpremises are listed separately as follows: P1, typed local closure and composableinformation budget hold; P2, the external source is given and dJ = 0; P3, the premetric translation preserves the local complex and source compatibility; P4, a singleAbelian sector is selected; P5, the constitutive law is local linear, metric-inducedprincipal axis, with skew and axion channels vanishing; P6, spacetime is fourdimensional flat Minkowski, of finite duration, with principal symbol hyperbolicand a common causal cone; P7, gauge, initial, boundary, and source data are compatible; P8, the discrete complex is stable, the observation family separates points,and each anomaly component tends to zero in the specified topology. The threeconclusions are, in order: the reliability direction, that every certified closure limitcorresponds, after the translation mapping, to a local Maxwell gauge-equivalencesolution; the completeness direction, that if the discrete realization theorem holds,every sufficiently regular Maxwell solution can be realized by a certified closurelimit; and the conditional equivalence direction, that when reliability, completeness,and the two observational obligations all hold, the translation mapping induces aone-to-one correspondence between the class of certified closure limits and the classof local Maxwell gauge-equivalence solutions, this equivalence being a conditionalstatement whose validity takes Obligation One and Obligation Two as additionalconditions. The structure of the full text is as follows: Chapter 2 discloses themachine-check ledger prior to all main-text propositions, its position being onlyafter the abstract and introduction and before Chapter 3; Chapter 3 treats theexternal baseline and the claim ceiling; Chapter 4 gives the complete hypothesisdependence DAG, including in Section 4.3 the typed definitions of the certificationpredicate, the translation mapping, the observation quotient, and the regularityclass; Chapter 5 gives the reliability theorem; Chapter 6 gives completeness andthe realization theorem, including in Section 6.3 the two proof obligations for theone-to-one correspondence; Chapter 7 gives the counterexample library and hypothesis independence; Chapter 8 gives the discriminative certificate for the anomalybudget; Chapter 9 gives formalization depth and computability boundaries; Chapter 10 gives originality and discriminative output; Chapter 11 gives the final openboundaries; thereafter follow the final main theorem statement block and Appendices A through G. All numerical assertions have been registered through machinechecking; machine-check items MC-F-01 through MC-F-05 are judged passed, andMC-F-06 is the zero-realization non-emptiness verification. This paper produces nonew electromagnetic numerical predictions.