Conditional Reconstruction Closure G; Negative Closure of Open Boundaries- Failure Constructions, Undecidability, and Discriminative Blind Spots

A conditional reconstruction program for classical field theory, founded on thetwo axioms of information conservation and computability, has registered eightopen boundaries: the existence and identification of limits of general infinite networks; effective construction in the absence of a computable modulus of convergence; complete classification of harmonic and obstruction classes in nontrivialtopology; systematic classification of nonlinear and non-Abelian alternative sectors; the material-structure origin of external sources; curved spacetime and Weylinvariance; model-dependent derivation of observable non-Maxwell corrections produced by coarse-graining; and the quantization interface. This article does notclaim to solve any of the positive statements among these eight boundaries; instead, it gives a negative closure of the eight boundaries: for each item, it determines whether the claim of unconditional solvability” can be closed, and in whatform it is closed. The three legitimate forms of closure are negative theorems,necessary conditions, and discriminative blind spots. Chapter 2 first registers themachine-checked ledger, fixing the precise arithmetic verification channel for thewhole article; Chapter 3 self-containedly fixes the objects, axioms, boundary list,and closability criteria, and registers the encoding-bridge layer in Section 3.5, sothat the computable family” claims of the subsequent reduction-type theorems havea verifiable constructive anchor; Chapter 4 constructs a network family satisfyingthe two axioms whose compatible inverse-system limit is empty, and a networkfamily whose inverse limit is nonempty but whose observation map does not separate points, proving that neither type of failure is detected by the loss budget(Theorem 1); Chapter 5 states and argues the core lemma of discriminative blindspots, gives an object pair that is layer-by-layer equivalent on four levels while inequivalent on the additional-structure level, and registers three counterargumentrecords and the Sunada non-reduction argument; Chapter 6 proves, by two independent routes—a halting reduction and a tiling reduction—that the modulusof convergence is noncomputable (Theorem 2); Chapter 7 gives the boundary between finite decidability and general undecidability for the obstruction classification(Theorem 3; the negative side holds in outline form, with encoding details listedas outstanding); Chapter 8, via the reconstruction lemma, reduces the transportisomorphism classification of alternative sectors to the undecidability of the Markovproperty for finitely presented groups (Theorem 4); Chapter 9 gives the admissionticket necessary condition for material construction and a non-sufficiency witness(Theorem 5); Chapter 10 closes the sufficiency claims of the two axioms for B6and B7 by means of a curvature blind pair and a correction-term blind pair (Theorems 6 and 7); Chapter 11 registers the quantization-interface outstanding itemand, by a meta-theorem, collects the closure status of the eight boundaries together with the item-by-item verification channel. The whole article produces nopositive physical prediction; the outstanding items B5 source, the Weyl subitem ofB6, the model-dependent derivation of B7, and B8 quantization all remain open,with restart conditions registered in the text. Appendices A to F register, in order, the machine-check index, algorithm descriptions, arbitration archive, theoremcross-reference, boundary ledger, and reproduction guide.