Riemann Strong Origas XII / XII+ — Zeta23 and the Conservative Reconstruction Boundary

Two papers. One reconstruction boundary. Part I supplies the witness; Part II supplies the framework. A correct projection is not automatically a complete reconstruction of its source.Prior supporting records are linked through the Related works section. Their canonical citation and provenance remain attached to their original DOI.The canonical citation and provenance of each supporting document remain attached to its original DOI listed in Related identifiers.This Zenodo record is intentionally composed of two complementary scientific papers forming a single Witness-and-Framework object. Part I Riemann Strong Origas XII: Zeta23 at the Residual Fibre treats the 2026 Alpöge–Furman / Zeta23 result and its public formalization as an external exact witness that preserving additional structural information including rank, multiplicity, block structure and Sylvester inertia can strictly enlarge what becomes provable from a mathematical certificate. At the current tight rank–trace boundary, a residual extremal fibre remains: distinct zero-side configurations receive the same certificate cost. Part I therefore identifies the joint Weil bridge K12=W(ψ1,ψ2) as a concrete non-reconstructible candidate channel beyond the two marginal wings. It does not claim a proof of the Riemann Hypothesis or an improved zero proportion. Part II Riemann Strong Origas XII+: The Conservative Reconstruction Framework develops the general mathematics exposed by that witness. It formulates reconstruction through an information preorder and a minimal conservative completion. A representation P may be exact for its declared output while remaining insufficient for a task variable J whenever J is non-constant on a fibre of P. In that situation, no closed downstream computation supplied only with P can universally reconstruct J. The resulting conservative lift is therefore not arbitrary. It is bounded below by the task-completion (P,J) and above by the information of the source: P ≺ (P, J) ⪯ (P, K, T) ⪯ id_X Part II further establishes a reversible four-sector encoding generated by two commuting self-adjoint involutions. With C = (3R + S) / 2 the four sectors are labelled +2,+1,−1,−2, while the original involutions are recovered exactly through R = (7C − C³) / 6S = (C³ − 3C) / 2 Thus this four-sector coding is a reversible coordinate representation rather than a destructive scalar reduction. Point 0 is likewise formalized as balance rather than collapse. For any normalized positive state satisfying Tr(ρC) = 0 1 ≤ Var_ρ(C) ≤ 4 so cancellation of the first moment does not erase the structured second-order content. Finally, the 1/2→1/4 decomposition extends without finite-dimensional truncation to the Hilbert space of Hilbert–Schmidt operators S2(H), preserving the exact Parseval identity across all four sectors. In this exact mathematical sense, discarding a hidden sector is a change of readout; it is not a proof that the corresponding source structure is absent. The two papers therefore separate local exactness from reconstructive sufficiency. Part I supplies the contemporary external witness; Part II supplies the general conservative-reconstruction framework. This record continues and consolidates the earlier Origas programme on conservative completeness, Cabin 1/2, Riemann spectral reconstruction, Kakeya A+B, provenance, order and task-relative scientific adjudication. The physical interpretation of +t, −t, an absolute physical T, EPR completion, RingCross or a unique physical World B is not promoted here to mathematical theorem. These hypotheses remain subject to independent empirical validation. The exact claim is narrower and stronger: a formally correct reduced representation cannot claim reconstructive sufficiency beyond the distinctions it actually preserves. The resulting adjudication question is operational: Before scientific, algorithmic or institutional authority is extended from a representation to a real system, has that representation preserved the distinctions required by the task? TWO-PART RECORD STRUCTURE Part I THE WITNESS Riemann Strong Origas XII Zeta23 at the Residual Fibre Black-Box Closure, Rank–Trace Tightness and the Joint Weil Bridge K12. Part II THE FRAMEWORK Riemann Strong Origas XII+ The Conservative Reconstruction Framework Minimal conservative completion, Enigma-2 closure, reversible four-sector coding, Point-0 non-collapse, infinite-dimensional Hilbert–Schmidt lifting and the bridge/inertia relation. These two papers are deliberately complementary and should be read together. Part I establishes the concrete contemporary witness. Part II establishes the general mathematical framework exposed by that witness. Prior published records listed under Related identifiers provide the mathematical, methodological and documentary chain from Kakeya A+B, the Riemann Strong corpus and Conservative Completeness to the present two-part formulation. CLAIM BOUNDARY The exact layer of this record concerns representation, fibres, information loss, conservative completion, four-sector operator decompositions, Point-0 non-collapse, Hilbert–Schmidt lifting and finite block/inertia identities. Physical identifications involving +t, −t, absolute physical time T, RingCross, EPR completion or a unique physical World B remain open unless independently established by experiment. A Zenodo DOI establishes a persistent archival record and provenance; it is not by itself scientific certification of the claims contained in the files.