Constrained-Value Enclosures and Identified Stationary Continuation in a Lorentzian Simplicial Model

This paper derives a source-bound constrained scalar-value enclosure from an already evaluated full normal-normal operator in a boundary-capped Lorentzian simplicial model. The identity Q=-int_0^1 u A_nn(y_u)[Z,Z] du gives |Q|<=L_NN U_0^2/2 for arbitrary independent complex normal directions on the admitted response homotopies. The replacement is propagated through all six normalized rows, every entry of the 6x6 Jacobian-defect matrix, and the full affine-tangent second variation. A prospectively frozen exact-anchor rebase and six fresh complete source evaluations verify locally unique stationary sections on [12288,196608] tau for both identified branches, extending connected source-conditional coverage to [3,196608] tau and recovering all 114 original stationary equations. A controlled old-D2 calculation on the same new geometry also passes, so the sharper bound improves the complete enclosure but is not shown necessary for the selected endpoint. The conclusions remain conditional on the stated source, analytic-membership, branch, and directed-enclosure premises; an accepted Lean supporting subset formalizes finite algebraic, exact-arithmetic, overlap, and recovery components but not the complete physical source or analytic existence argument. Supporting files: buildable LaTeX source, complete numerical supplement, and accepted formal supplement. The numerical and formal records retain their actual source-conditional and supporting-subset limits.

Authors

Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-11-01
DOI
https://doi.org/10.5281/zenodo.23873576
Primary Topic
Relativity and Gravitational Theory
Type
preprint
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preprint

Constrained-Value Enclosures and Identified Stationary Continuation in a Lorentzian Simplicial Model

Qingchun Zhang
Zenodo (CERN European Organization for Nuclear Research)
Relativity and Gravitational Theory
preprint

Constrained-Value Enclosures and Identified Stationary Continuation in a Lorentzian Simplicial Model

Qingchun Zhang
preprint en

Abstract

This paper derives a source-bound constrained scalar-value enclosure from an already evaluated full normal-normal operator in a boundary-capped Lorentzian simplicial model. The identity Q=-int_0^1 u A_nn(y_u)[Z,Z] du gives |Q|<=L_NN U_0^2/2 for arbitrary independent complex normal directions on the admitted response homotopies. The replacement is propagated through all six normalized rows, every entry of the 6x6 Jacobian-defect matrix, and the full affine-tangent second variation. A prospectively frozen exact-anchor rebase and six fresh complete source evaluations verify locally unique stationary sections on [12288,196608] tau for both identified branches, extending connected source-conditional coverage to [3,196608] tau and recovering all 114 original stationary equations. A controlled old-D2 calculation on the same new geometry also passes, so the sharper bound improves the complete enclosure but is not shown necessary for the selected endpoint. The conclusions remain conditional on the stated source, analytic-membership, branch, and directed-enclosure premises; an accepted Lean supporting subset formalizes finite algebraic, exact-arithmetic, overlap, and recovery components but not the complete physical source or analytic existence argument. Supporting files: buildable LaTeX source, complete numerical supplement, and accepted formal supplement. The numerical and formal records retain their actual source-conditional and supporting-subset limits.

Zenodo (CERN European Organization for Nuclear Research)
Relativity and Gravitational Theory
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