Finite Reclosure and Temporal Fisher Transport: A Local Lorentzian Response-Curvature Construction
- 1Independent Researcher, Japan
Abstract
We construct an explicit local Lorentzian response geometry with nonzero curvature from two previously separated ingredients: the Fisher–Rao geometry obtained as a hidden-flow quotient of a finite closure–residue system, and a continuous-time population flow induced by a finite-dimensional CPTP/GKSL dynamics. At the uniform four-state cell, the Fisher metric agrees with the metric used in the covariant finite-reclosure construction, and the exact quadratic reclosure map reproduces the constant-curvature Fisher tensor with a fixed coefficient. Transporting Fisher distinguishability by the observable Markov flow gives the unique pullback metric associated with operational tangent covariance. At a reversible stationary point the corresponding shape operator equals the Markov relaxation generator restricted to the probability tangent space. For an explicit anisotropic four-state reversible generator we compute a nonzero Codazzi defect and hence a nonzero mixed Lorentzian Riemann-curvature component. This supplies a finite, exact witness of local Lorentzian response curvature; it is not a derivation of the Einstein field equations, a universal physical light cone, or a global spacetime.
We further audit three stronger extensions. First, the reclosure-twist map admits a closed finite-cell formula; under a canonical Fisher-frame identification, torsion-free matching selects the normalization λ = 1. Second, exact microscopic propagation on the natural periodic K4 root lattice is anisotropic, while its quadratic infrared spatial symbol is forced to be Fisher-isotropic. Third, universal coupling and common propagating null branches follow conditionally from a single-master generative completeness principle, while a decoupled spectator construction shows that such completeness is not implied by the preceding finite reclosure results. These stronger statements are kept logically separate from the minimum curvature theorem.
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BibTeX
@misc{tagawa2026finite,
title = {{Finite Reclosure and Temporal Fisher Transport: A Local Lorentzian Response-Curvature Construction}},
author = {Katsuya Tagawa},
howpublished = {Zenodo},
year = {2026},
month = oct,
doi = {10.5281/zenodo.23416342},
url = {https://zenodo.org/records/23416342},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Finite Reclosure and Temporal Fisher Transport: A Local Lorentzian Response-Curvature Construction
AU - Katsuya Tagawa
PY - 2026
DA - 2026/10/16
PB - Zenodo
DO - 10.5281/zenodo.23416342
UR - https://zenodo.org/records/23416342
AB - We construct an explicit local Lorentzian response geometry with nonzero curvature from two previously separated ingredients: the Fisher–Rao geometry obtained as a hidden-flow quotient of a finite closure–residue system, and a continuous-time population flow induced by a finite-dimensional CPTP/GKSL dynamics. At the uniform four-state cell, the Fisher metric agrees with the metric used in the covariant finite-reclosure construction, and the exact quadratic reclosure map reproduces the constant-curvature Fisher tensor with a fixed coefficient. Transporting Fisher distinguishability by the observable Markov flow gives the unique pullback metric associated with operational tangent covariance. At a reversible stationary point the corresponding shape operator equals the Markov relaxation generator restricted to the probability tangent space. For an explicit anisotropic four-state reversible generator we compute a nonzero Codazzi defect and hence a nonzero mixed Lorentzian Riemann-curvature component. This supplies a finite, exact witness of local Lorentzian response curvature; it is not a derivation of the Einstein field equations, a universal physical light cone, or a global spacetime. We further audit three stronger extensions. First, the reclosure-twist map admits a closed finite-cell formula; under a canonical Fisher-frame identification, torsion-free matching selects the normalization λ = 1. Second, exact microscopic propagation on the natural periodic K4 root lattice is anisotropic, while its quadratic infrared spatial symbol is forced to be Fisher-isotropic. Third, universal coupling and common propagating null branches follow conditionally from a single-master generative completeness principle, while a decoupled spectator construction shows that such completeness is not implied by the preceding finite reclosure results. These stronger statements are kept logically separate from the minimum curvature theorem.
ER -