Pointwise Fisher–Presymplectic Compatibility Without Metric Descent: Exact Clock-Quotient Certificates in a Reversible Plücker–Markov Experiment

We establish a certified bridge from an explicitly specified affine Grassmann statistical experiment with Plücker weights and reversible Markov responses to clock-quotient curvature and transverse Fisher geometry, and identify an obstruction to metric descent in that same experiment. A complex 4×8 base matrix determines 61 selected positive determinantal weights and a fixed 435-edge Johnson network; seventeen prescribed affine directions in its pivot chart define the local parameter experiment. Four legal occupation sources, two spectral parameters, twenty independent unit-variance Gaussian responses, and one shared unknown logarithmic clock define an experiment with seventeen geometric parameters and one additional shared nuisance parameter. Across an exact one-percent birth-parameter interval, the curvature of its clock-regression one-form has rank sixteen; its unique characteristic line remains strictly visible to the profiled Fisher information. The induced sixteen-dimensional transverse Fisher–presymplectic pair has eight uniformly nonzero skew-adjoint spectral pairs. Nevertheless, at the authenticated central experiment, the Lie derivative of the Fisher-induced horizontal metric along the characteristic line is strictly nonzero. Thus pointwise positive transverse compatibility does not imply descent of that particular metric to the local symplectic leaf space. The central Lie obstruction and full-interval rank statements are kept distinct. The proof combines exact Plücker polynomial inequalities, reversible resolvent identities, outward rational intervals, two independent alternating-matrix eliminations, and a verified geometric mixed-jet certificate. Standard cotangent symplectic and nuisance-orthogonalization constructions are used, not claimed as new.

Authors

Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-10-31
DOI
https://doi.org/10.5281/zenodo.23837139
Primary Topic
Advanced Differential Geometry Research
Type
preprint
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preprint

Pointwise Fisher–Presymplectic Compatibility Without Metric Descent: Exact Clock-Quotient Certificates in a Reversible Plücker–Markov Experiment

Bin Du
Zenodo (CERN European Organization for Nuclear Research)
Advanced Differential Geometry Research
preprint

Pointwise Fisher–Presymplectic Compatibility Without Metric Descent: Exact Clock-Quotient Certificates in a Reversible Plücker–Markov Experiment

Bin Du
preprint en

Abstract

We establish a certified bridge from an explicitly specified affine Grassmann statistical experiment with Plücker weights and reversible Markov responses to clock-quotient curvature and transverse Fisher geometry, and identify an obstruction to metric descent in that same experiment. A complex 4×8 base matrix determines 61 selected positive determinantal weights and a fixed 435-edge Johnson network; seventeen prescribed affine directions in its pivot chart define the local parameter experiment. Four legal occupation sources, two spectral parameters, twenty independent unit-variance Gaussian responses, and one shared unknown logarithmic clock define an experiment with seventeen geometric parameters and one additional shared nuisance parameter. Across an exact one-percent birth-parameter interval, the curvature of its clock-regression one-form has rank sixteen; its unique characteristic line remains strictly visible to the profiled Fisher information. The induced sixteen-dimensional transverse Fisher–presymplectic pair has eight uniformly nonzero skew-adjoint spectral pairs. Nevertheless, at the authenticated central experiment, the Lie derivative of the Fisher-induced horizontal metric along the characteristic line is strictly nonzero. Thus pointwise positive transverse compatibility does not imply descent of that particular metric to the local symplectic leaf space. The central Lie obstruction and full-interval rank statements are kept distinct. The proof combines exact Plücker polynomial inequalities, reversible resolvent identities, outward rational intervals, two independent alternating-matrix eliminations, and a verified geometric mixed-jet certificate. Standard cotangent symplectic and nuisance-orthogonalization constructions are used, not claimed as new.

Zenodo (CERN European Organization for Nuclear Research)
Advanced Differential Geometry Research
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