University Foundation

Regular-Closed Flats of Matroids: Cocircuit Reconstruction, Reconstruction Defect, and Finite Obstruction Hierarchies

Matroid theory is naturally a theory of closure. A matroid M on ground set E determines a closure operatorcl_M:2^E→2^E,and the flats of M are precisely its closed sets.Once a closure operator is present, however, a second standard construction becomes available. One may define an...

Regular-Closed Flats of Matroids: Cocircuit Reconstruction, Reconstruction Defect, and Finite Obstruction Hierarchies

Matroid theory is naturally a theory of closure. A matroid M on ground set E determines a closure operatorcl_M:2^E→2^E,and the flats of M are precisely its closed sets.Once a closure operator is present, however, a second standard construction becomes available. One may define an...

Directional Probe Energy in Banded Fractional Hessians Fractional stiffness, angular completeness, spectral mixing, and the geometric-coercivity problem

We introduce a banded fractional-Hessian framework for measuring the scale-dependent energy of tube-localized directional probes. For an -normalized probe concentrated in a unit-length tube of transverse radius , a band with fractional stiffness index contributes energy of order...

Directional Probe Energy in Banded Fractional Hessians Fractional stiffness, angular completeness, spectral mixing, and the geometric-coercivity problem

We introduce a banded fractional-Hessian framework for measuring the scale-dependent energy of tube-localized directional probes. For an -normalized probe concentrated in a unit-length tube of transverse radius , a band with fractional stiffness index contributes energy of order...

Scientific Metadesign

Identifiability, Intervention, Structured Nulls, and Evidential Claim Ceilings The general framework is a completed methodological construction. This manuscript develops Scientific Metadesign, a framework for specifying the scientific objects, evidential gates, result classes, an...

From Phase-Spatial Closure to Einstein–Cartan Dynamics Global Frame Non-Closure and the Conditional Selection of the Tetrad–Palatini Action

This paper develops a gravitational extension of phase-spatial invariance in which relativistic geometry is not assumed as the primitive arena of physics. The construction begins with the generator structure and with a real, homogeneous, rotationally invariant closure scalar on t...

From Phase-Spatial Closure to Einstein–Cartan Dynamics Global Frame Non-Closure and the Conditional Selection of the Tetrad–Palatini Action

This paper develops a gravitational extension of phase-spatial invariance in which relativistic geometry is not assumed as the primitive arena of physics. The construction begins with the generator structure and with a real, homogeneous, rotationally invariant closure scalar on t...