6 papers
Radial Integration in Continuous Dimension: A Mellin-Gamma Classification of Euclidean Ball Volume
Andreu Ballus Santacana
We classify positive linear functionals on satisfying scaling covariance of degree and Gaussian normalization to . We prove that the unique su…
An Incremental Framework for Topological Dialogue Semantics: Efficient Reasoning in Discrete Spaces
Andreu Ballus Santacana
We present a tractable, incremental framework for topological dialogue semantics based on finite, discrete semantic spaces. Building on the intuition that utterances correspond to…
Proof-Carrying Analytic Approximation: Local-to-Global Evidence Transport at Encoding Cost
Andreu Ballus Santacana
Under quasi-uniform refinement, bounded local-encoding hypotheses, and local approximation of order in a rational piecewise-polynomial presentation of $W^{1,2}(0…
The Dimension-Shift Category and Its Mellin-Gamma Representation
Andreu Ballus Santacana
We define a thin category of dimension shifts and a category of positive Radon measures with Radon--Nikodym density morphisms. We classify scali…
From Copying to Corelations via Ancestry Partitions
Andreu Ballus Santacana
We study the free PROP on a single binary generator . The ancestry functor , defined by connected components of…
The Syncytial Mesh Model: A Mesoscale Control-Field Framework for Scale-Dependent Coherence in the Brain
Andreu Ballus Santacana
The Syncytial Mesh Model introduces a three-layered framework for large-scale brain dynamics integrating local neural circuitry, macrostructural connectivity, and a slow mesoscale…