arXiv:2603. 14169v2 Announce Type: replace-cross Abstract: Average treatment effects (ATE) and conditional average treatment effects (CATE) are foundational causal estimands, but they target changes in expected outcomes and can miss treatment-induced changes in the shape of outcome distributions.
arXiv:2606. 01184v1 Announce Type: cross Abstract: Many interventions alter the structure of an outcome distribution rather than its mean: they can split a population into disconnected regimes, create loops or holes, generate branches, or reorganize an outcome cloud while leaving the average response nearly unchanged.
arXiv:2512.23348v3 Announce Type: replace-cross Abstract: We introduce a data-analysis framework based on filtrations of finite topological spaces. Starting from a finite metric data set, we construc...
arXiv:2607. 15629v1 Announce Type: cross Abstract: Topos causal models recast causal inference inside a topos: a causal world is a presheaf, an intervention is a characteristic map into the subobject classifier, and reasoning is carried out in the intuitionistic internal language.
This paper introduces a categorical account of infinitesimal causality in Frobenius Markov categories equipped with tangent-bundle semantics. IDC captures the infinitesimal layer in which interventions act as tangent deformations of copy/discard structure.
arXiv:2606. 24621v1 Announce Type: cross Abstract: This paper introduces a categorical account of infinitesimal causality in Frobenius Markov categories equipped with tangent-bundle semantics.
HoloAegis is a minimally parametric topological inference framework that uses frozen representations to map text onto the unit sphere and makes decisions via Gibbs‑Boltzmann free‑energy differences over pre‑computed anchor centroids. On a frozen three‑benchmark protocol, it matches WildGuard‑7B on toxicity, outperforms it on harmful behaviors, but underperforms on oversafety detection, while ShieldGemma‑2B fails on indirect harms. The study demonstrates that geometric guardrails can substitute for LLM judges in some cases and must defer to them in others, with anchor banks reducing score variance and boundary displacement.
The paper introduces persistent magnitude homology as a functorial invariant for quantitative equational theories, providing a barcode that captures the metric structure of the free algebra generated by a metric space of generators. It shows how this invariant combines graded magnitude homology with persistence, yielding stability estimates and a method to compare barcodes when theories are extended. Four concrete examples illustrate the theory in each homological degree.
The article introduces a new non‑archimedean metric, the cophenetic metric, defined on persistent homology classes of all degrees. It demonstrates that zeroth persistent homology combined with this metric and various hierarchical clustering algorithms yields statistically verifiable, commensurate topological information on multiple datasets. The resulting clusters, evaluated by silhouette score and Rand index, perform well, and the metric enables visualization of inter‑relations among persistent homology classes across all degrees via rooted trees.
We propose ZX-Calculus (Knowledge Evolution Calculus), a conservative extension of Martin-Lof Dependent Type Theory (MLTT) integrating trace-indexed types, presheaf non-monotone semantics, and constructive AGM belief revision. A Coq mechanisation accompanies the paper (34 complete proofs; zero admits for the two central results).
arXiv:2506. 15020v2 Announce Type: replace-cross Abstract: We propose persistent discrete homology as a tool for topological data analysis and discuss its advantages over the existing methods.
arXiv:2607. 24425v1 Announce Type: new Abstract: Large language models place structured concepts on geometrically faithful manifolds: weekdays lie on a circle, months on another, usually taken to be a fixed world-model the network stores and looks up.
The paper introduces Positive Topology, a framework built on a basic relation between points (or models) and observable properties. It identifies two complementary structures: universal refinement and cover, and positivity and witnessed existence, showing that each can reconstruct the underlying relation. The authors present both information‑theoretic and game‑theoretic interpretations, and discuss how resource constraints can be integrated, illustrating applications in medical diagnosis, legal reasoning, and AI.