{"paper":{"title":"Isometric Invariant Quantification of Gaussian Divergence over Poincare Disc","license":"http://creativecommons.org/licenses/by/4.0/","headline":"The L2-embedded hyperbolic isometric invariant on the Poincaré disc equals the spherical squared-Hellinger distance for Gaussian measures.","cross_cats":["math.IT","math.PR"],"primary_cat":"cs.IT","authors_text":"Levent Ali Meng\\\"ut\\\"urk","submitted_at":"2026-02-19T08:14:56Z","abstract_excerpt":"The paper presents a geometric duality between the spherical squared-Hellinger distance and a hyperbolic isometric invariant of the Poincare disc under the action of the general Mobius group. Motivated by the geometric connection, we propose the usage of the L2-embedded hyperbolic isometric invariant as an alternative way to quantify divergence between Gaussian measures as a contribution to information theory."},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"presents a geometric duality between the spherical squared-Hellinger distance and a hyperbolic isometric invariant of the Poincare disc under the action of the general Mobius group","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"That the L2-embedded hyperbolic isometric invariant provides a practically useful and distinct quantification of divergence between Gaussian measures beyond existing methods.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Geometric duality connects squared-Hellinger distance to a Mobius-invariant hyperbolic quantity on the Poincare disc, proposed as a new divergence for Gaussians.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"The L2-embedded hyperbolic isometric invariant on the Poincaré disc equals the spherical squared-Hellinger distance for Gaussian measures.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"c9d7db6247845ead726a0810e6ba59a59a96eff36d3cc2b97cda735742354cfe"},"source":{"id":"2602.17159","kind":"arxiv","version":5},"verdict":{"id":"eb6174ed-f0ea-457a-9643-7cfc362211ed","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-15T21:12:53.002303Z","strongest_claim":"presents a geometric duality between the spherical squared-Hellinger distance and a hyperbolic isometric invariant of the Poincare disc under the action of the general Mobius group","one_line_summary":"Geometric duality connects squared-Hellinger distance to a Mobius-invariant hyperbolic quantity on the Poincare disc, proposed as a new divergence for Gaussians.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"That the L2-embedded hyperbolic isometric invariant provides a practically useful and distinct quantification of divergence between Gaussian measures beyond existing methods.","pith_extraction_headline":"The L2-embedded hyperbolic isometric invariant on the Poincaré disc equals the spherical squared-Hellinger distance for Gaussian measures."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2602.17159/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":2,"snapshot_sha256":"07829fb03828d491ef82922e5d68af8deee6ada8ad3f90f03aeae1e6600d6052"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}