{"paper":{"title":"Contact quasi-states and their applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.SG","authors_text":"Igor Uljarevi\\'c, Jun Zhang","submitted_at":"2025-03-24T14:58:51Z","abstract_excerpt":"We introduce the notions of partial contact quasi-state and contact quasi-measure. Using the contact spectral invariant from the work by Djordjevi\\'c-Uljarevi\\'c-Zhang, one can construct partial contact quasi-states and contact quasi-measures on each contact manifold fillable by a Liouville domain with non-vanishing and $\\mathbb{Z}$-graded symplectic homology. As an application, we present an alternative proof of the contact big fibre theorem from the recent work by Sun-Uljarevi\\'c-Varolgunes under a mild topological condition. Our proof follows a more \"classical\" approach developed by Entov-P"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2503.18750","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2503.18750/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":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}