{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:EDIC3XVO4PRYQGCZ24NMCPEGPC","short_pith_number":"pith:EDIC3XVO","schema_version":"1.0","canonical_sha256":"20d02ddeaee3e3881859d71ac13c8678a162e88e8053304428ab81dc21bd18a2","source":{"kind":"arxiv","id":"1812.10949","version":1},"attestation_state":"computed","paper":{"title":"Approximation of quasi-states on manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NA","math.SG"],"primary_cat":"math.FA","authors_text":"Adi Dickstein, Frol Zapolsky","submitted_at":"2018-12-28T10:40:22Z","abstract_excerpt":"Quasi-states are certain not necessarily linear functionals on the space of continuous functions on a compact Hausdorff space. They were discovered as a part of an attempt to understand the axioms of quantum mechanics due to von Neumann. A very interesting and fundamental example is given by the so-called median quasi-state on the 2-sphere. In this paper we present an algorithm which numerically computes it to any specified accuracy. The error estimate of the algorithm crucially relies on metric continuity properties of a map, which constructs quasi-states from probability measures, with respe"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1812.10949","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-12-28T10:40:22Z","cross_cats_sorted":["math.NA","math.SG"],"title_canon_sha256":"68c7daf4512f390b5241ae64ad5550b128413d783c26c56092adc703cfea5b1d","abstract_canon_sha256":"b39f0f5d8382a521bf2c21b036108bf67602f5c536c49d028c8f6d18781800b8"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:57:16.715234Z","signature_b64":"/9pfJdzrLx7v3cbdIr0NjTAiUCd/qWUDFqQEuHl6pbHrfFC7bmTgKJrdRhHDNjrY9FsdyA37NjJsQ7A5EGzCCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"20d02ddeaee3e3881859d71ac13c8678a162e88e8053304428ab81dc21bd18a2","last_reissued_at":"2026-05-17T23:57:16.714720Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:57:16.714720Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Approximation of quasi-states on manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NA","math.SG"],"primary_cat":"math.FA","authors_text":"Adi Dickstein, Frol Zapolsky","submitted_at":"2018-12-28T10:40:22Z","abstract_excerpt":"Quasi-states are certain not necessarily linear functionals on the space of continuous functions on a compact Hausdorff space. They were discovered as a part of an attempt to understand the axioms of quantum mechanics due to von Neumann. A very interesting and fundamental example is given by the so-called median quasi-state on the 2-sphere. In this paper we present an algorithm which numerically computes it to any specified accuracy. The error estimate of the algorithm crucially relies on metric continuity properties of a map, which constructs quasi-states from probability measures, with respe"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.10949","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":""},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1812.10949","created_at":"2026-05-17T23:57:16.714797+00:00"},{"alias_kind":"arxiv_version","alias_value":"1812.10949v1","created_at":"2026-05-17T23:57:16.714797+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1812.10949","created_at":"2026-05-17T23:57:16.714797+00:00"},{"alias_kind":"pith_short_12","alias_value":"EDIC3XVO4PRY","created_at":"2026-05-18T12:32:22.470017+00:00"},{"alias_kind":"pith_short_16","alias_value":"EDIC3XVO4PRYQGCZ","created_at":"2026-05-18T12:32:22.470017+00:00"},{"alias_kind":"pith_short_8","alias_value":"EDIC3XVO","created_at":"2026-05-18T12:32:22.470017+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/EDIC3XVO4PRYQGCZ24NMCPEGPC","json":"https://pith.science/pith/EDIC3XVO4PRYQGCZ24NMCPEGPC.json","graph_json":"https://pith.science/api/pith-number/EDIC3XVO4PRYQGCZ24NMCPEGPC/graph.json","events_json":"https://pith.science/api/pith-number/EDIC3XVO4PRYQGCZ24NMCPEGPC/events.json","paper":"https://pith.science/paper/EDIC3XVO"},"agent_actions":{"view_html":"https://pith.science/pith/EDIC3XVO4PRYQGCZ24NMCPEGPC","download_json":"https://pith.science/pith/EDIC3XVO4PRYQGCZ24NMCPEGPC.json","view_paper":"https://pith.science/paper/EDIC3XVO","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1812.10949&json=true","fetch_graph":"https://pith.science/api/pith-number/EDIC3XVO4PRYQGCZ24NMCPEGPC/graph.json","fetch_events":"https://pith.science/api/pith-number/EDIC3XVO4PRYQGCZ24NMCPEGPC/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/EDIC3XVO4PRYQGCZ24NMCPEGPC/action/timestamp_anchor","attest_storage":"https://pith.science/pith/EDIC3XVO4PRYQGCZ24NMCPEGPC/action/storage_attestation","attest_author":"https://pith.science/pith/EDIC3XVO4PRYQGCZ24NMCPEGPC/action/author_attestation","sign_citation":"https://pith.science/pith/EDIC3XVO4PRYQGCZ24NMCPEGPC/action/citation_signature","submit_replication":"https://pith.science/pith/EDIC3XVO4PRYQGCZ24NMCPEGPC/action/replication_record"}},"created_at":"2026-05-17T23:57:16.714797+00:00","updated_at":"2026-05-17T23:57:16.714797+00:00"}