{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2021:IQX6ZAI4KVIXAXWMPZDZ3UV4BU","short_pith_number":"pith:IQX6ZAI4","schema_version":"1.0","canonical_sha256":"442fec811c5551705ecc7e479dd2bc0d39f9a3c1b025986fe7e4dea3beb1013c","source":{"kind":"arxiv","id":"2107.06163","version":2},"attestation_state":"computed","paper":{"title":"Hunt's hypothesis and symmetrization for general 1-dimensional diffusions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Liping Li","submitted_at":"2021-07-13T15:24:20Z","abstract_excerpt":"In this paper, we will consider the problem that how far from Hunt's hypothesis (H) to symmetrization for a general 1-dimensional diffusion. A characterization of (H) involving the classification of points for this diffusion will be first obtained. Then the main result shows that such a process is symmetrizable, if and only if (H) holds and a certain family of asymmetric shunt points is empty. Furthermore, we will also derive the representation of associated Dirichlet forms of general 1-dimensional diffusions under symmetry."},"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":"2107.06163","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2021-07-13T15:24:20Z","cross_cats_sorted":[],"title_canon_sha256":"8ec1825b8c7ebec21f8110b278753243ba77a98b1971dbc821ce064dfe792e26","abstract_canon_sha256":"16c17893290f73a0cbfba34ebab89670557a8c6788718b6ae983d8a664092c80"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T03:00:10.269395Z","signature_b64":"CIHB16rbh176Fjx3qTnibgfIHpx/oxpNL9wi1JKooJEJ1ebDQHndkk7Uu05arM2G3qoceNteMjzfHgj2+PuRDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"442fec811c5551705ecc7e479dd2bc0d39f9a3c1b025986fe7e4dea3beb1013c","last_reissued_at":"2026-07-05T03:00:10.268960Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T03:00:10.268960Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Hunt's hypothesis and symmetrization for general 1-dimensional diffusions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Liping Li","submitted_at":"2021-07-13T15:24:20Z","abstract_excerpt":"In this paper, we will consider the problem that how far from Hunt's hypothesis (H) to symmetrization for a general 1-dimensional diffusion. A characterization of (H) involving the classification of points for this diffusion will be first obtained. Then the main result shows that such a process is symmetrizable, if and only if (H) holds and a certain family of asymmetric shunt points is empty. Furthermore, we will also derive the representation of associated Dirichlet forms of general 1-dimensional diffusions under symmetry."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2107.06163","kind":"arxiv","version":2},"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/2107.06163/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2107.06163","created_at":"2026-07-05T03:00:10.269031+00:00"},{"alias_kind":"arxiv_version","alias_value":"2107.06163v2","created_at":"2026-07-05T03:00:10.269031+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2107.06163","created_at":"2026-07-05T03:00:10.269031+00:00"},{"alias_kind":"pith_short_12","alias_value":"IQX6ZAI4KVIX","created_at":"2026-07-05T03:00:10.269031+00:00"},{"alias_kind":"pith_short_16","alias_value":"IQX6ZAI4KVIXAXWM","created_at":"2026-07-05T03:00:10.269031+00:00"},{"alias_kind":"pith_short_8","alias_value":"IQX6ZAI4","created_at":"2026-07-05T03:00:10.269031+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/IQX6ZAI4KVIXAXWMPZDZ3UV4BU","json":"https://pith.science/pith/IQX6ZAI4KVIXAXWMPZDZ3UV4BU.json","graph_json":"https://pith.science/api/pith-number/IQX6ZAI4KVIXAXWMPZDZ3UV4BU/graph.json","events_json":"https://pith.science/api/pith-number/IQX6ZAI4KVIXAXWMPZDZ3UV4BU/events.json","paper":"https://pith.science/paper/IQX6ZAI4"},"agent_actions":{"view_html":"https://pith.science/pith/IQX6ZAI4KVIXAXWMPZDZ3UV4BU","download_json":"https://pith.science/pith/IQX6ZAI4KVIXAXWMPZDZ3UV4BU.json","view_paper":"https://pith.science/paper/IQX6ZAI4","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2107.06163&json=true","fetch_graph":"https://pith.science/api/pith-number/IQX6ZAI4KVIXAXWMPZDZ3UV4BU/graph.json","fetch_events":"https://pith.science/api/pith-number/IQX6ZAI4KVIXAXWMPZDZ3UV4BU/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/IQX6ZAI4KVIXAXWMPZDZ3UV4BU/action/timestamp_anchor","attest_storage":"https://pith.science/pith/IQX6ZAI4KVIXAXWMPZDZ3UV4BU/action/storage_attestation","attest_author":"https://pith.science/pith/IQX6ZAI4KVIXAXWMPZDZ3UV4BU/action/author_attestation","sign_citation":"https://pith.science/pith/IQX6ZAI4KVIXAXWMPZDZ3UV4BU/action/citation_signature","submit_replication":"https://pith.science/pith/IQX6ZAI4KVIXAXWMPZDZ3UV4BU/action/replication_record"}},"created_at":"2026-07-05T03:00:10.269031+00:00","updated_at":"2026-07-05T03:00:10.269031+00:00"}