{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:WO2EP2KJ6LM6YWHOBW63PDDVPI","short_pith_number":"pith:WO2EP2KJ","schema_version":"1.0","canonical_sha256":"b3b447e949f2d9ec58ee0dbdb78c757a1d740253884a1e3d8cc826749f0dea56","source":{"kind":"arxiv","id":"1501.06128","version":2},"attestation_state":"computed","paper":{"title":"Intrinsic Contractivity of Feynman-Kac Semigroups for Symmetric Jump Processes with Infinite Range Jumps","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Jian Wang, Xin Chen","submitted_at":"2015-01-25T08:28:27Z","abstract_excerpt":"Let $(X_t)_{t\\ge 0}$ be a symmetric strong Markov process generated by non-local regular Dirichlet form $(D,\\D(D))$ as follows \\begin{equation*} \\begin{split} & D(f,g)=\\int_{\\R^d}\\int_{\\R^d}\\big(f(x)-f(y)\\big)\\big(g(x)-g(y)\\big) J(x,y)\\,dx\\,dy, \\quad f,g\\in \\D(D) \\end{split} \\end{equation*} where $J(x,y)$ is a strictly positive and symmetric measurable function on $\\R^d\\times \\R^d$. We study the intrinsic hypercontractivity, intrinsic supercontractivity and intrinsic ultracontractivity for the Feynman-Kac semigroup $$ T^V_t(f)(x)=\\Ee^x\\left(\\exp\\Big(-\\int_0^tV(X_s)\\,ds\\Big)f(X_t)\\right),\\,\\, x"},"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":"1501.06128","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-01-25T08:28:27Z","cross_cats_sorted":[],"title_canon_sha256":"c8b3bf37c4c36aff94079b494607c22c60710020c1ba043ad2f20ad5e18492dd","abstract_canon_sha256":"4b2e1619d02e7e07389f7010869c72919b5ec036796455212a73c277f09c47e0"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:17:54.261587Z","signature_b64":"jTIrJqEGaa56uiZWSM8x4GHdU1BG4Cl4G970jbPeXFCyq0LH2wfHIBhRyL+iwmeP86XWQhhO3a23qYk5qsFRBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b3b447e949f2d9ec58ee0dbdb78c757a1d740253884a1e3d8cc826749f0dea56","last_reissued_at":"2026-05-18T02:17:54.260946Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:17:54.260946Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Intrinsic Contractivity of Feynman-Kac Semigroups for Symmetric Jump Processes with Infinite Range Jumps","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Jian Wang, Xin Chen","submitted_at":"2015-01-25T08:28:27Z","abstract_excerpt":"Let $(X_t)_{t\\ge 0}$ be a symmetric strong Markov process generated by non-local regular Dirichlet form $(D,\\D(D))$ as follows \\begin{equation*} \\begin{split} & D(f,g)=\\int_{\\R^d}\\int_{\\R^d}\\big(f(x)-f(y)\\big)\\big(g(x)-g(y)\\big) J(x,y)\\,dx\\,dy, \\quad f,g\\in \\D(D) \\end{split} \\end{equation*} where $J(x,y)$ is a strictly positive and symmetric measurable function on $\\R^d\\times \\R^d$. We study the intrinsic hypercontractivity, intrinsic supercontractivity and intrinsic ultracontractivity for the Feynman-Kac semigroup $$ T^V_t(f)(x)=\\Ee^x\\left(\\exp\\Big(-\\int_0^tV(X_s)\\,ds\\Big)f(X_t)\\right),\\,\\, x"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.06128","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":""},"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":"1501.06128","created_at":"2026-05-18T02:17:54.261027+00:00"},{"alias_kind":"arxiv_version","alias_value":"1501.06128v2","created_at":"2026-05-18T02:17:54.261027+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.06128","created_at":"2026-05-18T02:17:54.261027+00:00"},{"alias_kind":"pith_short_12","alias_value":"WO2EP2KJ6LM6","created_at":"2026-05-18T12:29:47.479230+00:00"},{"alias_kind":"pith_short_16","alias_value":"WO2EP2KJ6LM6YWHO","created_at":"2026-05-18T12:29:47.479230+00:00"},{"alias_kind":"pith_short_8","alias_value":"WO2EP2KJ","created_at":"2026-05-18T12:29:47.479230+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/WO2EP2KJ6LM6YWHOBW63PDDVPI","json":"https://pith.science/pith/WO2EP2KJ6LM6YWHOBW63PDDVPI.json","graph_json":"https://pith.science/api/pith-number/WO2EP2KJ6LM6YWHOBW63PDDVPI/graph.json","events_json":"https://pith.science/api/pith-number/WO2EP2KJ6LM6YWHOBW63PDDVPI/events.json","paper":"https://pith.science/paper/WO2EP2KJ"},"agent_actions":{"view_html":"https://pith.science/pith/WO2EP2KJ6LM6YWHOBW63PDDVPI","download_json":"https://pith.science/pith/WO2EP2KJ6LM6YWHOBW63PDDVPI.json","view_paper":"https://pith.science/paper/WO2EP2KJ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1501.06128&json=true","fetch_graph":"https://pith.science/api/pith-number/WO2EP2KJ6LM6YWHOBW63PDDVPI/graph.json","fetch_events":"https://pith.science/api/pith-number/WO2EP2KJ6LM6YWHOBW63PDDVPI/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/WO2EP2KJ6LM6YWHOBW63PDDVPI/action/timestamp_anchor","attest_storage":"https://pith.science/pith/WO2EP2KJ6LM6YWHOBW63PDDVPI/action/storage_attestation","attest_author":"https://pith.science/pith/WO2EP2KJ6LM6YWHOBW63PDDVPI/action/author_attestation","sign_citation":"https://pith.science/pith/WO2EP2KJ6LM6YWHOBW63PDDVPI/action/citation_signature","submit_replication":"https://pith.science/pith/WO2EP2KJ6LM6YWHOBW63PDDVPI/action/replication_record"}},"created_at":"2026-05-18T02:17:54.261027+00:00","updated_at":"2026-05-18T02:17:54.261027+00:00"}