{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:EOKSVE275K5F5MJG4SWEFBKNCS","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"07d5fe7e9798bda4620b32ef2ab836abd0fc0d8e4da6bb5040a64bf7d16dc5f3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-03-31T08:23:17Z","title_canon_sha256":"dd4be102fc1bd845e4bdb36a75b7469cd2f30f6d50d0eeed2449698bbde29b4f"},"schema_version":"1.0","source":{"id":"1703.10790","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1703.10790","created_at":"2026-05-17T23:56:00Z"},{"alias_kind":"arxiv_version","alias_value":"1703.10790v2","created_at":"2026-05-17T23:56:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.10790","created_at":"2026-05-17T23:56:00Z"},{"alias_kind":"pith_short_12","alias_value":"EOKSVE275K5F","created_at":"2026-05-18T12:31:12Z"},{"alias_kind":"pith_short_16","alias_value":"EOKSVE275K5F5MJG","created_at":"2026-05-18T12:31:12Z"},{"alias_kind":"pith_short_8","alias_value":"EOKSVE27","created_at":"2026-05-18T12:31:12Z"}],"graph_snapshots":[{"event_id":"sha256:e85709792f7b6410c820b353fca8d0ca2500179323e4e38a75a888cd3232af0f","target":"graph","created_at":"2026-05-17T23:56:00Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"Let $\\mathbf{X}=\\{X_t\\}_{t\\geq 0}$ be a L\\'{e}vy process in $\\mathbb{R}^d$ and $\\Omega$ be an open subset of $\\mathbb{R}^d$ with finite Lebesgue measure. The quantity $H (t) = \\int_{\\Omega} \\mathbb{P}^{x} (X_t\\in \\Omega ^c) d x$ is called the heat content. In this article we consider its generalized version $H_g^\\mu (t) = \\int_{\\mathbb{R}^d}\\mathbb{E}^{x} g(X_t)\\mu( d x )$, where $g$ is a bounded function and $\\mu$ a finite Borel measure. We study its asymptotic behaviour at zero for various classes of L\\'{e}vy processes.","authors_text":"Tomasz Grzywny, Wojciech Cygan","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-03-31T08:23:17Z","title":"A note on the generalized heat content for L\\'evy processes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.10790","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:ad711eec9b4c489ff0de949208dffba18c08c47fd7c2857075050091386ad047","target":"record","created_at":"2026-05-17T23:56:00Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"07d5fe7e9798bda4620b32ef2ab836abd0fc0d8e4da6bb5040a64bf7d16dc5f3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-03-31T08:23:17Z","title_canon_sha256":"dd4be102fc1bd845e4bdb36a75b7469cd2f30f6d50d0eeed2449698bbde29b4f"},"schema_version":"1.0","source":{"id":"1703.10790","kind":"arxiv","version":2}},"canonical_sha256":"23952a935feaba5eb126e4ac42854d14abe083a2e3dc88695f39e7f8d1ff90ba","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"23952a935feaba5eb126e4ac42854d14abe083a2e3dc88695f39e7f8d1ff90ba","first_computed_at":"2026-05-17T23:56:00.391661Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:56:00.391661Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6pZobw9mlu+WYYaRkKpdcd5dhoutQjnf1i4YWchr6UBEzk8vmfmdBmgcy9pSMRK09fQBNAxWwpyYkfE69D4NDg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:56:00.392450Z","signed_message":"canonical_sha256_bytes"},"source_id":"1703.10790","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ad711eec9b4c489ff0de949208dffba18c08c47fd7c2857075050091386ad047","sha256:e85709792f7b6410c820b353fca8d0ca2500179323e4e38a75a888cd3232af0f"],"state_sha256":"f7e2094307d3484ddc1fe4a7d500ddd47a3ac3b89b013c6dc889ca471ccec83f"}