{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:4GPRFAX5NQARSINXZGFP6V6TPM","short_pith_number":"pith:4GPRFAX5","canonical_record":{"source":{"id":"1809.08611","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-09-23T15:04:04Z","cross_cats_sorted":[],"title_canon_sha256":"a702f90f61fe9ee2918ec816bb9c9cbd82c2c333621b8f8925beb516d8ab7720","abstract_canon_sha256":"c5b08c52dff9b46327f7d9e3e3b0e9d3102f7efdcae3c53ed74d7db11cd14c42"},"schema_version":"1.0"},"canonical_sha256":"e19f1282fd6c011921b7c98aff57d37b344ae50cc3615a7faf8c2c5dda69d98c","source":{"kind":"arxiv","id":"1809.08611","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1809.08611","created_at":"2026-05-17T23:44:07Z"},{"alias_kind":"arxiv_version","alias_value":"1809.08611v3","created_at":"2026-05-17T23:44:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1809.08611","created_at":"2026-05-17T23:44:07Z"},{"alias_kind":"pith_short_12","alias_value":"4GPRFAX5NQAR","created_at":"2026-05-18T12:32:05Z"},{"alias_kind":"pith_short_16","alias_value":"4GPRFAX5NQARSINX","created_at":"2026-05-18T12:32:05Z"},{"alias_kind":"pith_short_8","alias_value":"4GPRFAX5","created_at":"2026-05-18T12:32:05Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:4GPRFAX5NQARSINXZGFP6V6TPM","target":"record","payload":{"canonical_record":{"source":{"id":"1809.08611","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-09-23T15:04:04Z","cross_cats_sorted":[],"title_canon_sha256":"a702f90f61fe9ee2918ec816bb9c9cbd82c2c333621b8f8925beb516d8ab7720","abstract_canon_sha256":"c5b08c52dff9b46327f7d9e3e3b0e9d3102f7efdcae3c53ed74d7db11cd14c42"},"schema_version":"1.0"},"canonical_sha256":"e19f1282fd6c011921b7c98aff57d37b344ae50cc3615a7faf8c2c5dda69d98c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:44:07.625942Z","signature_b64":"cmOnM9R7tS/pmDNw5MIhj96hibrGSgnJ77hYKcIw+x2NxpRFwnlDKkOXqD9xs0ngVUkcMDFJM1AN/Zz7hE7uBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e19f1282fd6c011921b7c98aff57d37b344ae50cc3615a7faf8c2c5dda69d98c","last_reissued_at":"2026-05-17T23:44:07.625256Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:44:07.625256Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1809.08611","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:44:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lRtOBHG3nEcFO5IYM2KxwdgWTxrqM7ClgEz7hP64iM4MrLdoA1xaxE2uXYCmjU5x60z3oOhmfCv8C5KHW8qZCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T12:58:02.893289Z"},"content_sha256":"666450313622d7b219a6f3954c79602941a940f16f87e406d6607bf73b105335","schema_version":"1.0","event_id":"sha256:666450313622d7b219a6f3954c79602941a940f16f87e406d6607bf73b105335"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:4GPRFAX5NQARSINXZGFP6V6TPM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Nearly hyperharmonic functions are infima of excessive functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Ivan Netuka, Wolfhard Hansen","submitted_at":"2018-09-23T15:04:04Z","abstract_excerpt":"Let $\\mathfrak X$ be a Hunt process on a locally compact space $X$ such that the set $\\mathcal E_{\\mathfrak X}$ of its Borel measurable excessive functions separates points, every function in $\\mathcal E_{\\mathfrak X}$ is the supremum of its continuous minorants in $\\mathcal E_{\\mathfrak X}$ and there are strictly positive continuous functions $v,w\\in\\mathcal E_{\\mathfrak X}$ such that $v/w$ vanishes at infinity.\n  A numerical function $u\\ge 0$ on $X$ is said to be nearly hyperharmonic, if $\\int^\\ast u\\circ X_{\\tau_V}\\,dP^x\\le u(x)$ for all $x\\in X$ and relatively compact open neighborhoods $V"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.08611","kind":"arxiv","version":3},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:44:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"goeWQmzDEcvFbzhYiYYQwxyF1lh4FTeSe9ohMLMOcz6ZCPllWdZRm3+5kWv9p+hNxsEpF1HEp7jCIsZAbadfCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T12:58:02.893668Z"},"content_sha256":"16d9520ce6f3023e9d5a5a766d89e78f987cf2f44a4c9ea14a57602ce3f11046","schema_version":"1.0","event_id":"sha256:16d9520ce6f3023e9d5a5a766d89e78f987cf2f44a4c9ea14a57602ce3f11046"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4GPRFAX5NQARSINXZGFP6V6TPM/bundle.json","state_url":"https://pith.science/pith/4GPRFAX5NQARSINXZGFP6V6TPM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4GPRFAX5NQARSINXZGFP6V6TPM/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-25T12:58:02Z","links":{"resolver":"https://pith.science/pith/4GPRFAX5NQARSINXZGFP6V6TPM","bundle":"https://pith.science/pith/4GPRFAX5NQARSINXZGFP6V6TPM/bundle.json","state":"https://pith.science/pith/4GPRFAX5NQARSINXZGFP6V6TPM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4GPRFAX5NQARSINXZGFP6V6TPM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:4GPRFAX5NQARSINXZGFP6V6TPM","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":"c5b08c52dff9b46327f7d9e3e3b0e9d3102f7efdcae3c53ed74d7db11cd14c42","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-09-23T15:04:04Z","title_canon_sha256":"a702f90f61fe9ee2918ec816bb9c9cbd82c2c333621b8f8925beb516d8ab7720"},"schema_version":"1.0","source":{"id":"1809.08611","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1809.08611","created_at":"2026-05-17T23:44:07Z"},{"alias_kind":"arxiv_version","alias_value":"1809.08611v3","created_at":"2026-05-17T23:44:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1809.08611","created_at":"2026-05-17T23:44:07Z"},{"alias_kind":"pith_short_12","alias_value":"4GPRFAX5NQAR","created_at":"2026-05-18T12:32:05Z"},{"alias_kind":"pith_short_16","alias_value":"4GPRFAX5NQARSINX","created_at":"2026-05-18T12:32:05Z"},{"alias_kind":"pith_short_8","alias_value":"4GPRFAX5","created_at":"2026-05-18T12:32:05Z"}],"graph_snapshots":[{"event_id":"sha256:16d9520ce6f3023e9d5a5a766d89e78f987cf2f44a4c9ea14a57602ce3f11046","target":"graph","created_at":"2026-05-17T23:44:07Z","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 $\\mathfrak X$ be a Hunt process on a locally compact space $X$ such that the set $\\mathcal E_{\\mathfrak X}$ of its Borel measurable excessive functions separates points, every function in $\\mathcal E_{\\mathfrak X}$ is the supremum of its continuous minorants in $\\mathcal E_{\\mathfrak X}$ and there are strictly positive continuous functions $v,w\\in\\mathcal E_{\\mathfrak X}$ such that $v/w$ vanishes at infinity.\n  A numerical function $u\\ge 0$ on $X$ is said to be nearly hyperharmonic, if $\\int^\\ast u\\circ X_{\\tau_V}\\,dP^x\\le u(x)$ for all $x\\in X$ and relatively compact open neighborhoods $V","authors_text":"Ivan Netuka, Wolfhard Hansen","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-09-23T15:04:04Z","title":"Nearly hyperharmonic functions are infima of excessive functions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.08611","kind":"arxiv","version":3},"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":"sha256:666450313622d7b219a6f3954c79602941a940f16f87e406d6607bf73b105335","target":"record","created_at":"2026-05-17T23:44:07Z","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":"c5b08c52dff9b46327f7d9e3e3b0e9d3102f7efdcae3c53ed74d7db11cd14c42","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-09-23T15:04:04Z","title_canon_sha256":"a702f90f61fe9ee2918ec816bb9c9cbd82c2c333621b8f8925beb516d8ab7720"},"schema_version":"1.0","source":{"id":"1809.08611","kind":"arxiv","version":3}},"canonical_sha256":"e19f1282fd6c011921b7c98aff57d37b344ae50cc3615a7faf8c2c5dda69d98c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e19f1282fd6c011921b7c98aff57d37b344ae50cc3615a7faf8c2c5dda69d98c","first_computed_at":"2026-05-17T23:44:07.625256Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:44:07.625256Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"cmOnM9R7tS/pmDNw5MIhj96hibrGSgnJ77hYKcIw+x2NxpRFwnlDKkOXqD9xs0ngVUkcMDFJM1AN/Zz7hE7uBw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:44:07.625942Z","signed_message":"canonical_sha256_bytes"},"source_id":"1809.08611","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:666450313622d7b219a6f3954c79602941a940f16f87e406d6607bf73b105335","sha256:16d9520ce6f3023e9d5a5a766d89e78f987cf2f44a4c9ea14a57602ce3f11046"],"state_sha256":"8a4d2c6a99c3065023f8dd67a36106bf0314f736f5c8f199eeeb9ec7e86ce009"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pwBY1FS8JKz1enbDfdXa/iyQZtwMGaGgWW+odJ33IgHNc1nG8Lvy1U3lJ8Sjddadqj1IY4+GQbrGodIcT+kTDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-25T12:58:02.895663Z","bundle_sha256":"bb26bfc10a811a223b6bda59fab7059821a73d713d5d139b9212dcaadd9053da"}}