{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:3OGDLGB2M6I5RI3YGVUT2WEVYC","short_pith_number":"pith:3OGDLGB2","schema_version":"1.0","canonical_sha256":"db8c35983a6791d8a37835693d5895c09252c7b6bd032352bfb3877498ca2e3c","source":{"kind":"arxiv","id":"1407.3728","version":2},"attestation_state":"computed","paper":{"title":"On the study of processes of classes $\\sum(H)$ and $\\sum_{s}(H)$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Fulgence Eyi Obiang, Octave Moutsinga, Youssef Ouknine","submitted_at":"2014-07-14T17:04:21Z","abstract_excerpt":"In papers by Yor, a remarkable class $(\\Sigma)$ of submartingales is introduced, which, up to technicalities, are submartingales $(X_{t})_{t\\geq0}$ whose increasing process is carried by the times $t$ such that $X_{t}=0$. These submartingales have several applications in stochastic analysis: for example, the resolution of Skorokhod embedding problem, the study of Brownian local times and the study of zeros of continuous martingales. The submartingales of class $(\\Sigma)$ have been extensively studied in a series of articles by Nikeghbali (part of them in collaboration with Najnudel, some other"},"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":"1407.3728","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-07-14T17:04:21Z","cross_cats_sorted":[],"title_canon_sha256":"04c77c770a0beed493f3e301fa2d676d70d4a53ca73f62706e9d8a62e9d8bc2e","abstract_canon_sha256":"59f9bebc8a5d7ee951f37b3e326663419319f1c419d91e09b924ace1495e0f5b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:34:13.448038Z","signature_b64":"2V+5qJu7o/xeeo7nhMyWtyoS3by4s+YnnKBenjLZOW5cpRB3h7/KvznaMrVvj96uMkHp8ScLmX2d4Ys+S1PrAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"db8c35983a6791d8a37835693d5895c09252c7b6bd032352bfb3877498ca2e3c","last_reissued_at":"2026-05-18T01:34:13.447365Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:34:13.447365Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the study of processes of classes $\\sum(H)$ and $\\sum_{s}(H)$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Fulgence Eyi Obiang, Octave Moutsinga, Youssef Ouknine","submitted_at":"2014-07-14T17:04:21Z","abstract_excerpt":"In papers by Yor, a remarkable class $(\\Sigma)$ of submartingales is introduced, which, up to technicalities, are submartingales $(X_{t})_{t\\geq0}$ whose increasing process is carried by the times $t$ such that $X_{t}=0$. These submartingales have several applications in stochastic analysis: for example, the resolution of Skorokhod embedding problem, the study of Brownian local times and the study of zeros of continuous martingales. The submartingales of class $(\\Sigma)$ have been extensively studied in a series of articles by Nikeghbali (part of them in collaboration with Najnudel, some other"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.3728","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":"1407.3728","created_at":"2026-05-18T01:34:13.447468+00:00"},{"alias_kind":"arxiv_version","alias_value":"1407.3728v2","created_at":"2026-05-18T01:34:13.447468+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.3728","created_at":"2026-05-18T01:34:13.447468+00:00"},{"alias_kind":"pith_short_12","alias_value":"3OGDLGB2M6I5","created_at":"2026-05-18T12:28:11.866339+00:00"},{"alias_kind":"pith_short_16","alias_value":"3OGDLGB2M6I5RI3Y","created_at":"2026-05-18T12:28:11.866339+00:00"},{"alias_kind":"pith_short_8","alias_value":"3OGDLGB2","created_at":"2026-05-18T12:28:11.866339+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/3OGDLGB2M6I5RI3YGVUT2WEVYC","json":"https://pith.science/pith/3OGDLGB2M6I5RI3YGVUT2WEVYC.json","graph_json":"https://pith.science/api/pith-number/3OGDLGB2M6I5RI3YGVUT2WEVYC/graph.json","events_json":"https://pith.science/api/pith-number/3OGDLGB2M6I5RI3YGVUT2WEVYC/events.json","paper":"https://pith.science/paper/3OGDLGB2"},"agent_actions":{"view_html":"https://pith.science/pith/3OGDLGB2M6I5RI3YGVUT2WEVYC","download_json":"https://pith.science/pith/3OGDLGB2M6I5RI3YGVUT2WEVYC.json","view_paper":"https://pith.science/paper/3OGDLGB2","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1407.3728&json=true","fetch_graph":"https://pith.science/api/pith-number/3OGDLGB2M6I5RI3YGVUT2WEVYC/graph.json","fetch_events":"https://pith.science/api/pith-number/3OGDLGB2M6I5RI3YGVUT2WEVYC/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/3OGDLGB2M6I5RI3YGVUT2WEVYC/action/timestamp_anchor","attest_storage":"https://pith.science/pith/3OGDLGB2M6I5RI3YGVUT2WEVYC/action/storage_attestation","attest_author":"https://pith.science/pith/3OGDLGB2M6I5RI3YGVUT2WEVYC/action/author_attestation","sign_citation":"https://pith.science/pith/3OGDLGB2M6I5RI3YGVUT2WEVYC/action/citation_signature","submit_replication":"https://pith.science/pith/3OGDLGB2M6I5RI3YGVUT2WEVYC/action/replication_record"}},"created_at":"2026-05-18T01:34:13.447468+00:00","updated_at":"2026-05-18T01:34:13.447468+00:00"}