{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:4NDOIMRFTWZIEBRRYOJKKTFD7A","short_pith_number":"pith:4NDOIMRF","schema_version":"1.0","canonical_sha256":"e346e432259db2820631c392a54ca3f8082c2617f16bc765fa0db44efc0c3d25","source":{"kind":"arxiv","id":"1009.0109","version":2},"attestation_state":"computed","paper":{"title":"Characterizations of processes with stationary and independent increments under $G$-expectation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Yongsheng Song","submitted_at":"2010-09-01T07:51:53Z","abstract_excerpt":"Our purpose is to investigate properties for processes with stationary and independent increments under $G$-expectation. As applications, we prove the martingale characterization to $G$-Brownian motion and present a decomposition for generalized $G$-Brownian motion."},"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":"1009.0109","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-09-01T07:51:53Z","cross_cats_sorted":[],"title_canon_sha256":"e83a17640d0723b5c3f798965fbe170e941d15ec05f5186e55e4b2ab891f3d6e","abstract_canon_sha256":"b8a096438d2a696ac04267a94b35471b114f6ef12e4b194035c37fe01ab9cfbd"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:13:55.288866Z","signature_b64":"gN35yx1rJN77o5P/skEmevg0RxGEig2pTdppR4gu6sPxxIqFofxXoJH+bVfz4cNEX7foXAC45lWSFM6RLa0cCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e346e432259db2820631c392a54ca3f8082c2617f16bc765fa0db44efc0c3d25","last_reissued_at":"2026-05-18T04:13:55.288290Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:13:55.288290Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Characterizations of processes with stationary and independent increments under $G$-expectation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Yongsheng Song","submitted_at":"2010-09-01T07:51:53Z","abstract_excerpt":"Our purpose is to investigate properties for processes with stationary and independent increments under $G$-expectation. As applications, we prove the martingale characterization to $G$-Brownian motion and present a decomposition for generalized $G$-Brownian motion."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.0109","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":"1009.0109","created_at":"2026-05-18T04:13:55.288407+00:00"},{"alias_kind":"arxiv_version","alias_value":"1009.0109v2","created_at":"2026-05-18T04:13:55.288407+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1009.0109","created_at":"2026-05-18T04:13:55.288407+00:00"},{"alias_kind":"pith_short_12","alias_value":"4NDOIMRFTWZI","created_at":"2026-05-18T12:26:03.138858+00:00"},{"alias_kind":"pith_short_16","alias_value":"4NDOIMRFTWZIEBRR","created_at":"2026-05-18T12:26:03.138858+00:00"},{"alias_kind":"pith_short_8","alias_value":"4NDOIMRF","created_at":"2026-05-18T12:26:03.138858+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/4NDOIMRFTWZIEBRRYOJKKTFD7A","json":"https://pith.science/pith/4NDOIMRFTWZIEBRRYOJKKTFD7A.json","graph_json":"https://pith.science/api/pith-number/4NDOIMRFTWZIEBRRYOJKKTFD7A/graph.json","events_json":"https://pith.science/api/pith-number/4NDOIMRFTWZIEBRRYOJKKTFD7A/events.json","paper":"https://pith.science/paper/4NDOIMRF"},"agent_actions":{"view_html":"https://pith.science/pith/4NDOIMRFTWZIEBRRYOJKKTFD7A","download_json":"https://pith.science/pith/4NDOIMRFTWZIEBRRYOJKKTFD7A.json","view_paper":"https://pith.science/paper/4NDOIMRF","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1009.0109&json=true","fetch_graph":"https://pith.science/api/pith-number/4NDOIMRFTWZIEBRRYOJKKTFD7A/graph.json","fetch_events":"https://pith.science/api/pith-number/4NDOIMRFTWZIEBRRYOJKKTFD7A/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/4NDOIMRFTWZIEBRRYOJKKTFD7A/action/timestamp_anchor","attest_storage":"https://pith.science/pith/4NDOIMRFTWZIEBRRYOJKKTFD7A/action/storage_attestation","attest_author":"https://pith.science/pith/4NDOIMRFTWZIEBRRYOJKKTFD7A/action/author_attestation","sign_citation":"https://pith.science/pith/4NDOIMRFTWZIEBRRYOJKKTFD7A/action/citation_signature","submit_replication":"https://pith.science/pith/4NDOIMRFTWZIEBRRYOJKKTFD7A/action/replication_record"}},"created_at":"2026-05-18T04:13:55.288407+00:00","updated_at":"2026-05-18T04:13:55.288407+00:00"}