{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:RHXLFGUSIKAD4BZNOG2A56RBMR","short_pith_number":"pith:RHXLFGUS","schema_version":"1.0","canonical_sha256":"89eeb29a9242803e072d71b40efa21647e3110260ea41a724ffefc79ece6a4d0","source":{"kind":"arxiv","id":"1111.3732","version":1},"attestation_state":"computed","paper":{"title":"A probabilistic approach to some binomial identities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Christophe Vignat, Victor H. Moll","submitted_at":"2011-11-16T09:12:48Z","abstract_excerpt":"Classical binomial identities are established by giving probabilistic interpretations to the summands. The examples include Vandermonde identity and some generalizations."},"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":"1111.3732","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-11-16T09:12:48Z","cross_cats_sorted":[],"title_canon_sha256":"90288f297459a8badf52cd022ad399593271e29c3c506df64a171b926ad025a2","abstract_canon_sha256":"27b15ef4c52377fe58b178d6d0414a53aec47ce2c340c688efde811a4a9ac64d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:08:13.171357Z","signature_b64":"c44kP1nwI3ppoV2vnlfLqjHONPdMW7uOeJdOlZwcBvZDywR2tPSM2CCdDtSDI5d4emt3bHNO0UoF58kXGOTFCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"89eeb29a9242803e072d71b40efa21647e3110260ea41a724ffefc79ece6a4d0","last_reissued_at":"2026-05-18T04:08:13.170895Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:08:13.170895Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A probabilistic approach to some binomial identities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Christophe Vignat, Victor H. Moll","submitted_at":"2011-11-16T09:12:48Z","abstract_excerpt":"Classical binomial identities are established by giving probabilistic interpretations to the summands. The examples include Vandermonde identity and some generalizations."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.3732","kind":"arxiv","version":1},"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":"1111.3732","created_at":"2026-05-18T04:08:13.170962+00:00"},{"alias_kind":"arxiv_version","alias_value":"1111.3732v1","created_at":"2026-05-18T04:08:13.170962+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1111.3732","created_at":"2026-05-18T04:08:13.170962+00:00"},{"alias_kind":"pith_short_12","alias_value":"RHXLFGUSIKAD","created_at":"2026-05-18T12:26:41.206345+00:00"},{"alias_kind":"pith_short_16","alias_value":"RHXLFGUSIKAD4BZN","created_at":"2026-05-18T12:26:41.206345+00:00"},{"alias_kind":"pith_short_8","alias_value":"RHXLFGUS","created_at":"2026-05-18T12:26:41.206345+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/RHXLFGUSIKAD4BZNOG2A56RBMR","json":"https://pith.science/pith/RHXLFGUSIKAD4BZNOG2A56RBMR.json","graph_json":"https://pith.science/api/pith-number/RHXLFGUSIKAD4BZNOG2A56RBMR/graph.json","events_json":"https://pith.science/api/pith-number/RHXLFGUSIKAD4BZNOG2A56RBMR/events.json","paper":"https://pith.science/paper/RHXLFGUS"},"agent_actions":{"view_html":"https://pith.science/pith/RHXLFGUSIKAD4BZNOG2A56RBMR","download_json":"https://pith.science/pith/RHXLFGUSIKAD4BZNOG2A56RBMR.json","view_paper":"https://pith.science/paper/RHXLFGUS","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1111.3732&json=true","fetch_graph":"https://pith.science/api/pith-number/RHXLFGUSIKAD4BZNOG2A56RBMR/graph.json","fetch_events":"https://pith.science/api/pith-number/RHXLFGUSIKAD4BZNOG2A56RBMR/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/RHXLFGUSIKAD4BZNOG2A56RBMR/action/timestamp_anchor","attest_storage":"https://pith.science/pith/RHXLFGUSIKAD4BZNOG2A56RBMR/action/storage_attestation","attest_author":"https://pith.science/pith/RHXLFGUSIKAD4BZNOG2A56RBMR/action/author_attestation","sign_citation":"https://pith.science/pith/RHXLFGUSIKAD4BZNOG2A56RBMR/action/citation_signature","submit_replication":"https://pith.science/pith/RHXLFGUSIKAD4BZNOG2A56RBMR/action/replication_record"}},"created_at":"2026-05-18T04:08:13.170962+00:00","updated_at":"2026-05-18T04:08:13.170962+00:00"}