{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:TFIL2EWIIY2EJXZLM7RXBNJSGC","short_pith_number":"pith:TFIL2EWI","schema_version":"1.0","canonical_sha256":"9950bd12c8463444df2b67e370b5323091453d1066541f24959689457c47249e","source":{"kind":"arxiv","id":"1603.03881","version":2},"attestation_state":"computed","paper":{"title":"On alternating sums of binomial coefficients and $q$-binomial coefficients","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Mohamed El Bachraoui","submitted_at":"2016-03-12T09:40:38Z","abstract_excerpt":"In this paper we shall evaluate two alternating sums of binomial coefficients by a combinatorial argument. Moreover, by combining the same combinatorial idea with partition theoretic techniques, we provide $q$-analogues involving the $q$-binomial coefficients."},"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":"1603.03881","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-03-12T09:40:38Z","cross_cats_sorted":[],"title_canon_sha256":"7dcd68d006352fe9b991d7421f71c1b9155906229c2bc354e96c9510ce0f715d","abstract_canon_sha256":"a48543da8164049abf6bfe1c4671dcffce41d51d462189e694a5add778563a7a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:12:54.885795Z","signature_b64":"3QsakLWqU9RDPOfnphJqBActJalCtTJAaJ/zrJ8CvhLCpnf1cptwoqoWBQVmNd1kUDy3+CZBuYIY5gJebVGlAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9950bd12c8463444df2b67e370b5323091453d1066541f24959689457c47249e","last_reissued_at":"2026-05-18T01:12:54.885441Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:12:54.885441Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On alternating sums of binomial coefficients and $q$-binomial coefficients","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Mohamed El Bachraoui","submitted_at":"2016-03-12T09:40:38Z","abstract_excerpt":"In this paper we shall evaluate two alternating sums of binomial coefficients by a combinatorial argument. Moreover, by combining the same combinatorial idea with partition theoretic techniques, we provide $q$-analogues involving the $q$-binomial coefficients."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.03881","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":"1603.03881","created_at":"2026-05-18T01:12:54.885514+00:00"},{"alias_kind":"arxiv_version","alias_value":"1603.03881v2","created_at":"2026-05-18T01:12:54.885514+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.03881","created_at":"2026-05-18T01:12:54.885514+00:00"},{"alias_kind":"pith_short_12","alias_value":"TFIL2EWIIY2E","created_at":"2026-05-18T12:30:44.179134+00:00"},{"alias_kind":"pith_short_16","alias_value":"TFIL2EWIIY2EJXZL","created_at":"2026-05-18T12:30:44.179134+00:00"},{"alias_kind":"pith_short_8","alias_value":"TFIL2EWI","created_at":"2026-05-18T12:30:44.179134+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/TFIL2EWIIY2EJXZLM7RXBNJSGC","json":"https://pith.science/pith/TFIL2EWIIY2EJXZLM7RXBNJSGC.json","graph_json":"https://pith.science/api/pith-number/TFIL2EWIIY2EJXZLM7RXBNJSGC/graph.json","events_json":"https://pith.science/api/pith-number/TFIL2EWIIY2EJXZLM7RXBNJSGC/events.json","paper":"https://pith.science/paper/TFIL2EWI"},"agent_actions":{"view_html":"https://pith.science/pith/TFIL2EWIIY2EJXZLM7RXBNJSGC","download_json":"https://pith.science/pith/TFIL2EWIIY2EJXZLM7RXBNJSGC.json","view_paper":"https://pith.science/paper/TFIL2EWI","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1603.03881&json=true","fetch_graph":"https://pith.science/api/pith-number/TFIL2EWIIY2EJXZLM7RXBNJSGC/graph.json","fetch_events":"https://pith.science/api/pith-number/TFIL2EWIIY2EJXZLM7RXBNJSGC/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/TFIL2EWIIY2EJXZLM7RXBNJSGC/action/timestamp_anchor","attest_storage":"https://pith.science/pith/TFIL2EWIIY2EJXZLM7RXBNJSGC/action/storage_attestation","attest_author":"https://pith.science/pith/TFIL2EWIIY2EJXZLM7RXBNJSGC/action/author_attestation","sign_citation":"https://pith.science/pith/TFIL2EWIIY2EJXZLM7RXBNJSGC/action/citation_signature","submit_replication":"https://pith.science/pith/TFIL2EWIIY2EJXZLM7RXBNJSGC/action/replication_record"}},"created_at":"2026-05-18T01:12:54.885514+00:00","updated_at":"2026-05-18T01:12:54.885514+00:00"}