{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:YDAQK6HWLHVLG2P3QGVEWY5LAN","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":"47602362b4a163c7387f4796fb1450a3661d731e697a022ed31d28641a77be5b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2025-06-07T01:28:22Z","title_canon_sha256":"94179b5bbdbacfe23a7ad16ca503199197adbcf97af6be244a0cfe8613e897e6"},"schema_version":"1.0","source":{"id":"2506.06617","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2506.06617","created_at":"2026-07-05T11:17:52Z"},{"alias_kind":"arxiv_version","alias_value":"2506.06617v1","created_at":"2026-07-05T11:17:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.06617","created_at":"2026-07-05T11:17:52Z"},{"alias_kind":"pith_short_12","alias_value":"YDAQK6HWLHVL","created_at":"2026-07-05T11:17:52Z"},{"alias_kind":"pith_short_16","alias_value":"YDAQK6HWLHVLG2P3","created_at":"2026-07-05T11:17:52Z"},{"alias_kind":"pith_short_8","alias_value":"YDAQK6HW","created_at":"2026-07-05T11:17:52Z"}],"graph_snapshots":[{"event_id":"sha256:a8f902de948ebd68ea12e82ab743e57194e54c95c9b5f3323e6c6c0d0880864f","target":"graph","created_at":"2026-07-05T11:17:52Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2506.06617/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Using an elementary approach involving the Euler Beta function and the binomial theorem, we derive two polynomial identities; one of which is a generalization of a known polynomial identity. Two well-known combinatorial identities, namely Frisch's identity and Klamkin's identity, appear as immediate consequences of the polynomial identities. We subsequently establish several combinatorial identities, including a generalization of each of Frisch's identity and Klamkin's identity. Finally, we develop a scheme for deriving combinatorial identities associated with polynomial identities of a certai","authors_text":"Kunle Adegoke","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2025-06-07T01:28:22Z","title":"New Polynomial Identities and Some Consequences"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.06617","kind":"arxiv","version":1},"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":"sha256:7fd8749004e7bc3f9f5e5a00c94f6590474b443232ab569320cf424e0081ab6d","target":"record","created_at":"2026-07-05T11:17:52Z","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":"47602362b4a163c7387f4796fb1450a3661d731e697a022ed31d28641a77be5b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2025-06-07T01:28:22Z","title_canon_sha256":"94179b5bbdbacfe23a7ad16ca503199197adbcf97af6be244a0cfe8613e897e6"},"schema_version":"1.0","source":{"id":"2506.06617","kind":"arxiv","version":1}},"canonical_sha256":"c0c10578f659eab369fb81aa4b63ab036831a8a8af0ba6c79cda8900c62f0522","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c0c10578f659eab369fb81aa4b63ab036831a8a8af0ba6c79cda8900c62f0522","first_computed_at":"2026-07-05T11:17:52.943348Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:17:52.943348Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"eaHszTFXcbastBOnlhDHd2J5ULQJGs4l946LyGG1yRaXH9Cg8tQxNPlA3ZyO2O1WILh8dHMC6rP2tahUtBV5DA==","signature_status":"signed_v1","signed_at":"2026-07-05T11:17:52.943786Z","signed_message":"canonical_sha256_bytes"},"source_id":"2506.06617","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7fd8749004e7bc3f9f5e5a00c94f6590474b443232ab569320cf424e0081ab6d","sha256:a8f902de948ebd68ea12e82ab743e57194e54c95c9b5f3323e6c6c0d0880864f"],"state_sha256":"e860363476c310cd7125c836bae3b7a1d3dee81d3f5f7a528ef1d84803aac00b"}