{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:2P3TKILQKDD5PY25P6FJSQER4Z","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":"85a989a3a12d0a16ab1ac493769fa47c7a39042e72a4ea2d4c6e79ad8c0714e7","cross_cats_sorted":["math.ST","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-11-06T02:41:45Z","title_canon_sha256":"98c7ced5be051d1a3adc55207894944282c30875eb71e3d5711773c9e0bddc73"},"schema_version":"1.0","source":{"id":"1411.1477","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1411.1477","created_at":"2026-05-18T01:13:45Z"},{"alias_kind":"arxiv_version","alias_value":"1411.1477v2","created_at":"2026-05-18T01:13:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.1477","created_at":"2026-05-18T01:13:45Z"},{"alias_kind":"pith_short_12","alias_value":"2P3TKILQKDD5","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_16","alias_value":"2P3TKILQKDD5PY25","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_8","alias_value":"2P3TKILQ","created_at":"2026-05-18T12:28:11Z"}],"graph_snapshots":[{"event_id":"sha256:83fce55edae21f6b97429efbdf45e937e0858ba8ef192f4a85a75f2ecbb277c3","target":"graph","created_at":"2026-05-18T01:13:45Z","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"},"paper":{"abstract_excerpt":"We consider several families of binomial sum identities whose definition involves the absolute value function. In particular, we consider centered double sums of the form \\[S_{\\alpha,\\beta}(n) := \\sum_{k,\\;\\ell}\\binom{2n}{n+k}\\binom{2n}{n+\\ell} |k^\\alpha-\\ell^\\alpha|^\\beta,\\] obtaining new results in the cases $\\alpha = 1, 2$. We show that there is a close connection between these double sums in the case $\\alpha=1$ and the single centered binomial sums considered by Tuenter.","authors_text":"Helmut Prodinger, Hideyuki Ohtsuka, Judy-anne H. Osborn, Richard P. Brent","cross_cats":["math.ST","stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-11-06T02:41:45Z","title":"Some binomial sums involving absolute values"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.1477","kind":"arxiv","version":2},"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:aaa8c76a4d88f11305b0f150e3a4005023ef712cfe24e8a5574ddecdf7a96c36","target":"record","created_at":"2026-05-18T01:13:45Z","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":"85a989a3a12d0a16ab1ac493769fa47c7a39042e72a4ea2d4c6e79ad8c0714e7","cross_cats_sorted":["math.ST","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-11-06T02:41:45Z","title_canon_sha256":"98c7ced5be051d1a3adc55207894944282c30875eb71e3d5711773c9e0bddc73"},"schema_version":"1.0","source":{"id":"1411.1477","kind":"arxiv","version":2}},"canonical_sha256":"d3f735217050c7d7e35d7f8a994091e66e2dc75d2462d075e7256b2aefd97cb8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d3f735217050c7d7e35d7f8a994091e66e2dc75d2462d075e7256b2aefd97cb8","first_computed_at":"2026-05-18T01:13:45.020987Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:13:45.020987Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"UgdkUwIQq6tqNKtKUepX9aam7oYDHFVGyhd5Imuyuq3JGGPs8EjRqBnM5FmZ92EtImFinw6xSGTsd+jggIvvDg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:13:45.021612Z","signed_message":"canonical_sha256_bytes"},"source_id":"1411.1477","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:aaa8c76a4d88f11305b0f150e3a4005023ef712cfe24e8a5574ddecdf7a96c36","sha256:83fce55edae21f6b97429efbdf45e937e0858ba8ef192f4a85a75f2ecbb277c3"],"state_sha256":"24139571ce5d950dd9aeef0c203119aa99a910cdeee1ea56d95a1ff794525027"}