{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:QE4OKJZLDFVOVKTSQCXXBX6ONW","short_pith_number":"pith:QE4OKJZL","canonical_record":{"source":{"id":"1603.09156","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-03-30T12:34:49Z","cross_cats_sorted":[],"title_canon_sha256":"cca451e4d78c9ee3114738cfa2795b6954d9c7ee164637a0f094ac7fb451b751","abstract_canon_sha256":"9e7c6549c8623d9229f0cd9f54811f9928c77c6c5f3b200a890b3163e6d918b7"},"schema_version":"1.0"},"canonical_sha256":"8138e5272b196aeaaa7280af70dfce6d982d3580a6f61be5a5fb643552665438","source":{"kind":"arxiv","id":"1603.09156","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.09156","created_at":"2026-05-18T01:10:37Z"},{"alias_kind":"arxiv_version","alias_value":"1603.09156v2","created_at":"2026-05-18T01:10:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.09156","created_at":"2026-05-18T01:10:37Z"},{"alias_kind":"pith_short_12","alias_value":"QE4OKJZLDFVO","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_16","alias_value":"QE4OKJZLDFVOVKTS","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_8","alias_value":"QE4OKJZL","created_at":"2026-05-18T12:30:39Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:QE4OKJZLDFVOVKTSQCXXBX6ONW","target":"record","payload":{"canonical_record":{"source":{"id":"1603.09156","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-03-30T12:34:49Z","cross_cats_sorted":[],"title_canon_sha256":"cca451e4d78c9ee3114738cfa2795b6954d9c7ee164637a0f094ac7fb451b751","abstract_canon_sha256":"9e7c6549c8623d9229f0cd9f54811f9928c77c6c5f3b200a890b3163e6d918b7"},"schema_version":"1.0"},"canonical_sha256":"8138e5272b196aeaaa7280af70dfce6d982d3580a6f61be5a5fb643552665438","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:10:37.764931Z","signature_b64":"72Kxchu493H8csaLeIIvHb9psQq4AsnRmJPqPKo3oKNwd8ZI1d625ATytHIgRFw/AD4CbadbNbda2G0X+A0qAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8138e5272b196aeaaa7280af70dfce6d982d3580a6f61be5a5fb643552665438","last_reissued_at":"2026-05-18T01:10:37.764109Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:10:37.764109Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1603.09156","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:10:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"u5+teqfwC5NB2zBDFu//I+JWv7k3b5Sv16RVWD7mFLmK7NEzCLS2sr5hoRz85N8NCcMKq5tY71ZxPbX+AyuHAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-23T03:24:57.303523Z"},"content_sha256":"56efd48a68dca5d8f71cfcd40bd2e71027453faa0555deb3f1b922456254d1df","schema_version":"1.0","event_id":"sha256:56efd48a68dca5d8f71cfcd40bd2e71027453faa0555deb3f1b922456254d1df"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:QE4OKJZLDFVOVKTSQCXXBX6ONW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"New identities for binary Krawtchouk polynomials, binomial coefficients and Catalan numbers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Ricardo A. Podest\\'a","submitted_at":"2016-03-30T12:34:49Z","abstract_excerpt":"We obtain new combinatorial identities for integral values of binary Krawtchouk polynomials $K^{2m}_p(x)$, $0\\le p\\le 2m$, by computing the characters of the $p$-exterior representations on certain elements of order 2 of $\\mathrm{SO}(2m)$. From this identities, we deduce several new relations for binomial coefficients and Catalan numbers."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.09156","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:10:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gvl7CxDlAaZn2ar67foedTSVNI7HAG+j0qvkLF5rTF0/xUB/v9k4Tf7pzgZgcP+awfAVn1bZeKV9JozSqR3GCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-23T03:24:57.304349Z"},"content_sha256":"4354cf64f7613adb7bcad524818abb4f2a9660f18e06b525a6b8aa52f2f739bc","schema_version":"1.0","event_id":"sha256:4354cf64f7613adb7bcad524818abb4f2a9660f18e06b525a6b8aa52f2f739bc"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QE4OKJZLDFVOVKTSQCXXBX6ONW/bundle.json","state_url":"https://pith.science/pith/QE4OKJZLDFVOVKTSQCXXBX6ONW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QE4OKJZLDFVOVKTSQCXXBX6ONW/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-08-23T03:24:57Z","links":{"resolver":"https://pith.science/pith/QE4OKJZLDFVOVKTSQCXXBX6ONW","bundle":"https://pith.science/pith/QE4OKJZLDFVOVKTSQCXXBX6ONW/bundle.json","state":"https://pith.science/pith/QE4OKJZLDFVOVKTSQCXXBX6ONW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QE4OKJZLDFVOVKTSQCXXBX6ONW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:QE4OKJZLDFVOVKTSQCXXBX6ONW","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":"9e7c6549c8623d9229f0cd9f54811f9928c77c6c5f3b200a890b3163e6d918b7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-03-30T12:34:49Z","title_canon_sha256":"cca451e4d78c9ee3114738cfa2795b6954d9c7ee164637a0f094ac7fb451b751"},"schema_version":"1.0","source":{"id":"1603.09156","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.09156","created_at":"2026-05-18T01:10:37Z"},{"alias_kind":"arxiv_version","alias_value":"1603.09156v2","created_at":"2026-05-18T01:10:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.09156","created_at":"2026-05-18T01:10:37Z"},{"alias_kind":"pith_short_12","alias_value":"QE4OKJZLDFVO","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_16","alias_value":"QE4OKJZLDFVOVKTS","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_8","alias_value":"QE4OKJZL","created_at":"2026-05-18T12:30:39Z"}],"graph_snapshots":[{"event_id":"sha256:4354cf64f7613adb7bcad524818abb4f2a9660f18e06b525a6b8aa52f2f739bc","target":"graph","created_at":"2026-05-18T01:10:37Z","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 obtain new combinatorial identities for integral values of binary Krawtchouk polynomials $K^{2m}_p(x)$, $0\\le p\\le 2m$, by computing the characters of the $p$-exterior representations on certain elements of order 2 of $\\mathrm{SO}(2m)$. From this identities, we deduce several new relations for binomial coefficients and Catalan numbers.","authors_text":"Ricardo A. Podest\\'a","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-03-30T12:34:49Z","title":"New identities for binary Krawtchouk polynomials, binomial coefficients and Catalan numbers"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.09156","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":"sha256:56efd48a68dca5d8f71cfcd40bd2e71027453faa0555deb3f1b922456254d1df","target":"record","created_at":"2026-05-18T01:10:37Z","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":"9e7c6549c8623d9229f0cd9f54811f9928c77c6c5f3b200a890b3163e6d918b7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-03-30T12:34:49Z","title_canon_sha256":"cca451e4d78c9ee3114738cfa2795b6954d9c7ee164637a0f094ac7fb451b751"},"schema_version":"1.0","source":{"id":"1603.09156","kind":"arxiv","version":2}},"canonical_sha256":"8138e5272b196aeaaa7280af70dfce6d982d3580a6f61be5a5fb643552665438","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8138e5272b196aeaaa7280af70dfce6d982d3580a6f61be5a5fb643552665438","first_computed_at":"2026-05-18T01:10:37.764109Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:10:37.764109Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"72Kxchu493H8csaLeIIvHb9psQq4AsnRmJPqPKo3oKNwd8ZI1d625ATytHIgRFw/AD4CbadbNbda2G0X+A0qAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:10:37.764931Z","signed_message":"canonical_sha256_bytes"},"source_id":"1603.09156","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:56efd48a68dca5d8f71cfcd40bd2e71027453faa0555deb3f1b922456254d1df","sha256:4354cf64f7613adb7bcad524818abb4f2a9660f18e06b525a6b8aa52f2f739bc"],"state_sha256":"6da32eb8707a3814a81eb08473442f40beec0bd8e6e3ae40805bcabd0a73ceaf"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1J9Nhs4LBznTuDGgC05jt1uC4yPb7WnYYaq806oK39KQM5Kd1ImotEVfmysDhAEsVCwaSygo1v7b+f9HaBw5Dg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-23T03:24:57.315321Z","bundle_sha256":"8032feb3e53908625814deb32a786d3fb2879dada427690e4ec8bebd7675d154"}}