{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:SGP5JA5Z6EQQVQWHH76H57GLK3","short_pith_number":"pith:SGP5JA5Z","canonical_record":{"source":{"id":"1507.01703","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-07-07T08:32:20Z","cross_cats_sorted":["cs.SC","math.CO"],"title_canon_sha256":"c0b8b21f81596f61c8c7c4c4316d0f0b0f4155bb11600233e792fe98076cfcd1","abstract_canon_sha256":"a12dbcfdd7755cdec94ca7ca33ab9d2a533900892369eedb872a3e35ecacc191"},"schema_version":"1.0"},"canonical_sha256":"919fd483b9f1210ac2c73ffc7efccb56f34bdff10176d473245170787e335c5c","source":{"kind":"arxiv","id":"1507.01703","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1507.01703","created_at":"2026-05-18T01:28:34Z"},{"alias_kind":"arxiv_version","alias_value":"1507.01703v3","created_at":"2026-05-18T01:28:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.01703","created_at":"2026-05-18T01:28:34Z"},{"alias_kind":"pith_short_12","alias_value":"SGP5JA5Z6EQQ","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_16","alias_value":"SGP5JA5Z6EQQVQWH","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_8","alias_value":"SGP5JA5Z","created_at":"2026-05-18T12:29:42Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:SGP5JA5Z6EQQVQWHH76H57GLK3","target":"record","payload":{"canonical_record":{"source":{"id":"1507.01703","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-07-07T08:32:20Z","cross_cats_sorted":["cs.SC","math.CO"],"title_canon_sha256":"c0b8b21f81596f61c8c7c4c4316d0f0b0f4155bb11600233e792fe98076cfcd1","abstract_canon_sha256":"a12dbcfdd7755cdec94ca7ca33ab9d2a533900892369eedb872a3e35ecacc191"},"schema_version":"1.0"},"canonical_sha256":"919fd483b9f1210ac2c73ffc7efccb56f34bdff10176d473245170787e335c5c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:28:34.108400Z","signature_b64":"m/HqFocDZjfjnpFyGaD+08Y9f07+z6RsVIZG0CFkd5F/r3H11p2uCLWtswZqKAxLKJ7zrz2QlW6Mk3++RrLTCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"919fd483b9f1210ac2c73ffc7efccb56f34bdff10176d473245170787e335c5c","last_reissued_at":"2026-05-18T01:28:34.107790Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:28:34.107790Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1507.01703","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:28:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gQaKJRv8YGSTlkRg+NHPZSCiJXSVCjSnQfJN7F+yZypBXhe1RYEQfE4sVW0bFpD204+j0RONkpTxE+7P7dceDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T01:54:38.700444Z"},"content_sha256":"69fe0bf6f544dc38af01381ae334817e44d6feb851184687f1193214a6a90201","schema_version":"1.0","event_id":"sha256:69fe0bf6f544dc38af01381ae334817e44d6feb851184687f1193214a6a90201"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:SGP5JA5Z6EQQVQWHH76H57GLK3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Discovering and Proving Infinite Binomial Sums Identities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.SC","math.CO"],"primary_cat":"math.NT","authors_text":"Jakob Ablinger","submitted_at":"2015-07-07T08:32:20Z","abstract_excerpt":"We consider binomial and inverse binomial sums at infinity and rewrite them in terms of a small set of constants, such as powers of $\\pi$ or $\\log(2)$. In order to perform these simplifications, we view the series as specializations of generating series. For these generating series, we derive integral representations in terms of root-valued iterated integrals. Using substitutions, we express the interated integrals as cyclotomic harmonic polylogarithms. Finally, by applying known relations among the cyclotomic harmonic polylogarithms, we derive expressions in terms of several constants."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.01703","kind":"arxiv","version":3},"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":"2026-05-18T01:28:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7pqTZIbNoqGHU/I+wuDshUgZ1wjkLKb0rg3NQCESUJQcITF9fa+9jGnQsyoL7YJNJ5zLXzbLlYRtcrv9rz9yCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T01:54:38.700998Z"},"content_sha256":"b896793775076eccd034ba74a1f97ccde22763f875175838f9ad887cb9e0270d","schema_version":"1.0","event_id":"sha256:b896793775076eccd034ba74a1f97ccde22763f875175838f9ad887cb9e0270d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SGP5JA5Z6EQQVQWHH76H57GLK3/bundle.json","state_url":"https://pith.science/pith/SGP5JA5Z6EQQVQWHH76H57GLK3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SGP5JA5Z6EQQVQWHH76H57GLK3/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":"2026-05-31T01:54:38Z","links":{"resolver":"https://pith.science/pith/SGP5JA5Z6EQQVQWHH76H57GLK3","bundle":"https://pith.science/pith/SGP5JA5Z6EQQVQWHH76H57GLK3/bundle.json","state":"https://pith.science/pith/SGP5JA5Z6EQQVQWHH76H57GLK3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SGP5JA5Z6EQQVQWHH76H57GLK3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:SGP5JA5Z6EQQVQWHH76H57GLK3","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":"a12dbcfdd7755cdec94ca7ca33ab9d2a533900892369eedb872a3e35ecacc191","cross_cats_sorted":["cs.SC","math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-07-07T08:32:20Z","title_canon_sha256":"c0b8b21f81596f61c8c7c4c4316d0f0b0f4155bb11600233e792fe98076cfcd1"},"schema_version":"1.0","source":{"id":"1507.01703","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1507.01703","created_at":"2026-05-18T01:28:34Z"},{"alias_kind":"arxiv_version","alias_value":"1507.01703v3","created_at":"2026-05-18T01:28:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.01703","created_at":"2026-05-18T01:28:34Z"},{"alias_kind":"pith_short_12","alias_value":"SGP5JA5Z6EQQ","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_16","alias_value":"SGP5JA5Z6EQQVQWH","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_8","alias_value":"SGP5JA5Z","created_at":"2026-05-18T12:29:42Z"}],"graph_snapshots":[{"event_id":"sha256:b896793775076eccd034ba74a1f97ccde22763f875175838f9ad887cb9e0270d","target":"graph","created_at":"2026-05-18T01:28:34Z","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 binomial and inverse binomial sums at infinity and rewrite them in terms of a small set of constants, such as powers of $\\pi$ or $\\log(2)$. In order to perform these simplifications, we view the series as specializations of generating series. For these generating series, we derive integral representations in terms of root-valued iterated integrals. Using substitutions, we express the interated integrals as cyclotomic harmonic polylogarithms. Finally, by applying known relations among the cyclotomic harmonic polylogarithms, we derive expressions in terms of several constants.","authors_text":"Jakob Ablinger","cross_cats":["cs.SC","math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-07-07T08:32:20Z","title":"Discovering and Proving Infinite Binomial Sums Identities"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.01703","kind":"arxiv","version":3},"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":"sha256:69fe0bf6f544dc38af01381ae334817e44d6feb851184687f1193214a6a90201","target":"record","created_at":"2026-05-18T01:28:34Z","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":"a12dbcfdd7755cdec94ca7ca33ab9d2a533900892369eedb872a3e35ecacc191","cross_cats_sorted":["cs.SC","math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-07-07T08:32:20Z","title_canon_sha256":"c0b8b21f81596f61c8c7c4c4316d0f0b0f4155bb11600233e792fe98076cfcd1"},"schema_version":"1.0","source":{"id":"1507.01703","kind":"arxiv","version":3}},"canonical_sha256":"919fd483b9f1210ac2c73ffc7efccb56f34bdff10176d473245170787e335c5c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"919fd483b9f1210ac2c73ffc7efccb56f34bdff10176d473245170787e335c5c","first_computed_at":"2026-05-18T01:28:34.107790Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:28:34.107790Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"m/HqFocDZjfjnpFyGaD+08Y9f07+z6RsVIZG0CFkd5F/r3H11p2uCLWtswZqKAxLKJ7zrz2QlW6Mk3++RrLTCg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:28:34.108400Z","signed_message":"canonical_sha256_bytes"},"source_id":"1507.01703","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:69fe0bf6f544dc38af01381ae334817e44d6feb851184687f1193214a6a90201","sha256:b896793775076eccd034ba74a1f97ccde22763f875175838f9ad887cb9e0270d"],"state_sha256":"546718add4b02bc864af7687d03fcb6bb994320d90f02f7fab67886422080e75"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xrSBbJRw4TzFDKytdcDjDeZVQY2N5TCbUYV6FC5375HP5ctjHPUGtZPPNQ45epiZsWUIX5+DDhDnvK9OyMZeAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T01:54:38.705274Z","bundle_sha256":"545dd6873985a14d9419717d07691b938df9e961a3ba209c7f8b96507519f105"}}