{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:P47WYCLF6REP6TKKE7F3GLZRVN","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":"b7888a38871d77d532751a28376c34b33064de6d765dc9c706cea380e713246d","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2019-11-13T17:30:12Z","title_canon_sha256":"d586a1f1613a2b9cf4f2465c64b265ebeaa12316c7c0ee2dafc1ed1bec47181f"},"schema_version":"1.0","source":{"id":"1911.05456","kind":"arxiv","version":10}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1911.05456","created_at":"2026-07-05T01:19:37Z"},{"alias_kind":"arxiv_version","alias_value":"1911.05456v10","created_at":"2026-07-05T01:19:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1911.05456","created_at":"2026-07-05T01:19:37Z"},{"alias_kind":"pith_short_12","alias_value":"P47WYCLF6REP","created_at":"2026-07-05T01:19:37Z"},{"alias_kind":"pith_short_16","alias_value":"P47WYCLF6REP6TKK","created_at":"2026-07-05T01:19:37Z"},{"alias_kind":"pith_short_8","alias_value":"P47WYCLF","created_at":"2026-07-05T01:19:37Z"}],"graph_snapshots":[{"event_id":"sha256:e8e075d7943ec2561927f56f4ee49b8a5d1145a62860432a29ccd07e1d1064ea","target":"graph","created_at":"2026-07-05T01:19:37Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1911.05456/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Via symbolic computation we deduce 97 new type series for powers of $\\pi$ related to Ramanujan-type series. Here are three typical examples: $$\\sum_{k=0}^\\infty \\frac{P(k) \\binom{2k}k\\binom{3k}k \\binom{6k}{3k}}{(k+1)(2k-1)(6k-1)(-640320)^{3k}}\n  =\\frac{18\\times557403^3\\sqrt{10005}}{5\\pi}$$ with \\begin{align*}P(k) = &637379600041024803108 k^2 + 657229991696087780968 k \\\\&+ 19850391655004126179, \\end{align*} $$\\sum_{k=1}^\\infty \\frac{(3k+1)16^k}{(2k+1)^2k^3\\binom{2k}k^3} = \\frac{\\pi^2-8}2,$$ and $$\\sum_{n=0}^\\infty\\frac{3n+1}{(-100)^n} \\sum_{k=0}^n{n\\choose k}^2T_k(1,25)T_{n-k}(1,25) = \\frac{25}","authors_text":"Zhi-Wei Sun","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2019-11-13T17:30:12Z","title":"New series for powers of $\\pi$ and related congruences"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1911.05456","kind":"arxiv","version":10},"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":"sha256:54dfb602484b8c8f8808fcd9c0582d783c2b12755b6bf67e86f8cf722ae9f43e","target":"record","created_at":"2026-07-05T01:19:37Z","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":"b7888a38871d77d532751a28376c34b33064de6d765dc9c706cea380e713246d","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2019-11-13T17:30:12Z","title_canon_sha256":"d586a1f1613a2b9cf4f2465c64b265ebeaa12316c7c0ee2dafc1ed1bec47181f"},"schema_version":"1.0","source":{"id":"1911.05456","kind":"arxiv","version":10}},"canonical_sha256":"7f3f6c0965f448ff4d4a27cbb32f31ab51e1b4ddbeedbfecf1f87a7389a18ade","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7f3f6c0965f448ff4d4a27cbb32f31ab51e1b4ddbeedbfecf1f87a7389a18ade","first_computed_at":"2026-07-05T01:19:37.187371Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T01:19:37.187371Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"B5ydzEK+BE+0UiKbHPtVbxG+9v/1iH7vwLjDdcj2BCcj3SuBoNy7uJDMdcAdOdC7wHlGnh7FRdOU0hiEABJmBw==","signature_status":"signed_v1","signed_at":"2026-07-05T01:19:37.187835Z","signed_message":"canonical_sha256_bytes"},"source_id":"1911.05456","source_kind":"arxiv","source_version":10}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:54dfb602484b8c8f8808fcd9c0582d783c2b12755b6bf67e86f8cf722ae9f43e","sha256:e8e075d7943ec2561927f56f4ee49b8a5d1145a62860432a29ccd07e1d1064ea"],"state_sha256":"28ea47591a8954b900e9dc54cffec62331db8b722bd18625be5dc23751140189"}