{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:KO6VZRFCBGSQWMUYCAWHOHY7UP","short_pith_number":"pith:KO6VZRFC","canonical_record":{"source":{"id":"1302.5984","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-02-25T03:07:33Z","cross_cats_sorted":[],"title_canon_sha256":"6e5ffb570cacc9a381c4b71c3eb7059a00cdd5c807b98a7864c84a7782d93b93","abstract_canon_sha256":"c1f1e3f1ee442bc62ee1054f2877d1b39a16ea9115fce9dfc6c32b2f9f4556b4"},"schema_version":"1.0"},"canonical_sha256":"53bd5cc4a209a50b3298102c771f1fa3e9df49bd8b9c7e9800c0e2901b93dbc8","source":{"kind":"arxiv","id":"1302.5984","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1302.5984","created_at":"2026-05-18T03:32:32Z"},{"alias_kind":"arxiv_version","alias_value":"1302.5984v1","created_at":"2026-05-18T03:32:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1302.5984","created_at":"2026-05-18T03:32:32Z"},{"alias_kind":"pith_short_12","alias_value":"KO6VZRFCBGSQ","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_16","alias_value":"KO6VZRFCBGSQWMUY","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_8","alias_value":"KO6VZRFC","created_at":"2026-05-18T12:27:51Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:KO6VZRFCBGSQWMUYCAWHOHY7UP","target":"record","payload":{"canonical_record":{"source":{"id":"1302.5984","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-02-25T03:07:33Z","cross_cats_sorted":[],"title_canon_sha256":"6e5ffb570cacc9a381c4b71c3eb7059a00cdd5c807b98a7864c84a7782d93b93","abstract_canon_sha256":"c1f1e3f1ee442bc62ee1054f2877d1b39a16ea9115fce9dfc6c32b2f9f4556b4"},"schema_version":"1.0"},"canonical_sha256":"53bd5cc4a209a50b3298102c771f1fa3e9df49bd8b9c7e9800c0e2901b93dbc8","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:32:32.969546Z","signature_b64":"1/7mz0hfnnTI3d1DgME+YOeu5R7ZYF57CLbyiYSx0k7iixZsyrZ9I0XV1cf628e7yzA9ysSrVtsNRKp+mlXkBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"53bd5cc4a209a50b3298102c771f1fa3e9df49bd8b9c7e9800c0e2901b93dbc8","last_reissued_at":"2026-05-18T03:32:32.968807Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:32:32.968807Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1302.5984","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:32:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"luD60jOBiHwGoJA8rCsZk46zWkGQ0VaMfV2XOvYg6NsYlXVPTtGRiJ/1eA7B6jj8zzcaTg3+YUfOf7aaRarZAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T22:38:04.427993Z"},"content_sha256":"b966b25f3808d6ed1a2a8a19d7460fc13696436a0d5d4c150998de5585e0b38e","schema_version":"1.0","event_id":"sha256:b966b25f3808d6ed1a2a8a19d7460fc13696436a0d5d4c150998de5585e0b38e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:KO6VZRFCBGSQWMUYCAWHOHY7UP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Series for $1/\\pi$ Using Legendre's Relation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"James G. Wan","submitted_at":"2013-02-25T03:07:33Z","abstract_excerpt":"We present a new method for producing series for $1/\\pi$ and other constants using Legendre's relation, starting from a generation function that can be factorised into two elliptic $K$'s; this way we avoid much of modular theory or creative telescoping. Many of our series involve special values of Legendre polynomials; their relationship to the more traditional Ramanujan series is discussed."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.5984","kind":"arxiv","version":1},"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":"2026-05-18T03:32:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FCihjJagXpQ/Vb6VcItCPIePdxt/xT2tInT7/hAOkDsNZID5a+XxdmhO7ZerQmIVnTRJ1Tw5eJjr9XVj9EgmBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T22:38:04.428330Z"},"content_sha256":"445e789f73f2b4a96f1a59126d7e8250bcb7a0351e5c67272acbb4384a4c01cd","schema_version":"1.0","event_id":"sha256:445e789f73f2b4a96f1a59126d7e8250bcb7a0351e5c67272acbb4384a4c01cd"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KO6VZRFCBGSQWMUYCAWHOHY7UP/bundle.json","state_url":"https://pith.science/pith/KO6VZRFCBGSQWMUYCAWHOHY7UP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KO6VZRFCBGSQWMUYCAWHOHY7UP/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":"2026-06-01T22:38:04Z","links":{"resolver":"https://pith.science/pith/KO6VZRFCBGSQWMUYCAWHOHY7UP","bundle":"https://pith.science/pith/KO6VZRFCBGSQWMUYCAWHOHY7UP/bundle.json","state":"https://pith.science/pith/KO6VZRFCBGSQWMUYCAWHOHY7UP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KO6VZRFCBGSQWMUYCAWHOHY7UP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:KO6VZRFCBGSQWMUYCAWHOHY7UP","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":"c1f1e3f1ee442bc62ee1054f2877d1b39a16ea9115fce9dfc6c32b2f9f4556b4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-02-25T03:07:33Z","title_canon_sha256":"6e5ffb570cacc9a381c4b71c3eb7059a00cdd5c807b98a7864c84a7782d93b93"},"schema_version":"1.0","source":{"id":"1302.5984","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1302.5984","created_at":"2026-05-18T03:32:32Z"},{"alias_kind":"arxiv_version","alias_value":"1302.5984v1","created_at":"2026-05-18T03:32:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1302.5984","created_at":"2026-05-18T03:32:32Z"},{"alias_kind":"pith_short_12","alias_value":"KO6VZRFCBGSQ","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_16","alias_value":"KO6VZRFCBGSQWMUY","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_8","alias_value":"KO6VZRFC","created_at":"2026-05-18T12:27:51Z"}],"graph_snapshots":[{"event_id":"sha256:445e789f73f2b4a96f1a59126d7e8250bcb7a0351e5c67272acbb4384a4c01cd","target":"graph","created_at":"2026-05-18T03:32:32Z","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 present a new method for producing series for $1/\\pi$ and other constants using Legendre's relation, starting from a generation function that can be factorised into two elliptic $K$'s; this way we avoid much of modular theory or creative telescoping. Many of our series involve special values of Legendre polynomials; their relationship to the more traditional Ramanujan series is discussed.","authors_text":"James G. Wan","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-02-25T03:07:33Z","title":"Series for $1/\\pi$ Using Legendre's Relation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.5984","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:b966b25f3808d6ed1a2a8a19d7460fc13696436a0d5d4c150998de5585e0b38e","target":"record","created_at":"2026-05-18T03:32:32Z","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":"c1f1e3f1ee442bc62ee1054f2877d1b39a16ea9115fce9dfc6c32b2f9f4556b4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-02-25T03:07:33Z","title_canon_sha256":"6e5ffb570cacc9a381c4b71c3eb7059a00cdd5c807b98a7864c84a7782d93b93"},"schema_version":"1.0","source":{"id":"1302.5984","kind":"arxiv","version":1}},"canonical_sha256":"53bd5cc4a209a50b3298102c771f1fa3e9df49bd8b9c7e9800c0e2901b93dbc8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"53bd5cc4a209a50b3298102c771f1fa3e9df49bd8b9c7e9800c0e2901b93dbc8","first_computed_at":"2026-05-18T03:32:32.968807Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:32:32.968807Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1/7mz0hfnnTI3d1DgME+YOeu5R7ZYF57CLbyiYSx0k7iixZsyrZ9I0XV1cf628e7yzA9ysSrVtsNRKp+mlXkBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:32:32.969546Z","signed_message":"canonical_sha256_bytes"},"source_id":"1302.5984","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b966b25f3808d6ed1a2a8a19d7460fc13696436a0d5d4c150998de5585e0b38e","sha256:445e789f73f2b4a96f1a59126d7e8250bcb7a0351e5c67272acbb4384a4c01cd"],"state_sha256":"3baa4a05432bc76c0568f5e7fca419946330322d7f0f7ea09b0b6508545e3425"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Oq0cFGJFZRUIYNmNVOSrJO7lXS6CT3UxHTyrJaDCGDtHYlN1DTVlELezmHdI4Cu6Rh5cIjp9SnMHwQ1/zTSqAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T22:38:04.430482Z","bundle_sha256":"a52202bc8005468bd17edab1ce68c3c1c14d065ffb6f78a56924de655827949b"}}