{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:TFJ4NVFBER76MRJHCVZX5WYGAR","short_pith_number":"pith:TFJ4NVFB","canonical_record":{"source":{"id":"1801.07956","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-01-24T12:27:44Z","cross_cats_sorted":["math.CA","math.NT"],"title_canon_sha256":"121b7c5bf8c0e7ac73b29fc40a4798440932fc435919d421d78b38f0dcd553c6","abstract_canon_sha256":"d5d74dfd21cbb1be7726a7bceabe180da38176c92a33be9d41bdb91e12d01fee"},"schema_version":"1.0"},"canonical_sha256":"9953c6d4a1247fe6452715737edb06046f2c5f113b3d4df819a47866c3bda5ec","source":{"kind":"arxiv","id":"1801.07956","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1801.07956","created_at":"2026-05-18T00:25:10Z"},{"alias_kind":"arxiv_version","alias_value":"1801.07956v1","created_at":"2026-05-18T00:25:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1801.07956","created_at":"2026-05-18T00:25:10Z"},{"alias_kind":"pith_short_12","alias_value":"TFJ4NVFBER76","created_at":"2026-05-18T12:32:53Z"},{"alias_kind":"pith_short_16","alias_value":"TFJ4NVFBER76MRJH","created_at":"2026-05-18T12:32:53Z"},{"alias_kind":"pith_short_8","alias_value":"TFJ4NVFB","created_at":"2026-05-18T12:32:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:TFJ4NVFBER76MRJHCVZX5WYGAR","target":"record","payload":{"canonical_record":{"source":{"id":"1801.07956","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-01-24T12:27:44Z","cross_cats_sorted":["math.CA","math.NT"],"title_canon_sha256":"121b7c5bf8c0e7ac73b29fc40a4798440932fc435919d421d78b38f0dcd553c6","abstract_canon_sha256":"d5d74dfd21cbb1be7726a7bceabe180da38176c92a33be9d41bdb91e12d01fee"},"schema_version":"1.0"},"canonical_sha256":"9953c6d4a1247fe6452715737edb06046f2c5f113b3d4df819a47866c3bda5ec","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:25:10.455737Z","signature_b64":"RvWHsDmobcwdrlGCv/CUnNJ+wz7WCN9gWLLF10zqT3R4gaMK1jTOizVbiroSUn2uegDaL2QYlY4WvQ8+d/+pAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9953c6d4a1247fe6452715737edb06046f2c5f113b3d4df819a47866c3bda5ec","last_reissued_at":"2026-05-18T00:25:10.455075Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:25:10.455075Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1801.07956","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":"2026-05-18T00:25:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EAxmHM4A0dkjS5ko3+WmwLUl6X+9juj6ggFLPae3XFJRoFvMEy6Xs7qkQxOY9L7moMd5BNY8/nlpJGm9L6TQAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-03T07:07:22.307952Z"},"content_sha256":"da04bd22678c93476c8c03e340d252235841598edb89e42a9b7934ed1d4ea64d","schema_version":"1.0","event_id":"sha256:da04bd22678c93476c8c03e340d252235841598edb89e42a9b7934ed1d4ea64d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:TFJ4NVFBER76MRJHCVZX5WYGAR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"New Proofs of Ramanujan's Identities on False Theta Functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA","math.NT"],"primary_cat":"math.CO","authors_text":"Liuquan Wang","submitted_at":"2018-01-24T12:27:44Z","abstract_excerpt":"We provide new proofs to five of Ramanujan's intriguing identities on false theta functions without using the Rogers-Fine identity and Bailey transforms."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.07956","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":"2026-05-18T00:25:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"M3rWi3WkREUB25B76YZjPau7/U5mVOBOJf+JhjqP5tRdPrr/G1eAUvXxKtyHhi9uleKZMusBzg1vsG87botRAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-03T07:07:22.308291Z"},"content_sha256":"c2779615dd57f9601e51e1cbf8b8599817d5b7934241e8c2719f09b80bc1da61","schema_version":"1.0","event_id":"sha256:c2779615dd57f9601e51e1cbf8b8599817d5b7934241e8c2719f09b80bc1da61"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TFJ4NVFBER76MRJHCVZX5WYGAR/bundle.json","state_url":"https://pith.science/pith/TFJ4NVFBER76MRJHCVZX5WYGAR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TFJ4NVFBER76MRJHCVZX5WYGAR/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":"2026-07-03T07:07:22Z","links":{"resolver":"https://pith.science/pith/TFJ4NVFBER76MRJHCVZX5WYGAR","bundle":"https://pith.science/pith/TFJ4NVFBER76MRJHCVZX5WYGAR/bundle.json","state":"https://pith.science/pith/TFJ4NVFBER76MRJHCVZX5WYGAR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TFJ4NVFBER76MRJHCVZX5WYGAR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:TFJ4NVFBER76MRJHCVZX5WYGAR","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":"d5d74dfd21cbb1be7726a7bceabe180da38176c92a33be9d41bdb91e12d01fee","cross_cats_sorted":["math.CA","math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-01-24T12:27:44Z","title_canon_sha256":"121b7c5bf8c0e7ac73b29fc40a4798440932fc435919d421d78b38f0dcd553c6"},"schema_version":"1.0","source":{"id":"1801.07956","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1801.07956","created_at":"2026-05-18T00:25:10Z"},{"alias_kind":"arxiv_version","alias_value":"1801.07956v1","created_at":"2026-05-18T00:25:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1801.07956","created_at":"2026-05-18T00:25:10Z"},{"alias_kind":"pith_short_12","alias_value":"TFJ4NVFBER76","created_at":"2026-05-18T12:32:53Z"},{"alias_kind":"pith_short_16","alias_value":"TFJ4NVFBER76MRJH","created_at":"2026-05-18T12:32:53Z"},{"alias_kind":"pith_short_8","alias_value":"TFJ4NVFB","created_at":"2026-05-18T12:32:53Z"}],"graph_snapshots":[{"event_id":"sha256:c2779615dd57f9601e51e1cbf8b8599817d5b7934241e8c2719f09b80bc1da61","target":"graph","created_at":"2026-05-18T00:25:10Z","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 provide new proofs to five of Ramanujan's intriguing identities on false theta functions without using the Rogers-Fine identity and Bailey transforms.","authors_text":"Liuquan Wang","cross_cats":["math.CA","math.NT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-01-24T12:27:44Z","title":"New Proofs of Ramanujan's Identities on False Theta Functions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.07956","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:da04bd22678c93476c8c03e340d252235841598edb89e42a9b7934ed1d4ea64d","target":"record","created_at":"2026-05-18T00:25:10Z","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":"d5d74dfd21cbb1be7726a7bceabe180da38176c92a33be9d41bdb91e12d01fee","cross_cats_sorted":["math.CA","math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-01-24T12:27:44Z","title_canon_sha256":"121b7c5bf8c0e7ac73b29fc40a4798440932fc435919d421d78b38f0dcd553c6"},"schema_version":"1.0","source":{"id":"1801.07956","kind":"arxiv","version":1}},"canonical_sha256":"9953c6d4a1247fe6452715737edb06046f2c5f113b3d4df819a47866c3bda5ec","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9953c6d4a1247fe6452715737edb06046f2c5f113b3d4df819a47866c3bda5ec","first_computed_at":"2026-05-18T00:25:10.455075Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:25:10.455075Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"RvWHsDmobcwdrlGCv/CUnNJ+wz7WCN9gWLLF10zqT3R4gaMK1jTOizVbiroSUn2uegDaL2QYlY4WvQ8+d/+pAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:25:10.455737Z","signed_message":"canonical_sha256_bytes"},"source_id":"1801.07956","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:da04bd22678c93476c8c03e340d252235841598edb89e42a9b7934ed1d4ea64d","sha256:c2779615dd57f9601e51e1cbf8b8599817d5b7934241e8c2719f09b80bc1da61"],"state_sha256":"dfd22a019e24f31c3eb281bcdbb41b20011f6d07c9156abaabe034f0682efa8e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QfWgJzxvEKepVMq4lQWbKaBWaPAYzomr6nI4dVaEn6FR5vCIHq73ZuiuZX3yxvYf0FrNK2dPAjaW+6cNAq05Ag==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-03T07:07:22.310153Z","bundle_sha256":"dbbec48d843d44957948ad1fd8da6b84d36a17752303827fb53942992bdcf0c7"}}