{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:6MBN47XEJT2TWJRAW5QDKCEMOR","short_pith_number":"pith:6MBN47XE","canonical_record":{"source":{"id":"1209.0533","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-09-04T06:19:35Z","cross_cats_sorted":["cs.DS","cs.NA"],"title_canon_sha256":"82f48fee4dd1d5aba9b455a5b272364bc4a54f0099b074deda7b79c55168f9c7","abstract_canon_sha256":"a7af47d60cdad82ae71f5700d3b681c537977bcdf22423c4d232b03374ac104b"},"schema_version":"1.0"},"canonical_sha256":"f302de7ee44cf53b2620b76035088c744396d82241e1c7348854d0fdcde6b9d5","source":{"kind":"arxiv","id":"1209.0533","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1209.0533","created_at":"2026-05-18T03:26:42Z"},{"alias_kind":"arxiv_version","alias_value":"1209.0533v3","created_at":"2026-05-18T03:26:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1209.0533","created_at":"2026-05-18T03:26:42Z"},{"alias_kind":"pith_short_12","alias_value":"6MBN47XEJT2T","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_16","alias_value":"6MBN47XEJT2TWJRA","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_8","alias_value":"6MBN47XE","created_at":"2026-05-18T12:26:56Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:6MBN47XEJT2TWJRAW5QDKCEMOR","target":"record","payload":{"canonical_record":{"source":{"id":"1209.0533","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-09-04T06:19:35Z","cross_cats_sorted":["cs.DS","cs.NA"],"title_canon_sha256":"82f48fee4dd1d5aba9b455a5b272364bc4a54f0099b074deda7b79c55168f9c7","abstract_canon_sha256":"a7af47d60cdad82ae71f5700d3b681c537977bcdf22423c4d232b03374ac104b"},"schema_version":"1.0"},"canonical_sha256":"f302de7ee44cf53b2620b76035088c744396d82241e1c7348854d0fdcde6b9d5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:26:42.823406Z","signature_b64":"SW6a7xZFFeOqtUoaBiRX8rZUB8j9gQZUfobv3xvwb/v/bq2dm1TQk32cN/h0Dm1r7DH60pv8+HtrWveXVLTADQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f302de7ee44cf53b2620b76035088c744396d82241e1c7348854d0fdcde6b9d5","last_reissued_at":"2026-05-18T03:26:42.822612Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:26:42.822612Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1209.0533","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":"2026-05-18T03:26:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JZY/rKeazAJzVC0KBxYIGXwcUympvw5HVKhBhZ1dxElqtr7CrqnD4DC5fEhMg3/X18UmHSx2RWDqzBkv7iTPCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T19:30:10.524194Z"},"content_sha256":"cd971c7357bfbecb370c6ad96b2209037996fd4e408bf6d9206853345e300dbc","schema_version":"1.0","event_id":"sha256:cd971c7357bfbecb370c6ad96b2209037996fd4e408bf6d9206853345e300dbc"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:6MBN47XEJT2TWJRAW5QDKCEMOR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A subquadratic algorithm for computing the n-th Bernoulli number","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DS","cs.NA"],"primary_cat":"math.NT","authors_text":"David Harvey","submitted_at":"2012-09-04T06:19:35Z","abstract_excerpt":"We describe a new algorithm that computes the n-th Bernoulli number in n^(4/3 + o(1)) bit operations. This improves on previous algorithms that had complexity n^(2 + o(1))."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.0533","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":"2026-05-18T03:26:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ju6zO6u0SNdpBzPJMgj/RZwNVlBQ1zNtJTVqjH12ZG+cjkSz//BA2IB1DIBu3RTNF4Msu3IWZbl//yNyoa01BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T19:30:10.524941Z"},"content_sha256":"b4a31897a89c8f13a655de393a76d694ba810ed4e242d251dc32da67b2b902f1","schema_version":"1.0","event_id":"sha256:b4a31897a89c8f13a655de393a76d694ba810ed4e242d251dc32da67b2b902f1"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6MBN47XEJT2TWJRAW5QDKCEMOR/bundle.json","state_url":"https://pith.science/pith/6MBN47XEJT2TWJRAW5QDKCEMOR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6MBN47XEJT2TWJRAW5QDKCEMOR/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":"2026-06-08T19:30:10Z","links":{"resolver":"https://pith.science/pith/6MBN47XEJT2TWJRAW5QDKCEMOR","bundle":"https://pith.science/pith/6MBN47XEJT2TWJRAW5QDKCEMOR/bundle.json","state":"https://pith.science/pith/6MBN47XEJT2TWJRAW5QDKCEMOR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6MBN47XEJT2TWJRAW5QDKCEMOR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:6MBN47XEJT2TWJRAW5QDKCEMOR","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":"a7af47d60cdad82ae71f5700d3b681c537977bcdf22423c4d232b03374ac104b","cross_cats_sorted":["cs.DS","cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-09-04T06:19:35Z","title_canon_sha256":"82f48fee4dd1d5aba9b455a5b272364bc4a54f0099b074deda7b79c55168f9c7"},"schema_version":"1.0","source":{"id":"1209.0533","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1209.0533","created_at":"2026-05-18T03:26:42Z"},{"alias_kind":"arxiv_version","alias_value":"1209.0533v3","created_at":"2026-05-18T03:26:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1209.0533","created_at":"2026-05-18T03:26:42Z"},{"alias_kind":"pith_short_12","alias_value":"6MBN47XEJT2T","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_16","alias_value":"6MBN47XEJT2TWJRA","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_8","alias_value":"6MBN47XE","created_at":"2026-05-18T12:26:56Z"}],"graph_snapshots":[{"event_id":"sha256:b4a31897a89c8f13a655de393a76d694ba810ed4e242d251dc32da67b2b902f1","target":"graph","created_at":"2026-05-18T03:26:42Z","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 describe a new algorithm that computes the n-th Bernoulli number in n^(4/3 + o(1)) bit operations. This improves on previous algorithms that had complexity n^(2 + o(1)).","authors_text":"David Harvey","cross_cats":["cs.DS","cs.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-09-04T06:19:35Z","title":"A subquadratic algorithm for computing the n-th Bernoulli number"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.0533","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:cd971c7357bfbecb370c6ad96b2209037996fd4e408bf6d9206853345e300dbc","target":"record","created_at":"2026-05-18T03:26:42Z","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":"a7af47d60cdad82ae71f5700d3b681c537977bcdf22423c4d232b03374ac104b","cross_cats_sorted":["cs.DS","cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-09-04T06:19:35Z","title_canon_sha256":"82f48fee4dd1d5aba9b455a5b272364bc4a54f0099b074deda7b79c55168f9c7"},"schema_version":"1.0","source":{"id":"1209.0533","kind":"arxiv","version":3}},"canonical_sha256":"f302de7ee44cf53b2620b76035088c744396d82241e1c7348854d0fdcde6b9d5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f302de7ee44cf53b2620b76035088c744396d82241e1c7348854d0fdcde6b9d5","first_computed_at":"2026-05-18T03:26:42.822612Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:26:42.822612Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"SW6a7xZFFeOqtUoaBiRX8rZUB8j9gQZUfobv3xvwb/v/bq2dm1TQk32cN/h0Dm1r7DH60pv8+HtrWveXVLTADQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:26:42.823406Z","signed_message":"canonical_sha256_bytes"},"source_id":"1209.0533","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cd971c7357bfbecb370c6ad96b2209037996fd4e408bf6d9206853345e300dbc","sha256:b4a31897a89c8f13a655de393a76d694ba810ed4e242d251dc32da67b2b902f1"],"state_sha256":"d0f22608f4e648e1cdfbec1166f0e3e24e1f57cf2aa950ecc32bf253eda0bc3d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"65R9TkDhjR9Vj90T3ttrueUOscoOZRXCrSXzjEK715pWwreS8bNYiXbk8K5qCrBCPVQdryemaYVYdJvKCixyBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-08T19:30:10.529034Z","bundle_sha256":"8a1e96e0c8a44335bc0176e79c752999e2305a6bbbfb9dcf5927d9a910c9c389"}}