{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:N7E5N4WCDBMXORY7N3VW7PF6BM","short_pith_number":"pith:N7E5N4WC","canonical_record":{"source":{"id":"1403.4586","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-03-18T19:38:32Z","cross_cats_sorted":[],"title_canon_sha256":"afe8dcd4c4be940f06529ddc507e5eaf11ed3d41414985fe25aac17e066c46b3","abstract_canon_sha256":"176660cc7bdea0fe43b54a907f63741f5ca15d3ebe0f44bf46f034e28e567b85"},"schema_version":"1.0"},"canonical_sha256":"6fc9d6f2c2185977471f6eeb6fbcbe0b009630cd56037b6bd36c9b1b5f3b2fed","source":{"kind":"arxiv","id":"1403.4586","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1403.4586","created_at":"2026-05-18T01:24:04Z"},{"alias_kind":"arxiv_version","alias_value":"1403.4586v2","created_at":"2026-05-18T01:24:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1403.4586","created_at":"2026-05-18T01:24:04Z"},{"alias_kind":"pith_short_12","alias_value":"N7E5N4WCDBMX","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_16","alias_value":"N7E5N4WCDBMXORY7","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_8","alias_value":"N7E5N4WC","created_at":"2026-05-18T12:28:41Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:N7E5N4WCDBMXORY7N3VW7PF6BM","target":"record","payload":{"canonical_record":{"source":{"id":"1403.4586","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-03-18T19:38:32Z","cross_cats_sorted":[],"title_canon_sha256":"afe8dcd4c4be940f06529ddc507e5eaf11ed3d41414985fe25aac17e066c46b3","abstract_canon_sha256":"176660cc7bdea0fe43b54a907f63741f5ca15d3ebe0f44bf46f034e28e567b85"},"schema_version":"1.0"},"canonical_sha256":"6fc9d6f2c2185977471f6eeb6fbcbe0b009630cd56037b6bd36c9b1b5f3b2fed","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:24:04.373624Z","signature_b64":"JChbLTGyQn5aUtZKh8pm/6lkhw6uNwUALrS2bNvr54IlEfSViM7WUz+tqNnOQqcwaYJ6HySJuXGeerr3/yYiAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6fc9d6f2c2185977471f6eeb6fbcbe0b009630cd56037b6bd36c9b1b5f3b2fed","last_reissued_at":"2026-05-18T01:24:04.372944Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:24:04.372944Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1403.4586","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:24:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fVd0LXnBx2wOtcw71NKhmy3BI/4pYZGczWFtCyQQ9HRQAiteFacVxexrNMMH7+X3lSyAks/EhGCPykzUzQ9eAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T12:17:03.181650Z"},"content_sha256":"d7e93490aa58ac9272c0c7dd2cab1f61faa535e41d33cc62fff68ea2c5d933f6","schema_version":"1.0","event_id":"sha256:d7e93490aa58ac9272c0c7dd2cab1f61faa535e41d33cc62fff68ea2c5d933f6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:N7E5N4WCDBMXORY7N3VW7PF6BM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Triple Massey products over global fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Jan Minac, Nguyen Duy Tan","submitted_at":"2014-03-18T19:38:32Z","abstract_excerpt":"Let $K$ be a global field which contains a primitive $p$-th root of unity, where $p$ is a prime number. M. J. Hopkins and K. G. Wickelgren showed that for $p=2$, any triple Massey product over $K$ with respect to $\\mathbb{F}_p$, contains 0 whenever it is defined. We show that this is true for all primes $p$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.4586","kind":"arxiv","version":2},"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":"2026-05-18T01:24:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DUiR6O+KlAxNsw6oRP0HjN/2/MvDiueSBvJiGLe67Lgh5Ujogz86pWclRTqw5jP4Do9LBDF3bxH3/swRUhuJDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T12:17:03.181987Z"},"content_sha256":"6eefb72514e7597d40a799640edabd39eef50b6675140173c3b8cee5681a2216","schema_version":"1.0","event_id":"sha256:6eefb72514e7597d40a799640edabd39eef50b6675140173c3b8cee5681a2216"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/N7E5N4WCDBMXORY7N3VW7PF6BM/bundle.json","state_url":"https://pith.science/pith/N7E5N4WCDBMXORY7N3VW7PF6BM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/N7E5N4WCDBMXORY7N3VW7PF6BM/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":"2026-05-28T12:17:03Z","links":{"resolver":"https://pith.science/pith/N7E5N4WCDBMXORY7N3VW7PF6BM","bundle":"https://pith.science/pith/N7E5N4WCDBMXORY7N3VW7PF6BM/bundle.json","state":"https://pith.science/pith/N7E5N4WCDBMXORY7N3VW7PF6BM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/N7E5N4WCDBMXORY7N3VW7PF6BM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:N7E5N4WCDBMXORY7N3VW7PF6BM","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":"176660cc7bdea0fe43b54a907f63741f5ca15d3ebe0f44bf46f034e28e567b85","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-03-18T19:38:32Z","title_canon_sha256":"afe8dcd4c4be940f06529ddc507e5eaf11ed3d41414985fe25aac17e066c46b3"},"schema_version":"1.0","source":{"id":"1403.4586","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1403.4586","created_at":"2026-05-18T01:24:04Z"},{"alias_kind":"arxiv_version","alias_value":"1403.4586v2","created_at":"2026-05-18T01:24:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1403.4586","created_at":"2026-05-18T01:24:04Z"},{"alias_kind":"pith_short_12","alias_value":"N7E5N4WCDBMX","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_16","alias_value":"N7E5N4WCDBMXORY7","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_8","alias_value":"N7E5N4WC","created_at":"2026-05-18T12:28:41Z"}],"graph_snapshots":[{"event_id":"sha256:6eefb72514e7597d40a799640edabd39eef50b6675140173c3b8cee5681a2216","target":"graph","created_at":"2026-05-18T01:24:04Z","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":"Let $K$ be a global field which contains a primitive $p$-th root of unity, where $p$ is a prime number. M. J. Hopkins and K. G. Wickelgren showed that for $p=2$, any triple Massey product over $K$ with respect to $\\mathbb{F}_p$, contains 0 whenever it is defined. We show that this is true for all primes $p$.","authors_text":"Jan Minac, Nguyen Duy Tan","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-03-18T19:38:32Z","title":"Triple Massey products over global fields"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.4586","kind":"arxiv","version":2},"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:d7e93490aa58ac9272c0c7dd2cab1f61faa535e41d33cc62fff68ea2c5d933f6","target":"record","created_at":"2026-05-18T01:24:04Z","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":"176660cc7bdea0fe43b54a907f63741f5ca15d3ebe0f44bf46f034e28e567b85","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-03-18T19:38:32Z","title_canon_sha256":"afe8dcd4c4be940f06529ddc507e5eaf11ed3d41414985fe25aac17e066c46b3"},"schema_version":"1.0","source":{"id":"1403.4586","kind":"arxiv","version":2}},"canonical_sha256":"6fc9d6f2c2185977471f6eeb6fbcbe0b009630cd56037b6bd36c9b1b5f3b2fed","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6fc9d6f2c2185977471f6eeb6fbcbe0b009630cd56037b6bd36c9b1b5f3b2fed","first_computed_at":"2026-05-18T01:24:04.372944Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:24:04.372944Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"JChbLTGyQn5aUtZKh8pm/6lkhw6uNwUALrS2bNvr54IlEfSViM7WUz+tqNnOQqcwaYJ6HySJuXGeerr3/yYiAw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:24:04.373624Z","signed_message":"canonical_sha256_bytes"},"source_id":"1403.4586","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d7e93490aa58ac9272c0c7dd2cab1f61faa535e41d33cc62fff68ea2c5d933f6","sha256:6eefb72514e7597d40a799640edabd39eef50b6675140173c3b8cee5681a2216"],"state_sha256":"9ff7f6179eccad1d2b925e0613116f7ecfa01abeb9a7c8834d69d5c86235d02c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YHZZE+FZQJ7fdpwligW+sO5n0G065tzG/n5SOXTmOtTvYtBgzGd04Kd207Dn/HNqipvPQcImxZbLU6joMQUXCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T12:17:03.183966Z","bundle_sha256":"ad123af9aded1f24abbbe81d312482665f4edca4203cada730a3776bb9527e9c"}}