{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:N7E5N4WCDBMXORY7N3VW7PF6BM","short_pith_number":"pith:N7E5N4WC","schema_version":"1.0","canonical_sha256":"6fc9d6f2c2185977471f6eeb6fbcbe0b009630cd56037b6bd36c9b1b5f3b2fed","source":{"kind":"arxiv","id":"1403.4586","version":2},"attestation_state":"computed","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 $p$."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"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"},"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"},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1403.4586","created_at":"2026-05-18T01:24:04.373057+00:00"},{"alias_kind":"arxiv_version","alias_value":"1403.4586v2","created_at":"2026-05-18T01:24:04.373057+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1403.4586","created_at":"2026-05-18T01:24:04.373057+00:00"},{"alias_kind":"pith_short_12","alias_value":"N7E5N4WCDBMX","created_at":"2026-05-18T12:28:41.024544+00:00"},{"alias_kind":"pith_short_16","alias_value":"N7E5N4WCDBMXORY7","created_at":"2026-05-18T12:28:41.024544+00:00"},{"alias_kind":"pith_short_8","alias_value":"N7E5N4WC","created_at":"2026-05-18T12:28:41.024544+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/N7E5N4WCDBMXORY7N3VW7PF6BM","json":"https://pith.science/pith/N7E5N4WCDBMXORY7N3VW7PF6BM.json","graph_json":"https://pith.science/api/pith-number/N7E5N4WCDBMXORY7N3VW7PF6BM/graph.json","events_json":"https://pith.science/api/pith-number/N7E5N4WCDBMXORY7N3VW7PF6BM/events.json","paper":"https://pith.science/paper/N7E5N4WC"},"agent_actions":{"view_html":"https://pith.science/pith/N7E5N4WCDBMXORY7N3VW7PF6BM","download_json":"https://pith.science/pith/N7E5N4WCDBMXORY7N3VW7PF6BM.json","view_paper":"https://pith.science/paper/N7E5N4WC","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1403.4586&json=true","fetch_graph":"https://pith.science/api/pith-number/N7E5N4WCDBMXORY7N3VW7PF6BM/graph.json","fetch_events":"https://pith.science/api/pith-number/N7E5N4WCDBMXORY7N3VW7PF6BM/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/N7E5N4WCDBMXORY7N3VW7PF6BM/action/timestamp_anchor","attest_storage":"https://pith.science/pith/N7E5N4WCDBMXORY7N3VW7PF6BM/action/storage_attestation","attest_author":"https://pith.science/pith/N7E5N4WCDBMXORY7N3VW7PF6BM/action/author_attestation","sign_citation":"https://pith.science/pith/N7E5N4WCDBMXORY7N3VW7PF6BM/action/citation_signature","submit_replication":"https://pith.science/pith/N7E5N4WCDBMXORY7N3VW7PF6BM/action/replication_record"}},"created_at":"2026-05-18T01:24:04.373057+00:00","updated_at":"2026-05-18T01:24:04.373057+00:00"}