{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:HDPE6VOPS6FKAAUDEUDHX2QFA7","short_pith_number":"pith:HDPE6VOP","schema_version":"1.0","canonical_sha256":"38de4f55cf978aa0028325067bea0507f704ee90b9238ba4432a74018eecf8da","source":{"kind":"arxiv","id":"1412.7265","version":2},"attestation_state":"computed","paper":{"title":"Triple Massey products and absolute Galois groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Eliyahu Matzri, Ido Efrat","submitted_at":"2014-12-23T06:46:10Z","abstract_excerpt":"Let $p$ be a prime number, $F$ a field containing a root of unity of order $p$, and $G_F$ the absolute Galois group. Extending results of Hopkins, Wickelgren, Minac and Tan, we prove that the triple Massey product $H^1(G_F)^3\\to H^2(G_F)$ contains $0$ whenever it is nonempty. This gives a new restriction on the possible profinite group structure of $G_F$."},"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":"1412.7265","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-12-23T06:46:10Z","cross_cats_sorted":[],"title_canon_sha256":"f6f08130e50f4c8c315bd2089cfa395a15796a75191113900696d0fb935c51c7","abstract_canon_sha256":"e63639e4ec4f7ce7936762e9ecb0d59cc0bc8e5cfaadf9704a3031251b0f2595"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:32:50.621304Z","signature_b64":"qSC33cinDpQ4Y+l9ugeiN4WKfsnp3n+wFTYEYj2gfBUjorwfziepMRopeAWo8fFy/0vNy91FV8TySjJU/4ZPAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"38de4f55cf978aa0028325067bea0507f704ee90b9238ba4432a74018eecf8da","last_reissued_at":"2026-05-18T01:32:50.620631Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:32:50.620631Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Triple Massey products and absolute Galois groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Eliyahu Matzri, Ido Efrat","submitted_at":"2014-12-23T06:46:10Z","abstract_excerpt":"Let $p$ be a prime number, $F$ a field containing a root of unity of order $p$, and $G_F$ the absolute Galois group. Extending results of Hopkins, Wickelgren, Minac and Tan, we prove that the triple Massey product $H^1(G_F)^3\\to H^2(G_F)$ contains $0$ whenever it is nonempty. This gives a new restriction on the possible profinite group structure of $G_F$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.7265","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":"1412.7265","created_at":"2026-05-18T01:32:50.620730+00:00"},{"alias_kind":"arxiv_version","alias_value":"1412.7265v2","created_at":"2026-05-18T01:32:50.620730+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.7265","created_at":"2026-05-18T01:32:50.620730+00:00"},{"alias_kind":"pith_short_12","alias_value":"HDPE6VOPS6FK","created_at":"2026-05-18T12:28:30.664211+00:00"},{"alias_kind":"pith_short_16","alias_value":"HDPE6VOPS6FKAAUD","created_at":"2026-05-18T12:28:30.664211+00:00"},{"alias_kind":"pith_short_8","alias_value":"HDPE6VOP","created_at":"2026-05-18T12:28:30.664211+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/HDPE6VOPS6FKAAUDEUDHX2QFA7","json":"https://pith.science/pith/HDPE6VOPS6FKAAUDEUDHX2QFA7.json","graph_json":"https://pith.science/api/pith-number/HDPE6VOPS6FKAAUDEUDHX2QFA7/graph.json","events_json":"https://pith.science/api/pith-number/HDPE6VOPS6FKAAUDEUDHX2QFA7/events.json","paper":"https://pith.science/paper/HDPE6VOP"},"agent_actions":{"view_html":"https://pith.science/pith/HDPE6VOPS6FKAAUDEUDHX2QFA7","download_json":"https://pith.science/pith/HDPE6VOPS6FKAAUDEUDHX2QFA7.json","view_paper":"https://pith.science/paper/HDPE6VOP","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1412.7265&json=true","fetch_graph":"https://pith.science/api/pith-number/HDPE6VOPS6FKAAUDEUDHX2QFA7/graph.json","fetch_events":"https://pith.science/api/pith-number/HDPE6VOPS6FKAAUDEUDHX2QFA7/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/HDPE6VOPS6FKAAUDEUDHX2QFA7/action/timestamp_anchor","attest_storage":"https://pith.science/pith/HDPE6VOPS6FKAAUDEUDHX2QFA7/action/storage_attestation","attest_author":"https://pith.science/pith/HDPE6VOPS6FKAAUDEUDHX2QFA7/action/author_attestation","sign_citation":"https://pith.science/pith/HDPE6VOPS6FKAAUDEUDHX2QFA7/action/citation_signature","submit_replication":"https://pith.science/pith/HDPE6VOPS6FKAAUDEUDHX2QFA7/action/replication_record"}},"created_at":"2026-05-18T01:32:50.620730+00:00","updated_at":"2026-05-18T01:32:50.620730+00:00"}