{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:7M3PU3X6CPBI73EPFB5IVEGAGL","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":"dbf4074811d2481041f3e3b3752e49a2f9a283e653514bf262017aa062f8f081","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-03-16T17:15:42Z","title_canon_sha256":"81f8d33bd7e8ab91790162d78ead711c1dbc1338bcc9554defb3f2220e2fff8c"},"schema_version":"1.0","source":{"id":"1703.05729","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1703.05729","created_at":"2026-05-18T00:48:33Z"},{"alias_kind":"arxiv_version","alias_value":"1703.05729v1","created_at":"2026-05-18T00:48:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.05729","created_at":"2026-05-18T00:48:33Z"},{"alias_kind":"pith_short_12","alias_value":"7M3PU3X6CPBI","created_at":"2026-05-18T12:31:05Z"},{"alias_kind":"pith_short_16","alias_value":"7M3PU3X6CPBI73EP","created_at":"2026-05-18T12:31:05Z"},{"alias_kind":"pith_short_8","alias_value":"7M3PU3X6","created_at":"2026-05-18T12:31:05Z"}],"graph_snapshots":[{"event_id":"sha256:92107b523298c68e1a13446a6a4be6a9365106e471e5d5e218310dd3be4f2e06","target":"graph","created_at":"2026-05-18T00:48:33Z","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":"The main purpose of this paper is to describe the abelian part $\\mathcal G^{ab}_{K}$ of the absolute Galois group of a global function field $K$ as pro-finite group. We will show that the characteristic $p$ of $K$ and the non $p$-part of the class group of $K$ are determined by $\\mathcal G^{ab}_{K}$. The converse is almost true: isomorphism type of $\\mathcal G_K^{ab}$ as pro-finite group is determined by the invariant $d_K$ of the constant field $\\mathbb F_q$ introduced in first section and the non $p$-part of the class group.","authors_text":"Bart de Smit, Pavel Solomatin","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-03-16T17:15:42Z","title":"On Abelianized Absolute Galois Group of Global Function Fields"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.05729","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":"sha256:35dad52c2d2fa4b67639c04b2fcafe3c1f246f4ed3b1b22612377874c9441305","target":"record","created_at":"2026-05-18T00:48:33Z","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":"dbf4074811d2481041f3e3b3752e49a2f9a283e653514bf262017aa062f8f081","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-03-16T17:15:42Z","title_canon_sha256":"81f8d33bd7e8ab91790162d78ead711c1dbc1338bcc9554defb3f2220e2fff8c"},"schema_version":"1.0","source":{"id":"1703.05729","kind":"arxiv","version":1}},"canonical_sha256":"fb36fa6efe13c28fec8f287a8a90c032cf7fc13dc35c2c03ab0ccb0e42770cc0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fb36fa6efe13c28fec8f287a8a90c032cf7fc13dc35c2c03ab0ccb0e42770cc0","first_computed_at":"2026-05-18T00:48:33.525022Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:48:33.525022Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"wKI8NHJ76ocIF/J+Fd8NSBH5eC8/xbQcGdSxIioPOSi4IOH7wdOVyTCzKb99dg0R0CgntaNisFHLmiA/lseoAA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:48:33.525647Z","signed_message":"canonical_sha256_bytes"},"source_id":"1703.05729","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:35dad52c2d2fa4b67639c04b2fcafe3c1f246f4ed3b1b22612377874c9441305","sha256:92107b523298c68e1a13446a6a4be6a9365106e471e5d5e218310dd3be4f2e06"],"state_sha256":"623572e59a22af31c29bfbfc2064ab1b46ffd1b9b3347b15bec055cfd3e356f9"}