{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:GMBSOBFRBHUDMDYD3PGL7VM3GN","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":"008b4dc84fe03bc32e6a16425d1fb45331fa205664d15afefe165010a4c62998","cross_cats_sorted":["math.OA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2008-04-01T02:51:54Z","title_canon_sha256":"d0090b7ee15b6c14af0c2c92955a9610acab795cf2009ab38475460955814e11"},"schema_version":"1.0","source":{"id":"0804.0057","kind":"arxiv","version":9}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0804.0057","created_at":"2026-07-05T06:21:11Z"},{"alias_kind":"arxiv_version","alias_value":"0804.0057v9","created_at":"2026-07-05T06:21:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0804.0057","created_at":"2026-07-05T06:21:11Z"},{"alias_kind":"pith_short_12","alias_value":"GMBSOBFRBHUD","created_at":"2026-07-05T06:21:11Z"},{"alias_kind":"pith_short_16","alias_value":"GMBSOBFRBHUDMDYD","created_at":"2026-07-05T06:21:11Z"},{"alias_kind":"pith_short_8","alias_value":"GMBSOBFR","created_at":"2026-07-05T06:21:11Z"}],"graph_snapshots":[{"event_id":"sha256:6af42429c5713a5fe95987000b9e1206f1410924bd47fab3a25ebf1e16d17388","target":"graph","created_at":"2026-07-05T06:21:11Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/0804.0057/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Yu. I. Manin conjectured that the maximal abelian extensions of the real quadratic number fields are generated by the pseudo-lattices with real multiplication. We prove this conjecture using theory of measured foliations on the modular curves.","authors_text":"Igor Nikolaev","cross_cats":["math.OA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2008-04-01T02:51:54Z","title":"Measured foliations and Hilbert 12th problem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0804.0057","kind":"arxiv","version":9},"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":"sha256:8f410f6fe3ae7423088d1ba5b13f84817b74e0bf305feb29c4663a400bed5ed7","target":"record","created_at":"2026-07-05T06:21:11Z","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":"008b4dc84fe03bc32e6a16425d1fb45331fa205664d15afefe165010a4c62998","cross_cats_sorted":["math.OA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2008-04-01T02:51:54Z","title_canon_sha256":"d0090b7ee15b6c14af0c2c92955a9610acab795cf2009ab38475460955814e11"},"schema_version":"1.0","source":{"id":"0804.0057","kind":"arxiv","version":9}},"canonical_sha256":"33032704b109e8360f03dbccbfd59b336544cf240cd7e4fbaa1268ca85917418","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"33032704b109e8360f03dbccbfd59b336544cf240cd7e4fbaa1268ca85917418","first_computed_at":"2026-07-05T06:21:11.215034Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T06:21:11.215034Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"svOmeCsFJa9BmI8BL4k17HYb5y0lx9/ThUrOJLo0DAHIvBiP7ZBYw3kDYhyi5a9DIEDLlm2Bok4Irp39j7NCCw==","signature_status":"signed_v1","signed_at":"2026-07-05T06:21:11.215426Z","signed_message":"canonical_sha256_bytes"},"source_id":"0804.0057","source_kind":"arxiv","source_version":9}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8f410f6fe3ae7423088d1ba5b13f84817b74e0bf305feb29c4663a400bed5ed7","sha256:6af42429c5713a5fe95987000b9e1206f1410924bd47fab3a25ebf1e16d17388"],"state_sha256":"20806502acf22d44b4af882e801676ae51f273f71e61b318c92442bb15486993"}