{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:OSJRFJC7KRLSL7MMGMGBUFWUD5","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":"16098c3bffa7018c65da77b6166eede3bcd3194a7749ed3429ae9d9891ad4392","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2011-11-07T17:04:41Z","title_canon_sha256":"a7ebca35ae86d1037aef89152d37d94388d488eb96e2403481b408861ce02f00"},"schema_version":"1.0","source":{"id":"1111.1645","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1111.1645","created_at":"2026-05-18T03:55:46Z"},{"alias_kind":"arxiv_version","alias_value":"1111.1645v2","created_at":"2026-05-18T03:55:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1111.1645","created_at":"2026-05-18T03:55:46Z"},{"alias_kind":"pith_short_12","alias_value":"OSJRFJC7KRLS","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_16","alias_value":"OSJRFJC7KRLSL7MM","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_8","alias_value":"OSJRFJC7","created_at":"2026-05-18T12:26:37Z"}],"graph_snapshots":[{"event_id":"sha256:591477b8f815f31e6f899ea98acfacfb40d3253312d755667a3b28c991b6ee6f","target":"graph","created_at":"2026-05-18T03:55:46Z","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":"We give a survey on noncommutative main conjectures of Iwasawa theory in a geometric setting, i.e. for separated schemes of finite type over a finite field, as stated and proved by Burns and the author. We will also comment briefly on versions of the main conjecture for function fields.","authors_text":"Malte Witte","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2011-11-07T17:04:41Z","title":"Noncommutative Main Conjectures of Geometric Iwasawa Theory"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.1645","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:c6be51503ab887feda73d5add0726ce2196b003b093332c21a58c99500eaff6b","target":"record","created_at":"2026-05-18T03:55:46Z","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":"16098c3bffa7018c65da77b6166eede3bcd3194a7749ed3429ae9d9891ad4392","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2011-11-07T17:04:41Z","title_canon_sha256":"a7ebca35ae86d1037aef89152d37d94388d488eb96e2403481b408861ce02f00"},"schema_version":"1.0","source":{"id":"1111.1645","kind":"arxiv","version":2}},"canonical_sha256":"749312a45f545725fd8c330c1a16d41f63cb2f9d6c3e71b12e7deb5f12bfb70d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"749312a45f545725fd8c330c1a16d41f63cb2f9d6c3e71b12e7deb5f12bfb70d","first_computed_at":"2026-05-18T03:55:46.843866Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:55:46.843866Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3izj1Q4eo41eSmwQZzGzFmTpjz5luD94p6bRMmScBTanBhyJJYRq9do/AD6v/m0Ogl6oHFfUVOtx/2GgKq4XBA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:55:46.844502Z","signed_message":"canonical_sha256_bytes"},"source_id":"1111.1645","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c6be51503ab887feda73d5add0726ce2196b003b093332c21a58c99500eaff6b","sha256:591477b8f815f31e6f899ea98acfacfb40d3253312d755667a3b28c991b6ee6f"],"state_sha256":"2731bb30840c7110bf57dea392c82473f1de1c20d951b766bb61d8b4af2d9f6e"}