{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:A2R4B4LB3ALJYQ6PYQDV5GGHKD","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":"d21b93cee3f2318448c947389b375af887785a0b9c488ea687783c2e6a644451","cross_cats_sorted":["math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2011-12-24T03:25:02Z","title_canon_sha256":"ddbebfb38840e880612824088a66cf49ff78e1e70d06ad554606bdf25db7c969"},"schema_version":"1.0","source":{"id":"1112.5695","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1112.5695","created_at":"2026-05-18T04:05:37Z"},{"alias_kind":"arxiv_version","alias_value":"1112.5695v1","created_at":"2026-05-18T04:05:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1112.5695","created_at":"2026-05-18T04:05:37Z"},{"alias_kind":"pith_short_12","alias_value":"A2R4B4LB3ALJ","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_16","alias_value":"A2R4B4LB3ALJYQ6P","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_8","alias_value":"A2R4B4LB","created_at":"2026-05-18T12:26:22Z"}],"graph_snapshots":[{"event_id":"sha256:32badf5592c68b2159574d9d2d05c873a998877c44ebe40670d747f24f29ff2d","target":"graph","created_at":"2026-05-18T04:05:37Z","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":"For a mixed characteristic complete discrete valuation field $K$ which contains a $p^n$-th root of unity, we determine the graded quotients of the filtration on the Milnor $K$-groups $K_q^M(K)$ modulo $p^n$ in terms of differential forms of the residue field of $K$.","authors_text":"Toshiro Hiranouchi","cross_cats":["math.NT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2011-12-24T03:25:02Z","title":"Milnor $K$-groups modulo $p^n$ of a complete discrete valuation field"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.5695","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:f6bcd40dd837770d53daf2dcd6058525f2b56db553c5f0bd620d10b0b5b365b2","target":"record","created_at":"2026-05-18T04:05:37Z","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":"d21b93cee3f2318448c947389b375af887785a0b9c488ea687783c2e6a644451","cross_cats_sorted":["math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2011-12-24T03:25:02Z","title_canon_sha256":"ddbebfb38840e880612824088a66cf49ff78e1e70d06ad554606bdf25db7c969"},"schema_version":"1.0","source":{"id":"1112.5695","kind":"arxiv","version":1}},"canonical_sha256":"06a3c0f161d8169c43cfc4075e98c750f0dee394490d957e4771608314e2a881","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"06a3c0f161d8169c43cfc4075e98c750f0dee394490d957e4771608314e2a881","first_computed_at":"2026-05-18T04:05:37.799360Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:05:37.799360Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"RYXdmqpQGzdjNPHtGLmGBEXS30E7IlYa2a+RWdXyWgTzry0GeQj8EaoE3+u36ZKoMGqlONALjlsTbRD5H7EoCg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:05:37.799746Z","signed_message":"canonical_sha256_bytes"},"source_id":"1112.5695","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f6bcd40dd837770d53daf2dcd6058525f2b56db553c5f0bd620d10b0b5b365b2","sha256:32badf5592c68b2159574d9d2d05c873a998877c44ebe40670d747f24f29ff2d"],"state_sha256":"4777bee06f0b4686abd14656b85cb98922d2d569317d7d0f999b51a45350f908"}