{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:F2F4ENZ2PCF3DXRTSIY4RLJYXS","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":"7b0c0272dcd9ea1241d168fc0dd97741f1b16b1f51cc9f2d234a70f65925b042","cross_cats_sorted":["math.AC","math.KT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-03-06T02:17:54Z","title_canon_sha256":"c9b316d7e117eeb117f0ac78dbbac15d4992b9d097a1a02f08617e4345a8102a"},"schema_version":"1.0","source":{"id":"1303.1239","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1303.1239","created_at":"2026-05-18T03:30:40Z"},{"alias_kind":"arxiv_version","alias_value":"1303.1239v2","created_at":"2026-05-18T03:30:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1303.1239","created_at":"2026-05-18T03:30:40Z"},{"alias_kind":"pith_short_12","alias_value":"F2F4ENZ2PCF3","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_16","alias_value":"F2F4ENZ2PCF3DXRT","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_8","alias_value":"F2F4ENZ2","created_at":"2026-05-18T12:27:43Z"}],"graph_snapshots":[{"event_id":"sha256:45b176553f21ef87ade3b8b16e621d4d414972cd2c2f362fc40b6e4333bc524a","target":"graph","created_at":"2026-05-18T03:30:40Z","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 objective of this paper is to determine generators of the topological filtrations on the higher K-theory of a noetherian commutative ring with unit A. We introduce the concept of Koszul cubes and give a comparison theorem between the K-theory of Koszul cubes with that of topological filtrations.","authors_text":"Satoshi Mochizuki","cross_cats":["math.AC","math.KT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-03-06T02:17:54Z","title":"Higher K-theory of Koszul cubes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.1239","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:a43966635b4444ec0360d1e3091a9ec9c257b14d6c664b79bf565711b5433734","target":"record","created_at":"2026-05-18T03:30:40Z","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":"7b0c0272dcd9ea1241d168fc0dd97741f1b16b1f51cc9f2d234a70f65925b042","cross_cats_sorted":["math.AC","math.KT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-03-06T02:17:54Z","title_canon_sha256":"c9b316d7e117eeb117f0ac78dbbac15d4992b9d097a1a02f08617e4345a8102a"},"schema_version":"1.0","source":{"id":"1303.1239","kind":"arxiv","version":2}},"canonical_sha256":"2e8bc2373a788bb1de339231c8ad38bc86c743dbb6775c8747c33f8fa18969b8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2e8bc2373a788bb1de339231c8ad38bc86c743dbb6775c8747c33f8fa18969b8","first_computed_at":"2026-05-18T03:30:40.733675Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:30:40.733675Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"LVk8/+chJDqVPvvj3JJa72bRf9FtE5HgKPy2QDYVIlmJJp3O/tSUjVD8Cu9rnD5/Nwq6YCc2XzM6bQGXyX/HDw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:30:40.734479Z","signed_message":"canonical_sha256_bytes"},"source_id":"1303.1239","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a43966635b4444ec0360d1e3091a9ec9c257b14d6c664b79bf565711b5433734","sha256:45b176553f21ef87ade3b8b16e621d4d414972cd2c2f362fc40b6e4333bc524a"],"state_sha256":"c109203c216b27e313633f9370197759cd66c9684b91f81c716a6dfe40ff2099"}