{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:KMYNCDJS5L2ETEBCFWVREYRPD2","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":"f1f28eb86353a4438473b890bb659499a3a0fdaa62a4b803e50b02126dc90a66","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-01-11T12:47:22Z","title_canon_sha256":"f10482dd1f6e8ad2a0e04816ace67b62d9aa8313d318da0661ba8567588b781a"},"schema_version":"1.0","source":{"id":"1601.02422","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1601.02422","created_at":"2026-05-18T01:23:06Z"},{"alias_kind":"arxiv_version","alias_value":"1601.02422v1","created_at":"2026-05-18T01:23:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1601.02422","created_at":"2026-05-18T01:23:06Z"},{"alias_kind":"pith_short_12","alias_value":"KMYNCDJS5L2E","created_at":"2026-05-18T12:30:25Z"},{"alias_kind":"pith_short_16","alias_value":"KMYNCDJS5L2ETEBC","created_at":"2026-05-18T12:30:25Z"},{"alias_kind":"pith_short_8","alias_value":"KMYNCDJS","created_at":"2026-05-18T12:30:25Z"}],"graph_snapshots":[{"event_id":"sha256:2db631f21c84f8053f03cb037e5eb3692b5e7da4d988d410120c09211bd7e328","target":"graph","created_at":"2026-05-18T01:23:06Z","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":"A map of fine log schemes $X \\to Y$ induces a map from the scheme underlying $X$ to Olsson's algebraic stack of strict morphisms of fine log schemes over $Y$. A sheaf on $X$ is called \\emph{log flat over} $Y$ iff it is flat over this algebraic stack. This paper is a study of log flatness and the related notions of flatness for maps of monoids and graded rings. It is shown that log flatness is equivalent to a more general notion of \"formal log flatness\" that makes sense for an arbitrary map of log ringed topoi. Concrete log flatness criteria are given for many $X \\to Y$ that occur \"in nature,\" ","authors_text":"W. D. Gillam","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-01-11T12:47:22Z","title":"Logarithmic Flatness"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.02422","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:c9d7285740a69d0d81aa6371aa79c9f3c7c3b6b05a512e3f789a1a84e7871178","target":"record","created_at":"2026-05-18T01:23:06Z","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":"f1f28eb86353a4438473b890bb659499a3a0fdaa62a4b803e50b02126dc90a66","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-01-11T12:47:22Z","title_canon_sha256":"f10482dd1f6e8ad2a0e04816ace67b62d9aa8313d318da0661ba8567588b781a"},"schema_version":"1.0","source":{"id":"1601.02422","kind":"arxiv","version":1}},"canonical_sha256":"5330d10d32eaf44990222dab12622f1e91bd0a1fb5b47115f166295c3c94f8c8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5330d10d32eaf44990222dab12622f1e91bd0a1fb5b47115f166295c3c94f8c8","first_computed_at":"2026-05-18T01:23:06.499494Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:23:06.499494Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"38mkm6C68QnswFIBVnkddOK+VHBiJVYNJUT8yAonLy5CI4+056eVvKRsUrBuxncbPMTGH4v6mKz/GCVKBUejBw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:23:06.499953Z","signed_message":"canonical_sha256_bytes"},"source_id":"1601.02422","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c9d7285740a69d0d81aa6371aa79c9f3c7c3b6b05a512e3f789a1a84e7871178","sha256:2db631f21c84f8053f03cb037e5eb3692b5e7da4d988d410120c09211bd7e328"],"state_sha256":"3f3bf73e673ffd2504b921062e7789d13340790502784ae3b027e16f022370bf"}