{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:PGG2OXKEO4F6DRLW7XWH7G3NSH","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":"2e9a70ffef31413baa657b2b197b6f7a4b09f88a19e0c782e5e097da97af1896","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2017-08-22T02:28:03Z","title_canon_sha256":"d5cc43566951878dc07dd7340ae3e521fae97f0e80a4b84a1cc5fe0bbbf994ca"},"schema_version":"1.0","source":{"id":"1708.06481","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1708.06481","created_at":"2026-05-18T00:24:59Z"},{"alias_kind":"arxiv_version","alias_value":"1708.06481v2","created_at":"2026-05-18T00:24:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1708.06481","created_at":"2026-05-18T00:24:59Z"},{"alias_kind":"pith_short_12","alias_value":"PGG2OXKEO4F6","created_at":"2026-05-18T12:31:37Z"},{"alias_kind":"pith_short_16","alias_value":"PGG2OXKEO4F6DRLW","created_at":"2026-05-18T12:31:37Z"},{"alias_kind":"pith_short_8","alias_value":"PGG2OXKE","created_at":"2026-05-18T12:31:37Z"}],"graph_snapshots":[{"event_id":"sha256:8bf62806deaf4e0db2d3cd10f0fd17c5610c29561abb840c972fd0d8c5d820fa","target":"graph","created_at":"2026-05-18T00:24:59Z","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":"Let $M$ be either an $F$-finite $F$-module over a noetherian regular ring of characteristic $p > 0$ or a holonomic $D$-module over a formal power series ring over a field of characteristic zero. We prove that $\\injdim_R M$ enjoys a dichotomy property: it has only two possible values, $\\dim \\Supp_R M - 1$ or $\\dim \\Supp_R M$.","authors_text":"Nicholas Switala, Wenliang Zhang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2017-08-22T02:28:03Z","title":"A dichotomy for the injective dimension of $F$-finite $F$-modules and holonomic $D$-modules"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.06481","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":"sha256:4ff24dfb01ed047da67fe2ffc9e407ddfd36f1a24459ef74a323186de6efc192","target":"record","created_at":"2026-05-18T00:24:59Z","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":"2e9a70ffef31413baa657b2b197b6f7a4b09f88a19e0c782e5e097da97af1896","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2017-08-22T02:28:03Z","title_canon_sha256":"d5cc43566951878dc07dd7340ae3e521fae97f0e80a4b84a1cc5fe0bbbf994ca"},"schema_version":"1.0","source":{"id":"1708.06481","kind":"arxiv","version":2}},"canonical_sha256":"798da75d44770be1c576fdec7f9b6d91c1a9dcc1cb0d3efb13ccbd3fe70bccd4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"798da75d44770be1c576fdec7f9b6d91c1a9dcc1cb0d3efb13ccbd3fe70bccd4","first_computed_at":"2026-05-18T00:24:59.728267Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:24:59.728267Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"lG8n47K6V47SOr4XAj/NwRL/3O7B/8rSv5GH/hYRNi78ptQTAW3OyT3YkZZD77cGNz85uG+f65RDeNKdeBbIDA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:24:59.728727Z","signed_message":"canonical_sha256_bytes"},"source_id":"1708.06481","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4ff24dfb01ed047da67fe2ffc9e407ddfd36f1a24459ef74a323186de6efc192","sha256:8bf62806deaf4e0db2d3cd10f0fd17c5610c29561abb840c972fd0d8c5d820fa"],"state_sha256":"3a509eb2af6028cb86ea184de30bae5f10cc992f6e8bb7aac45a3e967da0280e"}