{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:TY7QM4RJP6TDDIUBDYKSLBJMLR","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":"ab9c65598012a6b381fbb65c18b6d6e35c8be3074f5f1c2ab9b0ee081c450961","cross_cats_sorted":["math.CV"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2018-06-28T09:36:52Z","title_canon_sha256":"f6f12b1b6737319c9808d7987776c0eb4ab621385e1dbadc2b8579a938b562bd"},"schema_version":"1.0","source":{"id":"1806.10847","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1806.10847","created_at":"2026-05-18T00:12:02Z"},{"alias_kind":"arxiv_version","alias_value":"1806.10847v1","created_at":"2026-05-18T00:12:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.10847","created_at":"2026-05-18T00:12:02Z"},{"alias_kind":"pith_short_12","alias_value":"TY7QM4RJP6TD","created_at":"2026-05-18T12:32:56Z"},{"alias_kind":"pith_short_16","alias_value":"TY7QM4RJP6TDDIUB","created_at":"2026-05-18T12:32:56Z"},{"alias_kind":"pith_short_8","alias_value":"TY7QM4RJ","created_at":"2026-05-18T12:32:56Z"}],"graph_snapshots":[{"event_id":"sha256:8253685a0b470bf037d7235d984a320169ad2e2fa1cdae99d00bd18ac479eeee","target":"graph","created_at":"2026-05-18T00:12:02Z","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 provide detailed holomorphic Morse estimates for the cohomology of sheaves of jet differentials and their dual sheaves. These estimates apply on arbitrary directed varieties, and a special attention has been given to the analysis of the singular situation. As a consequence, we obtain existence results for global jet differentials and global differential operators under positivity conditions for the canonical or anticanonical sheaf of the directedstructure.","authors_text":"Jean-Pierre Demailly (IF), Mohammad Reza Rahmati (IAG)","cross_cats":["math.CV"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2018-06-28T09:36:52Z","title":"Morse cohomology estimates for jet differential operators"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.10847","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":"sha256:274189a6938033b4c66fb8e4dbc1a4c27cc4c0b2fc709fb02d39d953be2fc0dd","target":"record","created_at":"2026-05-18T00:12:02Z","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":"ab9c65598012a6b381fbb65c18b6d6e35c8be3074f5f1c2ab9b0ee081c450961","cross_cats_sorted":["math.CV"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2018-06-28T09:36:52Z","title_canon_sha256":"f6f12b1b6737319c9808d7987776c0eb4ab621385e1dbadc2b8579a938b562bd"},"schema_version":"1.0","source":{"id":"1806.10847","kind":"arxiv","version":1}},"canonical_sha256":"9e3f0672297fa631a2811e1525852c5c5c3b8567a0849822a8023adafdfb2f65","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9e3f0672297fa631a2811e1525852c5c5c3b8567a0849822a8023adafdfb2f65","first_computed_at":"2026-05-18T00:12:02.138782Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:12:02.138782Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"m1C0pIaqJW9Zasqvn7dIB7p1xQa6L7Eg+GU5Hv6u1UXHYZodQmnPnq/VtmhFhIowk37ep2OfuyF1kQRQFYwEDA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:12:02.139449Z","signed_message":"canonical_sha256_bytes"},"source_id":"1806.10847","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:274189a6938033b4c66fb8e4dbc1a4c27cc4c0b2fc709fb02d39d953be2fc0dd","sha256:8253685a0b470bf037d7235d984a320169ad2e2fa1cdae99d00bd18ac479eeee"],"state_sha256":"c698ffd510ff1f1e23fa0431c45dd2ca102acd190ac3f49ac2a1334384780a4e"}