{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:3NDTRJX6KYLIPIPQQB2LIA4BJB","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":"aeb83d4de462c50598f713665990d4cd022a34f6d39e5e4872ab6b33682dab0d","cross_cats_sorted":["math.CV"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2018-11-11T10:18:18Z","title_canon_sha256":"6726a8512e37a00321279ae2e793618539ca6919ab151cc37e929d6f6101af06"},"schema_version":"1.0","source":{"id":"1811.04385","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1811.04385","created_at":"2026-05-18T00:01:05Z"},{"alias_kind":"arxiv_version","alias_value":"1811.04385v1","created_at":"2026-05-18T00:01:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1811.04385","created_at":"2026-05-18T00:01:05Z"},{"alias_kind":"pith_short_12","alias_value":"3NDTRJX6KYLI","created_at":"2026-05-18T12:32:02Z"},{"alias_kind":"pith_short_16","alias_value":"3NDTRJX6KYLIPIPQ","created_at":"2026-05-18T12:32:02Z"},{"alias_kind":"pith_short_8","alias_value":"3NDTRJX6","created_at":"2026-05-18T12:32:02Z"}],"graph_snapshots":[{"event_id":"sha256:6ee05ac61030a5a299e8ae2acd9668035879da77517d6b4bcecc4a944eeee493","target":"graph","created_at":"2026-05-18T00:01:05Z","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 purpose of this paper is to give two supplements for vanishing theorems: One is a relative version of the Kawamata-Viehweg-Nadel type vanishing theorem, which is obtained from an observation for the variation of the numerical dimension of singular hermitian line bundles. The other is an analytic injectivity theorem for log canonical pairs on surfaces, which can be seen as a partial answer for Fujino's conjecture.","authors_text":"Shin-ichi Matsumura","cross_cats":["math.CV"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2018-11-11T10:18:18Z","title":"Variation of numerical dimension of singular hermitian line bundles"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.04385","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":"sha256:19a44910493e5ddc2a059c8e4109eb43a8e2827d9c50b552503e84ef7cfab052","target":"record","created_at":"2026-05-18T00:01:05Z","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":"aeb83d4de462c50598f713665990d4cd022a34f6d39e5e4872ab6b33682dab0d","cross_cats_sorted":["math.CV"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2018-11-11T10:18:18Z","title_canon_sha256":"6726a8512e37a00321279ae2e793618539ca6919ab151cc37e929d6f6101af06"},"schema_version":"1.0","source":{"id":"1811.04385","kind":"arxiv","version":1}},"canonical_sha256":"db4738a6fe561687a1f08074b40381485c86ddeaa605da7e881dc3d20cbc07a6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"db4738a6fe561687a1f08074b40381485c86ddeaa605da7e881dc3d20cbc07a6","first_computed_at":"2026-05-18T00:01:05.318980Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:01:05.318980Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"TvychNsiKA7xltFThCMZg9q+J6o86fSogZrQQLu1fqVlproCB4rEo27i8Euuatp56ddeeCu6f1MckPt9B6G6Cw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:01:05.319652Z","signed_message":"canonical_sha256_bytes"},"source_id":"1811.04385","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:19a44910493e5ddc2a059c8e4109eb43a8e2827d9c50b552503e84ef7cfab052","sha256:6ee05ac61030a5a299e8ae2acd9668035879da77517d6b4bcecc4a944eeee493"],"state_sha256":"e3703c4f689cccf33413699006c6f738c530f4ab249727d9a02a8d066a66c6eb"}