{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:MKCFZ54XH2443C74ID64UTKXYF","short_pith_number":"pith:MKCFZ54X","canonical_record":{"source":{"id":"1601.00241","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2016-01-03T02:10:28Z","cross_cats_sorted":["math.DG"],"title_canon_sha256":"7faffe438f613d9de7797efe16db460e299edbab790d129e364bd6e55dd01e25","abstract_canon_sha256":"823b575db5e3df345d91cb0630a897c52c4b8f258671071e22ccac37d9d7cad3"},"schema_version":"1.0"},"canonical_sha256":"62845cf7973eb9cd8bfc40fdca4d57c17c5fc6bfbbd324084bc83358111e9db3","source":{"kind":"arxiv","id":"1601.00241","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1601.00241","created_at":"2026-05-18T00:19:42Z"},{"alias_kind":"arxiv_version","alias_value":"1601.00241v2","created_at":"2026-05-18T00:19:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1601.00241","created_at":"2026-05-18T00:19:42Z"},{"alias_kind":"pith_short_12","alias_value":"MKCFZ54XH244","created_at":"2026-05-18T12:30:32Z"},{"alias_kind":"pith_short_16","alias_value":"MKCFZ54XH2443C74","created_at":"2026-05-18T12:30:32Z"},{"alias_kind":"pith_short_8","alias_value":"MKCFZ54X","created_at":"2026-05-18T12:30:32Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:MKCFZ54XH2443C74ID64UTKXYF","target":"record","payload":{"canonical_record":{"source":{"id":"1601.00241","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2016-01-03T02:10:28Z","cross_cats_sorted":["math.DG"],"title_canon_sha256":"7faffe438f613d9de7797efe16db460e299edbab790d129e364bd6e55dd01e25","abstract_canon_sha256":"823b575db5e3df345d91cb0630a897c52c4b8f258671071e22ccac37d9d7cad3"},"schema_version":"1.0"},"canonical_sha256":"62845cf7973eb9cd8bfc40fdca4d57c17c5fc6bfbbd324084bc83358111e9db3","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:19:42.903533Z","signature_b64":"nh/5IMJL109JSmLTSE48hl+ArdfBgqJhy91+kNJFdYVmeMDVFntAp/f8n72YU/48S3LxRRBk5lDnUGQ+JR+yDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"62845cf7973eb9cd8bfc40fdca4d57c17c5fc6bfbbd324084bc83358111e9db3","last_reissued_at":"2026-05-18T00:19:42.902900Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:19:42.902900Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1601.00241","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:19:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6dGEFzfR1ePFglzJeFIjSXqiPUJVUX/GoOpyfejcm6qdt4l6thVcJUgJ6aH0EhTGKmLF/sd2a1Uy+FAwR8r/AA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T15:33:50.467746Z"},"content_sha256":"a567c4a676012c7bb04feca41c8e05c4d7783abd48eb613c0023696fa10b2fca","schema_version":"1.0","event_id":"sha256:a567c4a676012c7bb04feca41c8e05c4d7783abd48eb613c0023696fa10b2fca"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:MKCFZ54XH2443C74ID64UTKXYF","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the first order asymptotics of partial Bergman kernels","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.CV","authors_text":"Dan Coman, George Marinescu","submitted_at":"2016-01-03T02:10:28Z","abstract_excerpt":"We show that under very general assumptions the partial Bergman kernel function of sections vanishing along an analytic hypersurface has exponential decay in a neighborhood of the vanishing locus. Considering an ample line bundle, we obtain a uniform estimate of the Bergman kernel function associated to a singular metric along the hypersurface. Finally, we study the asymptotics of the partial Bergman kernel function on a given compact set and near the vanishing locus."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.00241","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:19:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EFIo9MkEUKCG6S30wUYa1heR0OhPhuz5Jz01hE3GIf4fP+VH/lTeaHBctTeS4vJUFr4YenkmFnN53KM3R2/iCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T15:33:50.468091Z"},"content_sha256":"bc4285ae10d4f4eefb7016e21d4e434b180b691eff95ae5566f12b8eed78f4a1","schema_version":"1.0","event_id":"sha256:bc4285ae10d4f4eefb7016e21d4e434b180b691eff95ae5566f12b8eed78f4a1"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MKCFZ54XH2443C74ID64UTKXYF/bundle.json","state_url":"https://pith.science/pith/MKCFZ54XH2443C74ID64UTKXYF/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MKCFZ54XH2443C74ID64UTKXYF/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-04T15:33:50Z","links":{"resolver":"https://pith.science/pith/MKCFZ54XH2443C74ID64UTKXYF","bundle":"https://pith.science/pith/MKCFZ54XH2443C74ID64UTKXYF/bundle.json","state":"https://pith.science/pith/MKCFZ54XH2443C74ID64UTKXYF/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MKCFZ54XH2443C74ID64UTKXYF/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:MKCFZ54XH2443C74ID64UTKXYF","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":"823b575db5e3df345d91cb0630a897c52c4b8f258671071e22ccac37d9d7cad3","cross_cats_sorted":["math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2016-01-03T02:10:28Z","title_canon_sha256":"7faffe438f613d9de7797efe16db460e299edbab790d129e364bd6e55dd01e25"},"schema_version":"1.0","source":{"id":"1601.00241","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1601.00241","created_at":"2026-05-18T00:19:42Z"},{"alias_kind":"arxiv_version","alias_value":"1601.00241v2","created_at":"2026-05-18T00:19:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1601.00241","created_at":"2026-05-18T00:19:42Z"},{"alias_kind":"pith_short_12","alias_value":"MKCFZ54XH244","created_at":"2026-05-18T12:30:32Z"},{"alias_kind":"pith_short_16","alias_value":"MKCFZ54XH2443C74","created_at":"2026-05-18T12:30:32Z"},{"alias_kind":"pith_short_8","alias_value":"MKCFZ54X","created_at":"2026-05-18T12:30:32Z"}],"graph_snapshots":[{"event_id":"sha256:bc4285ae10d4f4eefb7016e21d4e434b180b691eff95ae5566f12b8eed78f4a1","target":"graph","created_at":"2026-05-18T00:19:42Z","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 show that under very general assumptions the partial Bergman kernel function of sections vanishing along an analytic hypersurface has exponential decay in a neighborhood of the vanishing locus. Considering an ample line bundle, we obtain a uniform estimate of the Bergman kernel function associated to a singular metric along the hypersurface. Finally, we study the asymptotics of the partial Bergman kernel function on a given compact set and near the vanishing locus.","authors_text":"Dan Coman, George Marinescu","cross_cats":["math.DG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2016-01-03T02:10:28Z","title":"On the first order asymptotics of partial Bergman kernels"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.00241","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:a567c4a676012c7bb04feca41c8e05c4d7783abd48eb613c0023696fa10b2fca","target":"record","created_at":"2026-05-18T00:19:42Z","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":"823b575db5e3df345d91cb0630a897c52c4b8f258671071e22ccac37d9d7cad3","cross_cats_sorted":["math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2016-01-03T02:10:28Z","title_canon_sha256":"7faffe438f613d9de7797efe16db460e299edbab790d129e364bd6e55dd01e25"},"schema_version":"1.0","source":{"id":"1601.00241","kind":"arxiv","version":2}},"canonical_sha256":"62845cf7973eb9cd8bfc40fdca4d57c17c5fc6bfbbd324084bc83358111e9db3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"62845cf7973eb9cd8bfc40fdca4d57c17c5fc6bfbbd324084bc83358111e9db3","first_computed_at":"2026-05-18T00:19:42.902900Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:19:42.902900Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"nh/5IMJL109JSmLTSE48hl+ArdfBgqJhy91+kNJFdYVmeMDVFntAp/f8n72YU/48S3LxRRBk5lDnUGQ+JR+yDA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:19:42.903533Z","signed_message":"canonical_sha256_bytes"},"source_id":"1601.00241","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a567c4a676012c7bb04feca41c8e05c4d7783abd48eb613c0023696fa10b2fca","sha256:bc4285ae10d4f4eefb7016e21d4e434b180b691eff95ae5566f12b8eed78f4a1"],"state_sha256":"84211107ea14f5c99000d3b176cc1ba1098612871a48fdc510924ea8a71ee562"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Q5DDBKq0Tt4mBtrICvgIr/MLBJKTVRowrEbwCKck0BaIs5qx9dm5nzJ8WAz1xLw1B/AzC9KsttKpGe/bGAVnCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T15:33:50.470051Z","bundle_sha256":"97f04e76bbcf550b73c94ece491f91145ed899dbb9367d27beee31031f47c24c"}}