{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:C3747R6YYT7KAQC35UVK4XJZAE","short_pith_number":"pith:C3747R6Y","canonical_record":{"source":{"id":"1807.00204","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2018-06-30T16:53:08Z","cross_cats_sorted":["math.AP","math.DG"],"title_canon_sha256":"813f02356650872a41755b8f0331438aef79e64ef084639a6b83f7a9648e8328","abstract_canon_sha256":"1c0b9ce0029f96bd50dcadc8a306c165ac00df88bdca968b22e16114defa88c6"},"schema_version":"1.0"},"canonical_sha256":"16ffcfc7d8c4fea0405bed2aae5d39011473504688f41e54439b9c58bc3695a9","source":{"kind":"arxiv","id":"1807.00204","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1807.00204","created_at":"2026-05-18T00:11:55Z"},{"alias_kind":"arxiv_version","alias_value":"1807.00204v1","created_at":"2026-05-18T00:11:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1807.00204","created_at":"2026-05-18T00:11:55Z"},{"alias_kind":"pith_short_12","alias_value":"C3747R6YYT7K","created_at":"2026-05-18T12:32:16Z"},{"alias_kind":"pith_short_16","alias_value":"C3747R6YYT7KAQC3","created_at":"2026-05-18T12:32:16Z"},{"alias_kind":"pith_short_8","alias_value":"C3747R6Y","created_at":"2026-05-18T12:32:16Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:C3747R6YYT7KAQC35UVK4XJZAE","target":"record","payload":{"canonical_record":{"source":{"id":"1807.00204","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2018-06-30T16:53:08Z","cross_cats_sorted":["math.AP","math.DG"],"title_canon_sha256":"813f02356650872a41755b8f0331438aef79e64ef084639a6b83f7a9648e8328","abstract_canon_sha256":"1c0b9ce0029f96bd50dcadc8a306c165ac00df88bdca968b22e16114defa88c6"},"schema_version":"1.0"},"canonical_sha256":"16ffcfc7d8c4fea0405bed2aae5d39011473504688f41e54439b9c58bc3695a9","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:11:55.698526Z","signature_b64":"ciAKO+zneqqa4agMU2oIUeo4F6o9AIYzRVf1C7ehwW/P1lRhxRaFNNaGu/uRqXYvWkqY40L8A/gEMl3iwJBmDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"16ffcfc7d8c4fea0405bed2aae5d39011473504688f41e54439b9c58bc3695a9","last_reissued_at":"2026-05-18T00:11:55.697811Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:11:55.697811Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1807.00204","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:11:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LaqBFtTfpn8I4DnBUXkAJ8q7FNCMOiA5lKUiHAfmlApw5z5n2YSdPgJox+bhlXtCGPFNBpQXqVFvvpbrVlKQAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T02:07:27.757669Z"},"content_sha256":"a34f171130cb438bf222fdc361e9e6fa19861ee0dccad4b1876946945de794cd","schema_version":"1.0","event_id":"sha256:a34f171130cb438bf222fdc361e9e6fa19861ee0dccad4b1876946945de794cd"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:C3747R6YYT7KAQC35UVK4XJZAE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Quantitative upper bounds for Bergman kernels associated to smooth K\\\"ahler potentials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.DG"],"primary_cat":"math.CV","authors_text":"Hamid Hezari, Hang Xu","submitted_at":"2018-06-30T16:53:08Z","abstract_excerpt":"We give upper bounds for the Bergman kernels associated to tensor powers of a smooth positive line bundle in terms of the rate of growth of the Taylor coefficients of the K\\\"ahler potential. As applications, we obtain improved off-diagonal rate of decay for the classes of analytic, quasi-analytic, and more generally Gevrey potentials."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.00204","kind":"arxiv","version":1},"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":"2026-05-18T00:11:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nGt6oAtjXCTj2VG62imC2Y7LtEURJ/6Tc1IzDnZIhEQhqKF2ouiYT/fGqGYcGzcgHnIjfX6Tit9dn37qRYs+Ag==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T02:07:27.758389Z"},"content_sha256":"6e9f14928e501c3e4c59b5077cf0d0c8371dca70ae53066c3bb5a3a69ebc6b8a","schema_version":"1.0","event_id":"sha256:6e9f14928e501c3e4c59b5077cf0d0c8371dca70ae53066c3bb5a3a69ebc6b8a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/C3747R6YYT7KAQC35UVK4XJZAE/bundle.json","state_url":"https://pith.science/pith/C3747R6YYT7KAQC35UVK4XJZAE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/C3747R6YYT7KAQC35UVK4XJZAE/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":"2026-06-11T02:07:27Z","links":{"resolver":"https://pith.science/pith/C3747R6YYT7KAQC35UVK4XJZAE","bundle":"https://pith.science/pith/C3747R6YYT7KAQC35UVK4XJZAE/bundle.json","state":"https://pith.science/pith/C3747R6YYT7KAQC35UVK4XJZAE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/C3747R6YYT7KAQC35UVK4XJZAE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:C3747R6YYT7KAQC35UVK4XJZAE","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":"1c0b9ce0029f96bd50dcadc8a306c165ac00df88bdca968b22e16114defa88c6","cross_cats_sorted":["math.AP","math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2018-06-30T16:53:08Z","title_canon_sha256":"813f02356650872a41755b8f0331438aef79e64ef084639a6b83f7a9648e8328"},"schema_version":"1.0","source":{"id":"1807.00204","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1807.00204","created_at":"2026-05-18T00:11:55Z"},{"alias_kind":"arxiv_version","alias_value":"1807.00204v1","created_at":"2026-05-18T00:11:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1807.00204","created_at":"2026-05-18T00:11:55Z"},{"alias_kind":"pith_short_12","alias_value":"C3747R6YYT7K","created_at":"2026-05-18T12:32:16Z"},{"alias_kind":"pith_short_16","alias_value":"C3747R6YYT7KAQC3","created_at":"2026-05-18T12:32:16Z"},{"alias_kind":"pith_short_8","alias_value":"C3747R6Y","created_at":"2026-05-18T12:32:16Z"}],"graph_snapshots":[{"event_id":"sha256:6e9f14928e501c3e4c59b5077cf0d0c8371dca70ae53066c3bb5a3a69ebc6b8a","target":"graph","created_at":"2026-05-18T00:11:55Z","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 give upper bounds for the Bergman kernels associated to tensor powers of a smooth positive line bundle in terms of the rate of growth of the Taylor coefficients of the K\\\"ahler potential. As applications, we obtain improved off-diagonal rate of decay for the classes of analytic, quasi-analytic, and more generally Gevrey potentials.","authors_text":"Hamid Hezari, Hang Xu","cross_cats":["math.AP","math.DG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2018-06-30T16:53:08Z","title":"Quantitative upper bounds for Bergman kernels associated to smooth K\\\"ahler potentials"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.00204","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:a34f171130cb438bf222fdc361e9e6fa19861ee0dccad4b1876946945de794cd","target":"record","created_at":"2026-05-18T00:11:55Z","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":"1c0b9ce0029f96bd50dcadc8a306c165ac00df88bdca968b22e16114defa88c6","cross_cats_sorted":["math.AP","math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2018-06-30T16:53:08Z","title_canon_sha256":"813f02356650872a41755b8f0331438aef79e64ef084639a6b83f7a9648e8328"},"schema_version":"1.0","source":{"id":"1807.00204","kind":"arxiv","version":1}},"canonical_sha256":"16ffcfc7d8c4fea0405bed2aae5d39011473504688f41e54439b9c58bc3695a9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"16ffcfc7d8c4fea0405bed2aae5d39011473504688f41e54439b9c58bc3695a9","first_computed_at":"2026-05-18T00:11:55.697811Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:11:55.697811Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ciAKO+zneqqa4agMU2oIUeo4F6o9AIYzRVf1C7ehwW/P1lRhxRaFNNaGu/uRqXYvWkqY40L8A/gEMl3iwJBmDw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:11:55.698526Z","signed_message":"canonical_sha256_bytes"},"source_id":"1807.00204","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a34f171130cb438bf222fdc361e9e6fa19861ee0dccad4b1876946945de794cd","sha256:6e9f14928e501c3e4c59b5077cf0d0c8371dca70ae53066c3bb5a3a69ebc6b8a"],"state_sha256":"9e456ffe3136db94dfadeb915dbd94983e12cc4164c0e1640ce1b861e4c6ca1f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"O5AevaX+CGnAMwNt1Fl+CkC7BUpLL2OhkgwVmGXj5fquJJUNwdkZmbGc0mYRo3mhdWJUDXSvLIVFlmx6f8OoBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T02:07:27.762131Z","bundle_sha256":"7dbe9d6415d1805e127b277d6838b3402b1a430ed234ed2b41738d77b3535b0d"}}