{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2022:U3XOUKBP3QFEXAKMRNNNCZZ73R","short_pith_number":"pith:U3XOUKBP","canonical_record":{"source":{"id":"2212.01561","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2022-12-03T07:23:54Z","cross_cats_sorted":[],"title_canon_sha256":"827ffded28c73f9144919f8d2cc85676270e0bf7674ea85203af304c6f8f7b74","abstract_canon_sha256":"4a85ddbecb7b43c5036291352f055d1e69282ca7577f5d40aa2920280bc7799f"},"schema_version":"1.0"},"canonical_sha256":"a6eeea282fdc0a4b814c8b5ad1673fdc7e6a51d52d0cddfbaf2ba0f3d3a34be9","source":{"kind":"arxiv","id":"2212.01561","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2212.01561","created_at":"2026-07-05T11:36:17Z"},{"alias_kind":"arxiv_version","alias_value":"2212.01561v2","created_at":"2026-07-05T11:36:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2212.01561","created_at":"2026-07-05T11:36:17Z"},{"alias_kind":"pith_short_12","alias_value":"U3XOUKBP3QFE","created_at":"2026-07-05T11:36:17Z"},{"alias_kind":"pith_short_16","alias_value":"U3XOUKBP3QFEXAKM","created_at":"2026-07-05T11:36:17Z"},{"alias_kind":"pith_short_8","alias_value":"U3XOUKBP","created_at":"2026-07-05T11:36:17Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2022:U3XOUKBP3QFEXAKMRNNNCZZ73R","target":"record","payload":{"canonical_record":{"source":{"id":"2212.01561","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2022-12-03T07:23:54Z","cross_cats_sorted":[],"title_canon_sha256":"827ffded28c73f9144919f8d2cc85676270e0bf7674ea85203af304c6f8f7b74","abstract_canon_sha256":"4a85ddbecb7b43c5036291352f055d1e69282ca7577f5d40aa2920280bc7799f"},"schema_version":"1.0"},"canonical_sha256":"a6eeea282fdc0a4b814c8b5ad1673fdc7e6a51d52d0cddfbaf2ba0f3d3a34be9","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:36:17.149566Z","signature_b64":"86oX1GFsOOUIsu4zhhY58CeiJpfh3Hld6EsLssioypwXNp0kljOnbJCC3+eW5Yz9a/mrZrrCf6obNdABPn5wCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a6eeea282fdc0a4b814c8b5ad1673fdc7e6a51d52d0cddfbaf2ba0f3d3a34be9","last_reissued_at":"2026-07-05T11:36:17.149111Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:36:17.149111Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2212.01561","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":"2026-07-05T11:36:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YCT5PLcRNYl2PNv9vJyrZnwVJyUOsDeMIw45ayYE1ymD3OJ6hZM2hPPIm27TWCqdMGGQa6JRzeWlGi9Y2GqiBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-11T08:24:55.624668Z"},"content_sha256":"fe472934386a0e2c5816a5ddd6acf409fcb62e9e2e2c4519753f81dff6d48f2a","schema_version":"1.0","event_id":"sha256:fe472934386a0e2c5816a5ddd6acf409fcb62e9e2e2c4519753f81dff6d48f2a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2022:U3XOUKBP3QFEXAKMRNNNCZZ73R","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A note on $\\xi-$Bergman kernels","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Qi'an Guan, Shijie Bao, Zheng Yuan","submitted_at":"2022-12-03T07:23:54Z","abstract_excerpt":"In the present note, we introduce the $\\xi-$complex singularity exponents, which come from the asymptotic property of $\\xi-$Bergman kernels on sub-level sets of plurisubharmonic functions; give some relations (including a closedness property) among $\\xi-$complex singularity exponents, complex singularity exponents, and jumping numbers; generalize some properties of complex singularity exponents (such as the restriction formula and subadditivity property) to $\\xi-$complex singularity exponents."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2212.01561","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2212.01561/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T11:36:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"d/nifrBx6QxqQG7dPrtrlmHj2oovxzLJ9E0MTZgcxYEbV8S2XL9gKV699Cs1szCOaR2YwyeF1Sk92X5IgIGFDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-11T08:24:55.625156Z"},"content_sha256":"b272cb0b26d61db85f6d1025e3ff3fa15d4e214604baf72a4c4113aa732a6b8e","schema_version":"1.0","event_id":"sha256:b272cb0b26d61db85f6d1025e3ff3fa15d4e214604baf72a4c4113aa732a6b8e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/U3XOUKBP3QFEXAKMRNNNCZZ73R/bundle.json","state_url":"https://pith.science/pith/U3XOUKBP3QFEXAKMRNNNCZZ73R/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/U3XOUKBP3QFEXAKMRNNNCZZ73R/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":"2026-08-11T08:24:55Z","links":{"resolver":"https://pith.science/pith/U3XOUKBP3QFEXAKMRNNNCZZ73R","bundle":"https://pith.science/pith/U3XOUKBP3QFEXAKMRNNNCZZ73R/bundle.json","state":"https://pith.science/pith/U3XOUKBP3QFEXAKMRNNNCZZ73R/state.json","well_known_bundle":"https://pith.science/.well-known/pith/U3XOUKBP3QFEXAKMRNNNCZZ73R/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:U3XOUKBP3QFEXAKMRNNNCZZ73R","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":"4a85ddbecb7b43c5036291352f055d1e69282ca7577f5d40aa2920280bc7799f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2022-12-03T07:23:54Z","title_canon_sha256":"827ffded28c73f9144919f8d2cc85676270e0bf7674ea85203af304c6f8f7b74"},"schema_version":"1.0","source":{"id":"2212.01561","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2212.01561","created_at":"2026-07-05T11:36:17Z"},{"alias_kind":"arxiv_version","alias_value":"2212.01561v2","created_at":"2026-07-05T11:36:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2212.01561","created_at":"2026-07-05T11:36:17Z"},{"alias_kind":"pith_short_12","alias_value":"U3XOUKBP3QFE","created_at":"2026-07-05T11:36:17Z"},{"alias_kind":"pith_short_16","alias_value":"U3XOUKBP3QFEXAKM","created_at":"2026-07-05T11:36:17Z"},{"alias_kind":"pith_short_8","alias_value":"U3XOUKBP","created_at":"2026-07-05T11:36:17Z"}],"graph_snapshots":[{"event_id":"sha256:b272cb0b26d61db85f6d1025e3ff3fa15d4e214604baf72a4c4113aa732a6b8e","target":"graph","created_at":"2026-07-05T11:36:17Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2212.01561/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In the present note, we introduce the $\\xi-$complex singularity exponents, which come from the asymptotic property of $\\xi-$Bergman kernels on sub-level sets of plurisubharmonic functions; give some relations (including a closedness property) among $\\xi-$complex singularity exponents, complex singularity exponents, and jumping numbers; generalize some properties of complex singularity exponents (such as the restriction formula and subadditivity property) to $\\xi-$complex singularity exponents.","authors_text":"Qi'an Guan, Shijie Bao, Zheng Yuan","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2022-12-03T07:23:54Z","title":"A note on $\\xi-$Bergman kernels"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2212.01561","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:fe472934386a0e2c5816a5ddd6acf409fcb62e9e2e2c4519753f81dff6d48f2a","target":"record","created_at":"2026-07-05T11:36:17Z","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":"4a85ddbecb7b43c5036291352f055d1e69282ca7577f5d40aa2920280bc7799f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2022-12-03T07:23:54Z","title_canon_sha256":"827ffded28c73f9144919f8d2cc85676270e0bf7674ea85203af304c6f8f7b74"},"schema_version":"1.0","source":{"id":"2212.01561","kind":"arxiv","version":2}},"canonical_sha256":"a6eeea282fdc0a4b814c8b5ad1673fdc7e6a51d52d0cddfbaf2ba0f3d3a34be9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a6eeea282fdc0a4b814c8b5ad1673fdc7e6a51d52d0cddfbaf2ba0f3d3a34be9","first_computed_at":"2026-07-05T11:36:17.149111Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:36:17.149111Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"86oX1GFsOOUIsu4zhhY58CeiJpfh3Hld6EsLssioypwXNp0kljOnbJCC3+eW5Yz9a/mrZrrCf6obNdABPn5wCA==","signature_status":"signed_v1","signed_at":"2026-07-05T11:36:17.149566Z","signed_message":"canonical_sha256_bytes"},"source_id":"2212.01561","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fe472934386a0e2c5816a5ddd6acf409fcb62e9e2e2c4519753f81dff6d48f2a","sha256:b272cb0b26d61db85f6d1025e3ff3fa15d4e214604baf72a4c4113aa732a6b8e"],"state_sha256":"f7ffeeb601ebe534f781fbc664d622df6e9876ef2d95f0dfefec20f05395fd36"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"y9PeHOdEXRhnsU6/7PU1Sg2rR7qI2Nf9ALqwqk+4YBCO/4eq8N9Q8oMj53/taBHz5Wv500DhcLRNfzzSksHPBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-11T08:24:55.629766Z","bundle_sha256":"49e75bbafa2af8e7461ca64939cc906a251d3983a41dd6b57bd6a8feec4d6838"}}