{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:7S2JPURMQRCWQRYKEPF54JEZHG","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":"e6f745e4dde997dd106ea0108f19be9827a70fdced5b5d774ae8b696da7a2947","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2015-06-03T07:22:01Z","title_canon_sha256":"3780c701554e089a7346ceeb53b7984fdfa402f3b63409dc62753ea1836174bf"},"schema_version":"1.0","source":{"id":"1506.01146","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1506.01146","created_at":"2026-05-18T01:24:14Z"},{"alias_kind":"arxiv_version","alias_value":"1506.01146v2","created_at":"2026-05-18T01:24:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.01146","created_at":"2026-05-18T01:24:14Z"},{"alias_kind":"pith_short_12","alias_value":"7S2JPURMQRCW","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_16","alias_value":"7S2JPURMQRCWQRYK","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_8","alias_value":"7S2JPURM","created_at":"2026-05-18T12:29:10Z"}],"graph_snapshots":[{"event_id":"sha256:ca60e7724aed13dff1fd551f5feb21e084d8e8ad32455b7e8909dd0cf8a5c703","target":"graph","created_at":"2026-05-18T01:24:14Z","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":"Let $\\{\\Omega_t:-1<t<1\\}$ be a family of bounded pseudoconvex domains and $\\varphi_t\\in PSH(\\Omega_t)$. Let $K_t(z,w)$ denote the Bergman kernel with weight $\\varphi_t$ on $\\Omega_t$. We study the continuity and H\\\"older continuity of $K_t(z,w)$ in $t$. Several applications to singularity theory of psh functions are given, including a new proof of the openness theorem.","authors_text":"Bo-Yong Chen","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2015-06-03T07:22:01Z","title":"Parameter dependence of the Bergman kernels"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.01146","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:dbeaec38881d683e39ca6de52661e3222bd55543c2aa8b23be71438596534983","target":"record","created_at":"2026-05-18T01:24:14Z","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":"e6f745e4dde997dd106ea0108f19be9827a70fdced5b5d774ae8b696da7a2947","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2015-06-03T07:22:01Z","title_canon_sha256":"3780c701554e089a7346ceeb53b7984fdfa402f3b63409dc62753ea1836174bf"},"schema_version":"1.0","source":{"id":"1506.01146","kind":"arxiv","version":2}},"canonical_sha256":"fcb497d22c844568470a23cbde249939a7c8cc54da528dbaf8b7f24c97e42b50","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fcb497d22c844568470a23cbde249939a7c8cc54da528dbaf8b7f24c97e42b50","first_computed_at":"2026-05-18T01:24:14.453580Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:24:14.453580Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"sSX6KlHFGpKNDEjeFPdxurzHiK0UWb0/Jbl8zLUscRRUdSIMPenRT/ZDpoy3kGh+dz1/by/MLPYyIgaS+Ep6Bw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:24:14.454088Z","signed_message":"canonical_sha256_bytes"},"source_id":"1506.01146","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:dbeaec38881d683e39ca6de52661e3222bd55543c2aa8b23be71438596534983","sha256:ca60e7724aed13dff1fd551f5feb21e084d8e8ad32455b7e8909dd0cf8a5c703"],"state_sha256":"0b8cf6943555f757d00bebb4b5e9b3ac8584ae3bab3a59f1193c4aa0fc374807"}