{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:RU6PWCKDLLYJX343Q75Y7UJ5UX","short_pith_number":"pith:RU6PWCKD","canonical_record":{"source":{"id":"1507.01056","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2015-07-04T01:53:00Z","cross_cats_sorted":[],"title_canon_sha256":"a385df9bfc1b48fdd04044c211d96c68df4eea447860337eb600c5dbc16ccd5c","abstract_canon_sha256":"a8073a95593b7f3d4070432d2b108454fe70ca22ec3fdf9cb96f7c1b119ae2b2"},"schema_version":"1.0"},"canonical_sha256":"8d3cfb09435af09bef9b87fb8fd13da5f20cfe294792393e8dfabc788fa250e3","source":{"kind":"arxiv","id":"1507.01056","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1507.01056","created_at":"2026-05-18T01:37:18Z"},{"alias_kind":"arxiv_version","alias_value":"1507.01056v1","created_at":"2026-05-18T01:37:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.01056","created_at":"2026-05-18T01:37:18Z"},{"alias_kind":"pith_short_12","alias_value":"RU6PWCKDLLYJ","created_at":"2026-05-18T12:29:39Z"},{"alias_kind":"pith_short_16","alias_value":"RU6PWCKDLLYJX343","created_at":"2026-05-18T12:29:39Z"},{"alias_kind":"pith_short_8","alias_value":"RU6PWCKD","created_at":"2026-05-18T12:29:39Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:RU6PWCKDLLYJX343Q75Y7UJ5UX","target":"record","payload":{"canonical_record":{"source":{"id":"1507.01056","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2015-07-04T01:53:00Z","cross_cats_sorted":[],"title_canon_sha256":"a385df9bfc1b48fdd04044c211d96c68df4eea447860337eb600c5dbc16ccd5c","abstract_canon_sha256":"a8073a95593b7f3d4070432d2b108454fe70ca22ec3fdf9cb96f7c1b119ae2b2"},"schema_version":"1.0"},"canonical_sha256":"8d3cfb09435af09bef9b87fb8fd13da5f20cfe294792393e8dfabc788fa250e3","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:37:18.308101Z","signature_b64":"PwmBu5Qz9dWbAPq7s0Rs9R0+M1Ia+WCd+w1Yp38j3+9Iol6TlLtX1vF/q8BMO9R3kngPMM3KoCSoswJBWFVMBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8d3cfb09435af09bef9b87fb8fd13da5f20cfe294792393e8dfabc788fa250e3","last_reissued_at":"2026-05-18T01:37:18.307403Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:37:18.307403Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1507.01056","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":"2026-05-18T01:37:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"x+XfIbSD3q9UFwXJj4gsagqYfS4FiUfaM1r/cKN9xFYVPdE8xZ5TrZeudZ+IDhbroKZbLQGwyo1I2h9Q7e3HAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-03T06:50:29.162401Z"},"content_sha256":"8951889cbd8092f34a9679dac3c6afdf89797984c6cd67e20ec3fda0953c4d6e","schema_version":"1.0","event_id":"sha256:8951889cbd8092f34a9679dac3c6afdf89797984c6cd67e20ec3fda0953c4d6e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:RU6PWCKDLLYJX343Q75Y7UJ5UX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Convergence of Riemannian surfaces and convergence of the Bergman kernel","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Bo-Yong Chen","submitted_at":"2015-07-04T01:53:00Z","abstract_excerpt":"Let $\\{M_j\\}$ be a sequence of complete Riemannian surfaces which converges in the sense of Cheeger-Gromov to a complete Riemannian surface $M$. We study the convergence of the Bergman kernel $K_{M_j}$ of $M_j$ by using isoperimetric inequalities."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.01056","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":"2026-05-18T01:37:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2GRIBUo0h211RLJX4Sqy1IQ2H8Fov5vnzcs9LOchbe+9UREKolh2A2W3UhCp/1j1/vF5npNKfLcwFssW6NH6Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-03T06:50:29.162753Z"},"content_sha256":"eea101a8380998e1b1bd3fe66f19dcbc029ce1d908eb5d8b4c5d469b3dc9c670","schema_version":"1.0","event_id":"sha256:eea101a8380998e1b1bd3fe66f19dcbc029ce1d908eb5d8b4c5d469b3dc9c670"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/RU6PWCKDLLYJX343Q75Y7UJ5UX/bundle.json","state_url":"https://pith.science/pith/RU6PWCKDLLYJX343Q75Y7UJ5UX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/RU6PWCKDLLYJX343Q75Y7UJ5UX/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":"2026-07-03T06:50:29Z","links":{"resolver":"https://pith.science/pith/RU6PWCKDLLYJX343Q75Y7UJ5UX","bundle":"https://pith.science/pith/RU6PWCKDLLYJX343Q75Y7UJ5UX/bundle.json","state":"https://pith.science/pith/RU6PWCKDLLYJX343Q75Y7UJ5UX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/RU6PWCKDLLYJX343Q75Y7UJ5UX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:RU6PWCKDLLYJX343Q75Y7UJ5UX","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":"a8073a95593b7f3d4070432d2b108454fe70ca22ec3fdf9cb96f7c1b119ae2b2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2015-07-04T01:53:00Z","title_canon_sha256":"a385df9bfc1b48fdd04044c211d96c68df4eea447860337eb600c5dbc16ccd5c"},"schema_version":"1.0","source":{"id":"1507.01056","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1507.01056","created_at":"2026-05-18T01:37:18Z"},{"alias_kind":"arxiv_version","alias_value":"1507.01056v1","created_at":"2026-05-18T01:37:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.01056","created_at":"2026-05-18T01:37:18Z"},{"alias_kind":"pith_short_12","alias_value":"RU6PWCKDLLYJ","created_at":"2026-05-18T12:29:39Z"},{"alias_kind":"pith_short_16","alias_value":"RU6PWCKDLLYJX343","created_at":"2026-05-18T12:29:39Z"},{"alias_kind":"pith_short_8","alias_value":"RU6PWCKD","created_at":"2026-05-18T12:29:39Z"}],"graph_snapshots":[{"event_id":"sha256:eea101a8380998e1b1bd3fe66f19dcbc029ce1d908eb5d8b4c5d469b3dc9c670","target":"graph","created_at":"2026-05-18T01:37:18Z","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 $\\{M_j\\}$ be a sequence of complete Riemannian surfaces which converges in the sense of Cheeger-Gromov to a complete Riemannian surface $M$. We study the convergence of the Bergman kernel $K_{M_j}$ of $M_j$ by using isoperimetric inequalities.","authors_text":"Bo-Yong Chen","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2015-07-04T01:53:00Z","title":"Convergence of Riemannian surfaces and convergence of the Bergman kernel"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.01056","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":"sha256:8951889cbd8092f34a9679dac3c6afdf89797984c6cd67e20ec3fda0953c4d6e","target":"record","created_at":"2026-05-18T01:37:18Z","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":"a8073a95593b7f3d4070432d2b108454fe70ca22ec3fdf9cb96f7c1b119ae2b2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2015-07-04T01:53:00Z","title_canon_sha256":"a385df9bfc1b48fdd04044c211d96c68df4eea447860337eb600c5dbc16ccd5c"},"schema_version":"1.0","source":{"id":"1507.01056","kind":"arxiv","version":1}},"canonical_sha256":"8d3cfb09435af09bef9b87fb8fd13da5f20cfe294792393e8dfabc788fa250e3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8d3cfb09435af09bef9b87fb8fd13da5f20cfe294792393e8dfabc788fa250e3","first_computed_at":"2026-05-18T01:37:18.307403Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:37:18.307403Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"PwmBu5Qz9dWbAPq7s0Rs9R0+M1Ia+WCd+w1Yp38j3+9Iol6TlLtX1vF/q8BMO9R3kngPMM3KoCSoswJBWFVMBg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:37:18.308101Z","signed_message":"canonical_sha256_bytes"},"source_id":"1507.01056","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8951889cbd8092f34a9679dac3c6afdf89797984c6cd67e20ec3fda0953c4d6e","sha256:eea101a8380998e1b1bd3fe66f19dcbc029ce1d908eb5d8b4c5d469b3dc9c670"],"state_sha256":"9c9620db5bb4931cdeb2a605588134c93f3e3fecd902aee60e044d15da6d02bc"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2m7azgxqnVy4moo16EfcWy/Mf1ZouwGDooagRoiWTfOSmxQPUAJdJ4Po+Laq+gFg57I8kx+RRUn7vB6Fmvw7Dw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-03T06:50:29.164664Z","bundle_sha256":"d67b40e96840581178758dc24a3fb004fe6f61c6aacb2584ab922a2e26895552"}}