{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:KF2OQHEVYP6Z7HZ3SITR552BT7","short_pith_number":"pith:KF2OQHEV","canonical_record":{"source":{"id":"1407.0417","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2014-07-01T22:04:50Z","cross_cats_sorted":[],"title_canon_sha256":"79d46c69a720d9b4b932c323111879cf3bf23920c166e8d5c545ed0c293147c8","abstract_canon_sha256":"8086572a447326ae6a98b99ad752c3fd2fb764b4e324b5f1f5f768afc8e78310"},"schema_version":"1.0"},"canonical_sha256":"5174e81c95c3fd9f9f3b92271ef7419fe87506d2a21c0cba31d88e4ea25138e5","source":{"kind":"arxiv","id":"1407.0417","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1407.0417","created_at":"2026-05-18T00:32:21Z"},{"alias_kind":"arxiv_version","alias_value":"1407.0417v2","created_at":"2026-05-18T00:32:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.0417","created_at":"2026-05-18T00:32:21Z"},{"alias_kind":"pith_short_12","alias_value":"KF2OQHEVYP6Z","created_at":"2026-05-18T12:28:35Z"},{"alias_kind":"pith_short_16","alias_value":"KF2OQHEVYP6Z7HZ3","created_at":"2026-05-18T12:28:35Z"},{"alias_kind":"pith_short_8","alias_value":"KF2OQHEV","created_at":"2026-05-18T12:28:35Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:KF2OQHEVYP6Z7HZ3SITR552BT7","target":"record","payload":{"canonical_record":{"source":{"id":"1407.0417","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2014-07-01T22:04:50Z","cross_cats_sorted":[],"title_canon_sha256":"79d46c69a720d9b4b932c323111879cf3bf23920c166e8d5c545ed0c293147c8","abstract_canon_sha256":"8086572a447326ae6a98b99ad752c3fd2fb764b4e324b5f1f5f768afc8e78310"},"schema_version":"1.0"},"canonical_sha256":"5174e81c95c3fd9f9f3b92271ef7419fe87506d2a21c0cba31d88e4ea25138e5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:32:21.905940Z","signature_b64":"1zX8giG0Ar0wY6uFVe6N3X2CoWHGU392K3CunbqSi5OlapWJ7MV9HSaihsClnR9wHRpp6wC4zUarEmtJI8ZXDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5174e81c95c3fd9f9f3b92271ef7419fe87506d2a21c0cba31d88e4ea25138e5","last_reissued_at":"2026-05-18T00:32:21.905411Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:32:21.905411Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1407.0417","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":"2026-05-18T00:32:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"aKutMvwKPt4r/F4J0/D8fH8fk16OptTES1Tmvsv9mXeOXK1B5zeBFybvx3eiuhfX55wqldmrCxQW2xmts2+IAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T23:44:24.714418Z"},"content_sha256":"8c0dfab01191710b1f54721f36cdf017f2f5df7093bdf84df0d6b99094054804","schema_version":"1.0","event_id":"sha256:8c0dfab01191710b1f54721f36cdf017f2f5df7093bdf84df0d6b99094054804"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:KF2OQHEVYP6Z7HZ3SITR552BT7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Convergence of multipole Green functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Nguyen Quand Dieu, Pascal J. Thomas","submitted_at":"2014-07-01T22:04:50Z","abstract_excerpt":"We continue the study of convergence of multipole pluricomplex Green functions for a bounded hyperconvex domain of $\\mathbb C^n$, in the case where poles collide. We consider the case where all poles do not converge to the same point in the domain, and some of them might go to the boundary of the domain. We prove that weak convergence will imply convergence in capacity; that it implies convergence uniformly on compacta away from the poles when no poles tend to the boundary; and that the study can be reduced, in a sense, to the case where poles tend to a single point. Furthermore, we prove that"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.0417","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":"2026-05-18T00:32:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WT07bWHknrTtWEUeHHgwOEqwT1TtY1uVs+XuHJVS74NGP6642uUNeCsGGvNEWO7XShsjXLW4pk0NOOTXIgYbCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T23:44:24.714768Z"},"content_sha256":"87cac65ceee15886897500c090279e3b7e5805a53c65cf25ca684807737e87c0","schema_version":"1.0","event_id":"sha256:87cac65ceee15886897500c090279e3b7e5805a53c65cf25ca684807737e87c0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KF2OQHEVYP6Z7HZ3SITR552BT7/bundle.json","state_url":"https://pith.science/pith/KF2OQHEVYP6Z7HZ3SITR552BT7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KF2OQHEVYP6Z7HZ3SITR552BT7/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":"2026-06-22T23:44:24Z","links":{"resolver":"https://pith.science/pith/KF2OQHEVYP6Z7HZ3SITR552BT7","bundle":"https://pith.science/pith/KF2OQHEVYP6Z7HZ3SITR552BT7/bundle.json","state":"https://pith.science/pith/KF2OQHEVYP6Z7HZ3SITR552BT7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KF2OQHEVYP6Z7HZ3SITR552BT7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:KF2OQHEVYP6Z7HZ3SITR552BT7","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":"8086572a447326ae6a98b99ad752c3fd2fb764b4e324b5f1f5f768afc8e78310","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2014-07-01T22:04:50Z","title_canon_sha256":"79d46c69a720d9b4b932c323111879cf3bf23920c166e8d5c545ed0c293147c8"},"schema_version":"1.0","source":{"id":"1407.0417","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1407.0417","created_at":"2026-05-18T00:32:21Z"},{"alias_kind":"arxiv_version","alias_value":"1407.0417v2","created_at":"2026-05-18T00:32:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.0417","created_at":"2026-05-18T00:32:21Z"},{"alias_kind":"pith_short_12","alias_value":"KF2OQHEVYP6Z","created_at":"2026-05-18T12:28:35Z"},{"alias_kind":"pith_short_16","alias_value":"KF2OQHEVYP6Z7HZ3","created_at":"2026-05-18T12:28:35Z"},{"alias_kind":"pith_short_8","alias_value":"KF2OQHEV","created_at":"2026-05-18T12:28:35Z"}],"graph_snapshots":[{"event_id":"sha256:87cac65ceee15886897500c090279e3b7e5805a53c65cf25ca684807737e87c0","target":"graph","created_at":"2026-05-18T00:32:21Z","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 continue the study of convergence of multipole pluricomplex Green functions for a bounded hyperconvex domain of $\\mathbb C^n$, in the case where poles collide. We consider the case where all poles do not converge to the same point in the domain, and some of them might go to the boundary of the domain. We prove that weak convergence will imply convergence in capacity; that it implies convergence uniformly on compacta away from the poles when no poles tend to the boundary; and that the study can be reduced, in a sense, to the case where poles tend to a single point. Furthermore, we prove that","authors_text":"Nguyen Quand Dieu, Pascal J. Thomas","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2014-07-01T22:04:50Z","title":"Convergence of multipole Green functions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.0417","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":"sha256:8c0dfab01191710b1f54721f36cdf017f2f5df7093bdf84df0d6b99094054804","target":"record","created_at":"2026-05-18T00:32:21Z","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":"8086572a447326ae6a98b99ad752c3fd2fb764b4e324b5f1f5f768afc8e78310","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2014-07-01T22:04:50Z","title_canon_sha256":"79d46c69a720d9b4b932c323111879cf3bf23920c166e8d5c545ed0c293147c8"},"schema_version":"1.0","source":{"id":"1407.0417","kind":"arxiv","version":2}},"canonical_sha256":"5174e81c95c3fd9f9f3b92271ef7419fe87506d2a21c0cba31d88e4ea25138e5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5174e81c95c3fd9f9f3b92271ef7419fe87506d2a21c0cba31d88e4ea25138e5","first_computed_at":"2026-05-18T00:32:21.905411Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:32:21.905411Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1zX8giG0Ar0wY6uFVe6N3X2CoWHGU392K3CunbqSi5OlapWJ7MV9HSaihsClnR9wHRpp6wC4zUarEmtJI8ZXDA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:32:21.905940Z","signed_message":"canonical_sha256_bytes"},"source_id":"1407.0417","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8c0dfab01191710b1f54721f36cdf017f2f5df7093bdf84df0d6b99094054804","sha256:87cac65ceee15886897500c090279e3b7e5805a53c65cf25ca684807737e87c0"],"state_sha256":"822a2d9bcff87fc16a1ed40d6b2ddd7b6da08ee5d7b37f9a227826884050f2f4"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Re4U32i9ioQqV7WWjToWgdevtQxLPxwdsEz5WNH8px/pa/mgxBfRHnsPbtkzhZKBAjj42sj8Hsul2zswEPgIBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-22T23:44:24.716642Z","bundle_sha256":"b4da2ff3802e8f3ef6697b12f64f0d9e43ea8112940d0d1d65ad80b25237a22b"}}