{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:DCXPCNOQMQJDBL2O324DA4R5PB","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":"3c8829713a10537eb60ae1715788ac751d86a361555796435ebda939b0fc6559","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2011-03-11T15:41:28Z","title_canon_sha256":"a478129638a94a54ca5538acd066ad177544196dd5c0c806b41b99e5b868363d"},"schema_version":"1.0","source":{"id":"1103.2296","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1103.2296","created_at":"2026-05-18T04:01:23Z"},{"alias_kind":"arxiv_version","alias_value":"1103.2296v2","created_at":"2026-05-18T04:01:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1103.2296","created_at":"2026-05-18T04:01:23Z"},{"alias_kind":"pith_short_12","alias_value":"DCXPCNOQMQJD","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_16","alias_value":"DCXPCNOQMQJDBL2O","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_8","alias_value":"DCXPCNOQ","created_at":"2026-05-18T12:26:26Z"}],"graph_snapshots":[{"event_id":"sha256:a9fdbcdeac84a4d6f9022158eab94490507497c889464e646ad8a5bb1ed24e87","target":"graph","created_at":"2026-05-18T04:01:23Z","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 $S_\\epsilon$ be a set of $N$ points in a bounded hyperconvex domain in $C^n$, all tending to 0 as$\\epsilon$ tends to 0. To each set $S_\\epsilon$ we associate its vanishing ideal $I_\\epsilon$ and the pluricomplex Green function $G_\\epsilon$ with poles on the set. Suppose that, as $\\epsilon$ tends to 0, the vanishing ideals converge to $I$ (local uniform convergence, or equivalently convergence in the Douady space), and that $G_\\epsilon$ converges to $G$, locally uniformly away from the origin; then the length (i.e. codimension) of $I$ is equal to $N$ and $G \\ge G_I$. If the Hilbert-Samuel m","authors_text":"Alexander Rashkovskii, Jon I. Magnusson, Pascal J. Thomas, Ragnar Sigurdsson","cross_cats":["math.AG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2011-03-11T15:41:28Z","title":"Limits of multipole pluricomplex Green functions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.2296","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":"sha256:0007b396c56afbf89eb7f6c150939293937770c258673ff45549f5c6f9375fcc","target":"record","created_at":"2026-05-18T04:01:23Z","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":"3c8829713a10537eb60ae1715788ac751d86a361555796435ebda939b0fc6559","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2011-03-11T15:41:28Z","title_canon_sha256":"a478129638a94a54ca5538acd066ad177544196dd5c0c806b41b99e5b868363d"},"schema_version":"1.0","source":{"id":"1103.2296","kind":"arxiv","version":2}},"canonical_sha256":"18aef135d0641230af4edeb830723d784fe88624c486f960f1588036e97239a3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"18aef135d0641230af4edeb830723d784fe88624c486f960f1588036e97239a3","first_computed_at":"2026-05-18T04:01:23.306773Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:01:23.306773Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"wXjCMQec2fEX/bFDfWrs5oyHCwbUCqb+eXdvWUMvfyKWl0oYfRIFw6cCAuzM8iMA3xRLCkfoPDFN0TJ83KquCA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:01:23.307445Z","signed_message":"canonical_sha256_bytes"},"source_id":"1103.2296","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0007b396c56afbf89eb7f6c150939293937770c258673ff45549f5c6f9375fcc","sha256:a9fdbcdeac84a4d6f9022158eab94490507497c889464e646ad8a5bb1ed24e87"],"state_sha256":"021000237bf94b66c3b6a6d7bc7cd150c6d969c4e4104d7a065270e8758e6e50"}