{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:HISY62KDJALKCTCP3OI5DSLTXG","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":"886c808f07a0c32b8955281387f8a18267f7fc43b1705f564b257acf2a96b4f5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-03-23T21:21:41Z","title_canon_sha256":"e804628a9e64c30b9e472dc737fe2cb33a5502424a72bfefbda425663a0979ec"},"schema_version":"1.0","source":{"id":"1103.4633","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1103.4633","created_at":"2026-05-18T04:26:01Z"},{"alias_kind":"arxiv_version","alias_value":"1103.4633v1","created_at":"2026-05-18T04:26:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1103.4633","created_at":"2026-05-18T04:26:01Z"},{"alias_kind":"pith_short_12","alias_value":"HISY62KDJALK","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_16","alias_value":"HISY62KDJALKCTCP","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_8","alias_value":"HISY62KD","created_at":"2026-05-18T12:26:30Z"}],"graph_snapshots":[{"event_id":"sha256:acb6c43c1a2c9f45a4f7f4227888b651f8660e621fd1bf2db4b0e175097145f1","target":"graph","created_at":"2026-05-18T04:26:01Z","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":"Given a holomorphic self-map of complex projective space of degree larger than one, we prove that there exists a finite collection of totally invariant algebraic sets with the following property: given any positive closed (1,1)-current of mass 1 with no mass on any element of this family, the sequence of normalized pull-backs of the current converges to the Green current. Under suitable geometric conditions on the collection of totally invariant algebraic sets, we prove a sharper equidistribution result.","authors_text":"Manuel Rodrigo Parra","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-03-23T21:21:41Z","title":"The Jacobian cocycle and equidistribution towards the Green current"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.4633","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":"sha256:90358d6af0e806a3c0bf3ab3b2d5b432795ee96b18e4b6fa1212e24d946ffd5f","target":"record","created_at":"2026-05-18T04:26:01Z","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":"886c808f07a0c32b8955281387f8a18267f7fc43b1705f564b257acf2a96b4f5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-03-23T21:21:41Z","title_canon_sha256":"e804628a9e64c30b9e472dc737fe2cb33a5502424a72bfefbda425663a0979ec"},"schema_version":"1.0","source":{"id":"1103.4633","kind":"arxiv","version":1}},"canonical_sha256":"3a258f69434816a14c4fdb91d1c973b9bd33feed07c31e0c557c7fc8b9c549e0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3a258f69434816a14c4fdb91d1c973b9bd33feed07c31e0c557c7fc8b9c549e0","first_computed_at":"2026-05-18T04:26:01.194113Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:26:01.194113Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5gshfmu41DBvMe7IWECQOxD0hw02fG1G53T8BM3I8Z1Cz+okaxLY4lwGvHdsaS/8g+1NmA5YCm5tJaypzJy7Bg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:26:01.194636Z","signed_message":"canonical_sha256_bytes"},"source_id":"1103.4633","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:90358d6af0e806a3c0bf3ab3b2d5b432795ee96b18e4b6fa1212e24d946ffd5f","sha256:acb6c43c1a2c9f45a4f7f4227888b651f8660e621fd1bf2db4b0e175097145f1"],"state_sha256":"8330c6a46cfbe31c1803e1ebd12dcebbfa7269e46dcdf204052ee4231b34cd98"}