{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:UK3I7JBUO7DRNUBHSRJ246UBFK","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":"47de604ff5dcf6b4a28f9c2fae90517b47eadf3e6b1d3021943b875649f6d82b","cross_cats_sorted":["math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-08-22T13:15:53Z","title_canon_sha256":"e6fcc187b87ba4f332e7c9c1a5b3e5abb0bfffe0c2ccf69321e829c18408ad6f"},"schema_version":"1.0","source":{"id":"1508.05509","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1508.05509","created_at":"2026-05-18T00:36:10Z"},{"alias_kind":"arxiv_version","alias_value":"1508.05509v2","created_at":"2026-05-18T00:36:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.05509","created_at":"2026-05-18T00:36:10Z"},{"alias_kind":"pith_short_12","alias_value":"UK3I7JBUO7DR","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_16","alias_value":"UK3I7JBUO7DRNUBH","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_8","alias_value":"UK3I7JBU","created_at":"2026-05-18T12:29:44Z"}],"graph_snapshots":[{"event_id":"sha256:5c1b25d79c00173c034a47163452b1827d805151b9bff77b70ed7369623c3630","target":"graph","created_at":"2026-05-18T00:36:10Z","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 construct a branched center manifold in a neighborhood of a singular point of a $2$-dimensional integral current which is almost minimizing in a suitable sense. Our construction is the first half of an argument which shows the discreteness of the singular set for the following three classes of $2$-dimensional currents: area minimizing in Riemannian manifolds, semicalibrated and spherical cross sections of $3$-dimensional area minimizing cones.","authors_text":"Camillo De Lellis, Emanuele Spadaro, Luca Spolaor","cross_cats":["math.DG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-08-22T13:15:53Z","title":"Regularity theory for $2$-dimensional almost minimal currents II: branched center manifold"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.05509","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":"sha256:6d7d4ce79bc587477594efe1fd56bdea30bd03a9242beb8d870fe1b7e3237db1","target":"record","created_at":"2026-05-18T00:36:10Z","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":"47de604ff5dcf6b4a28f9c2fae90517b47eadf3e6b1d3021943b875649f6d82b","cross_cats_sorted":["math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-08-22T13:15:53Z","title_canon_sha256":"e6fcc187b87ba4f332e7c9c1a5b3e5abb0bfffe0c2ccf69321e829c18408ad6f"},"schema_version":"1.0","source":{"id":"1508.05509","kind":"arxiv","version":2}},"canonical_sha256":"a2b68fa43477c716d0279453ae7a812a898f8c30667f0ba5764969a38c804ba0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a2b68fa43477c716d0279453ae7a812a898f8c30667f0ba5764969a38c804ba0","first_computed_at":"2026-05-18T00:36:10.079368Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:36:10.079368Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"HxEZRKdhreuiBT+MGLi9H2A8wnQouKwPCuCtKyp7CnEVIr7xW8S8kj79pF/cM8SFc/S5enGFg4tedMqsJL+tCw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:36:10.080070Z","signed_message":"canonical_sha256_bytes"},"source_id":"1508.05509","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6d7d4ce79bc587477594efe1fd56bdea30bd03a9242beb8d870fe1b7e3237db1","sha256:5c1b25d79c00173c034a47163452b1827d805151b9bff77b70ed7369623c3630"],"state_sha256":"78dbea6767d0751341395aa1dfddfd3182e84cc7b26755d5270c54ad0d7c0e92"}