{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:CEJPP7GKNO3PP3MSGFHNHTPUCB","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":"83a5f678b6553767e1c9aabcb83cdd1bd098e5421bf9ba66ea938ba4da41056c","cross_cats_sorted":["math.AP","math.MP","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2014-03-26T20:59:02Z","title_canon_sha256":"eccd73c35164d21ec25300c9d42cf8a4b73189ab611d3cef5f25d72268e26a67"},"schema_version":"1.0","source":{"id":"1403.6860","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1403.6860","created_at":"2026-05-18T01:36:36Z"},{"alias_kind":"arxiv_version","alias_value":"1403.6860v4","created_at":"2026-05-18T01:36:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1403.6860","created_at":"2026-05-18T01:36:36Z"},{"alias_kind":"pith_short_12","alias_value":"CEJPP7GKNO3P","created_at":"2026-05-18T12:28:22Z"},{"alias_kind":"pith_short_16","alias_value":"CEJPP7GKNO3PP3MS","created_at":"2026-05-18T12:28:22Z"},{"alias_kind":"pith_short_8","alias_value":"CEJPP7GK","created_at":"2026-05-18T12:28:22Z"}],"graph_snapshots":[{"event_id":"sha256:4671dae21d858fc0fd6346f233be8ce13eabd8bba79c8ff96caea24cabdfaa75","target":"graph","created_at":"2026-05-18T01:36:36Z","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":"These are the lecture notes of a \"Nachdiplomvorlesung\" course taught at ETH Zurich in the Spring of 2013. They appeared in the EMS series Zurich Lectures in Advanced Mathematics.","authors_text":"Sylvia Serfaty","cross_cats":["math.AP","math.MP","math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2014-03-26T20:59:02Z","title":"Coulomb Gases and Ginzburg-Landau Vortices"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.6860","kind":"arxiv","version":4},"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:effc1dcac01632e34fdefc4f2f4c20a891eb161176b4dff40bea9cee05594255","target":"record","created_at":"2026-05-18T01:36:36Z","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":"83a5f678b6553767e1c9aabcb83cdd1bd098e5421bf9ba66ea938ba4da41056c","cross_cats_sorted":["math.AP","math.MP","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2014-03-26T20:59:02Z","title_canon_sha256":"eccd73c35164d21ec25300c9d42cf8a4b73189ab611d3cef5f25d72268e26a67"},"schema_version":"1.0","source":{"id":"1403.6860","kind":"arxiv","version":4}},"canonical_sha256":"1112f7fcca6bb6f7ed92314ed3cdf410755015cef84f979544aa02138759e3b4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1112f7fcca6bb6f7ed92314ed3cdf410755015cef84f979544aa02138759e3b4","first_computed_at":"2026-05-18T01:36:36.110401Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:36:36.110401Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"IYtiAHsOw8sxjoA6iZV6E8jTbhqKAEffH1ribsyYZwMTBlrhpscRgVMdl0Y/MiAF+m3+/Iv1U9ZJC9rte7sUDw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:36:36.111097Z","signed_message":"canonical_sha256_bytes"},"source_id":"1403.6860","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:effc1dcac01632e34fdefc4f2f4c20a891eb161176b4dff40bea9cee05594255","sha256:4671dae21d858fc0fd6346f233be8ce13eabd8bba79c8ff96caea24cabdfaa75"],"state_sha256":"faab4c58703bcf1212ac481b58426a02c58678ac274d4617b31a5aaea497ce28"}