{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:JMDHGIVXVLNA3CRGQXVFZTAWFJ","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":"bec0b449d3c9f160366c2e4fcd2fc02a12d4d19e7a40ed25920a3e6c93ed7567","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.quant-gas","submitted_at":"2013-04-25T19:13:31Z","title_canon_sha256":"2b2b370ee4ba3fcb979552df4ecdb8c4104b25825028aae17ed8270baa98fb63"},"schema_version":"1.0","source":{"id":"1304.6980","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1304.6980","created_at":"2026-05-18T03:27:10Z"},{"alias_kind":"arxiv_version","alias_value":"1304.6980v1","created_at":"2026-05-18T03:27:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.6980","created_at":"2026-05-18T03:27:10Z"},{"alias_kind":"pith_short_12","alias_value":"JMDHGIVXVLNA","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_16","alias_value":"JMDHGIVXVLNA3CRG","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_8","alias_value":"JMDHGIVX","created_at":"2026-05-18T12:27:49Z"}],"graph_snapshots":[{"event_id":"sha256:806d7e39f5e2871b31fdda89c91e36017c7e2a503bf47fc42a4bce6449fdc33b","target":"graph","created_at":"2026-05-18T03:27:10Z","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":"Phase transitions give crucial insight into many-body systems, as crossovers between different regimes of order are determined by the underlying dynamics. These dynamics, in turn, are often constrained by dimensionality and geometry. For example, in one- and two-dimensional systems with continuous symmetry, thermal fluctuations prevent the formation of long-range order[1,2]. Two-dimensional systems are particularly significant, as vortices can form in the plane but cannot tilt out of it. At high temperatures, random motion of these vortices destroys large-scale coherence. At low temperatures, ","authors_text":"Guohai Situ, Jason W. Fleischer, Stefan Muenzel","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.quant-gas","submitted_at":"2013-04-25T19:13:31Z","title":"Berezinskii-Kosterlitz-Thouless transition in a photonic lattice"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.6980","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":"sha256:0c99c0daf353e47a75ee504d8f1dc49c895f9d966984fb1bf868812c45b6f167","target":"record","created_at":"2026-05-18T03:27:10Z","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":"bec0b449d3c9f160366c2e4fcd2fc02a12d4d19e7a40ed25920a3e6c93ed7567","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.quant-gas","submitted_at":"2013-04-25T19:13:31Z","title_canon_sha256":"2b2b370ee4ba3fcb979552df4ecdb8c4104b25825028aae17ed8270baa98fb63"},"schema_version":"1.0","source":{"id":"1304.6980","kind":"arxiv","version":1}},"canonical_sha256":"4b067322b7aada0d8a2685ea5ccc162a6bdb5994fcd4fbb32834ace43e668aef","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4b067322b7aada0d8a2685ea5ccc162a6bdb5994fcd4fbb32834ace43e668aef","first_computed_at":"2026-05-18T03:27:10.656061Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:27:10.656061Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"SSEambMXmjEqfjkBKebKUpEfmrNQE7ba3ambXd7WoxRrfi9JvC9KbxX7MUjALhyjaipe1mTiXbIyR1Djui5CAA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:27:10.656954Z","signed_message":"canonical_sha256_bytes"},"source_id":"1304.6980","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0c99c0daf353e47a75ee504d8f1dc49c895f9d966984fb1bf868812c45b6f167","sha256:806d7e39f5e2871b31fdda89c91e36017c7e2a503bf47fc42a4bce6449fdc33b"],"state_sha256":"8ba9ddf1a4e03975bf52d8b46fe05b44f548a2cbb30f6b886dc99810c0eb4a59"}