{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:WULS6ETOYOMGUYVE5EWO4EDPEA","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":"004de4730d7d7d597030d54f5762b30833a9cbb07160aef801825adb1c0e1f8f","cross_cats_sorted":["cond-mat.stat-mech","math-ph","math.MP","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.str-el","submitted_at":"2018-05-17T18:00:07Z","title_canon_sha256":"df72da7e8d856b9fe280e27b7c4432b5fddf534f97aa8eef77e91231f44f0b1b"},"schema_version":"1.0","source":{"id":"1805.06904","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1805.06904","created_at":"2026-05-17T23:43:18Z"},{"alias_kind":"arxiv_version","alias_value":"1805.06904v2","created_at":"2026-05-17T23:43:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.06904","created_at":"2026-05-17T23:43:18Z"},{"alias_kind":"pith_short_12","alias_value":"WULS6ETOYOMG","created_at":"2026-05-18T12:33:01Z"},{"alias_kind":"pith_short_16","alias_value":"WULS6ETOYOMGUYVE","created_at":"2026-05-18T12:33:01Z"},{"alias_kind":"pith_short_8","alias_value":"WULS6ETO","created_at":"2026-05-18T12:33:01Z"}],"graph_snapshots":[{"event_id":"sha256:4d466a842647b56477b012f06f6b9bccd78c5bbfd03bdb4e19c2da50358f429e","target":"graph","created_at":"2026-05-17T23:43:18Z","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":"Topological phases protected by symmetry can occur in gapped and---surprisingly---in critical systems. We consider non-interacting fermions in one dimension with spinless time-reversal symmetry. It is known that the phases are classified by a topological invariant $\\omega$ and a central charge $c$. We investigate the correlations of string operators, giving insight into the interplay between topology and criticality. In the gapped phases, these non-local string order parameters allow us to extract $\\omega$. Remarkably, ratios of correlation lengths are universal. In the critical phases, the sc","authors_text":"Nick G. Jones, Ruben Verresen","cross_cats":["cond-mat.stat-mech","math-ph","math.MP","quant-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.str-el","submitted_at":"2018-05-17T18:00:07Z","title":"Asymptotic Correlations in Gapped and Critical Topological Phases of 1D Quantum Systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.06904","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":"sha256:66c512cb7e0da627e25b4b119e64cb76cc261736749d941e52abbb0b2c7ca1cb","target":"record","created_at":"2026-05-17T23:43:18Z","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":"004de4730d7d7d597030d54f5762b30833a9cbb07160aef801825adb1c0e1f8f","cross_cats_sorted":["cond-mat.stat-mech","math-ph","math.MP","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.str-el","submitted_at":"2018-05-17T18:00:07Z","title_canon_sha256":"df72da7e8d856b9fe280e27b7c4432b5fddf534f97aa8eef77e91231f44f0b1b"},"schema_version":"1.0","source":{"id":"1805.06904","kind":"arxiv","version":2}},"canonical_sha256":"b5172f126ec3986a62a4e92cee106f202368e7d4b3da4e1e30e0623d38cef033","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b5172f126ec3986a62a4e92cee106f202368e7d4b3da4e1e30e0623d38cef033","first_computed_at":"2026-05-17T23:43:18.028823Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:43:18.028823Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"XECauUQaJlsz94tLGLXaSk65o6ILbCL2Nz2Mnl07dZdfsXC9G1Bg3mlbSAohsgu0sOCmqK3QSYpPMFCc05sgDQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:43:18.029406Z","signed_message":"canonical_sha256_bytes"},"source_id":"1805.06904","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:66c512cb7e0da627e25b4b119e64cb76cc261736749d941e52abbb0b2c7ca1cb","sha256:4d466a842647b56477b012f06f6b9bccd78c5bbfd03bdb4e19c2da50358f429e"],"state_sha256":"d4693a511f7c5e367e048d9d555b4ec42b90fb6a20c47ca7c2acec29bef000f6"}