{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:XIJY4ZPJTRWTWM35WORN2QWLJ3","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":"ee8e7bbdd288cfe037dc979437dc75a41d30431fadce393f47064190ace3d017","cross_cats_sorted":["cond-mat.mes-hall"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.supr-con","submitted_at":"2013-07-28T10:30:40Z","title_canon_sha256":"e25e29c9248f157853be917d0373e9d883a32f5aa904aa9221f954baceaf1fae"},"schema_version":"1.0","source":{"id":"1307.7347","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1307.7347","created_at":"2026-05-18T02:59:18Z"},{"alias_kind":"arxiv_version","alias_value":"1307.7347v3","created_at":"2026-05-18T02:59:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.7347","created_at":"2026-05-18T02:59:18Z"},{"alias_kind":"pith_short_12","alias_value":"XIJY4ZPJTRWT","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_16","alias_value":"XIJY4ZPJTRWTWM35","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_8","alias_value":"XIJY4ZPJ","created_at":"2026-05-18T12:28:06Z"}],"graph_snapshots":[{"event_id":"sha256:78cac93c4c7236557c564c0155bb36c151eb13c08a68758301ef79a1682f4d42","target":"graph","created_at":"2026-05-18T02:59:18Z","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 phase transition is accompanied with a change of topological numbers. It has been believed that the gap closing and the breakdown of the adiabaticity at the transition point is necessary in general. However, the gap closing is not always needed to make the topological index ill-defined. In this paper, we show that the states with different topological numbers can be continuously connected \\textit{without} gap closing in some cases, where the symmetry of the system changes during the process. Here we propose the generic principles how this is possible (impossible) by demonstrating v","authors_text":"Motohiko Ezawa, Naoto Nagaosa, Yukio Tanaka","cross_cats":["cond-mat.mes-hall"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.supr-con","submitted_at":"2013-07-28T10:30:40Z","title":"Topological Phase Transition without Gap Closing"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.7347","kind":"arxiv","version":3},"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:d29989e05fcf9047eab9c29fd00bf90c5ada91760c9001519a159da125197ffd","target":"record","created_at":"2026-05-18T02:59:18Z","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":"ee8e7bbdd288cfe037dc979437dc75a41d30431fadce393f47064190ace3d017","cross_cats_sorted":["cond-mat.mes-hall"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.supr-con","submitted_at":"2013-07-28T10:30:40Z","title_canon_sha256":"e25e29c9248f157853be917d0373e9d883a32f5aa904aa9221f954baceaf1fae"},"schema_version":"1.0","source":{"id":"1307.7347","kind":"arxiv","version":3}},"canonical_sha256":"ba138e65e99c6d3b337db3a2dd42cb4ec22801d8dd93e8d0acf17a2a60505a98","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ba138e65e99c6d3b337db3a2dd42cb4ec22801d8dd93e8d0acf17a2a60505a98","first_computed_at":"2026-05-18T02:59:18.338789Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:59:18.338789Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"i/3hManYFEkj4jni6NvW6cUe5H/8UiBLnePJ6Kk9U+fP7m1H1lPukHQP2qL6G/uYOfGkpWYOcm5PGBGshhHRCA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:59:18.339699Z","signed_message":"canonical_sha256_bytes"},"source_id":"1307.7347","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d29989e05fcf9047eab9c29fd00bf90c5ada91760c9001519a159da125197ffd","sha256:78cac93c4c7236557c564c0155bb36c151eb13c08a68758301ef79a1682f4d42"],"state_sha256":"f61f1a6b7134648f50f99eca59205abf1bbaa8d0b68f98cc8d2789279e69d919"}