{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:2XAWA3QQE7XBTE3VG6XSFCQMSY","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":"e626c59028faa0113c205018a77cfdf33403c57c5cbc6a61984d3332449416fb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.mes-hall","submitted_at":"2019-01-31T16:53:42Z","title_canon_sha256":"182f1dedee5f8029afd585aa0f2ff6d7bb2ac218da9e4fcd3d4770f2457d0f20"},"schema_version":"1.0","source":{"id":"1901.11468","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1901.11468","created_at":"2026-05-17T23:39:47Z"},{"alias_kind":"arxiv_version","alias_value":"1901.11468v1","created_at":"2026-05-17T23:39:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1901.11468","created_at":"2026-05-17T23:39:47Z"},{"alias_kind":"pith_short_12","alias_value":"2XAWA3QQE7XB","created_at":"2026-05-18T12:33:07Z"},{"alias_kind":"pith_short_16","alias_value":"2XAWA3QQE7XBTE3V","created_at":"2026-05-18T12:33:07Z"},{"alias_kind":"pith_short_8","alias_value":"2XAWA3QQ","created_at":"2026-05-18T12:33:07Z"}],"graph_snapshots":[{"event_id":"sha256:61a8226fd0724bcee3fc358d7499c82aaeb14043c93061e3a40517d89253d72f","target":"graph","created_at":"2026-05-17T23:39:47Z","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":"In topological insulators and topological superconductors, the discrete jump of the topological invariant upon tuning a certain system parameter defines a topological phase transition. A unified framework is employed to address the quantum criticality of the topological phase transitions in one to three spatial dimensions, which simultaneously incorporates the symmetry classification, order of band crossing, $m$-fold rotational symmetry, correlation functions, critical exponents, scaling laws, and renormalization group approach. We first classify higher-order Dirac models according to the time","authors_text":"Andreas P. Schnyder, Wei Chen","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.mes-hall","submitted_at":"2019-01-31T16:53:42Z","title":"Universality classes of topological phase transitions with higher-order band crossing"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1901.11468","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:b4619880de87231944eda6e5af673b256f327997be1372c20356034112087259","target":"record","created_at":"2026-05-17T23:39:47Z","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":"e626c59028faa0113c205018a77cfdf33403c57c5cbc6a61984d3332449416fb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.mes-hall","submitted_at":"2019-01-31T16:53:42Z","title_canon_sha256":"182f1dedee5f8029afd585aa0f2ff6d7bb2ac218da9e4fcd3d4770f2457d0f20"},"schema_version":"1.0","source":{"id":"1901.11468","kind":"arxiv","version":1}},"canonical_sha256":"d5c1606e1027ee19937537af228a0c96169668590b32c8c9be92feb2e2295a65","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d5c1606e1027ee19937537af228a0c96169668590b32c8c9be92feb2e2295a65","first_computed_at":"2026-05-17T23:39:47.115357Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:39:47.115357Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3N+514t1cMiZQne7sxVtwRaDyWq2BckEpGmcbQZqdpoEn+5XyJ5VTNpgXRqUGG5E8U/5eTlEizVvbqYP8O1vAg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:39:47.115982Z","signed_message":"canonical_sha256_bytes"},"source_id":"1901.11468","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b4619880de87231944eda6e5af673b256f327997be1372c20356034112087259","sha256:61a8226fd0724bcee3fc358d7499c82aaeb14043c93061e3a40517d89253d72f"],"state_sha256":"9ba7f045afacb9486a21f2937bfcf0aebf57b84b611da810f292220affe99a52"}