{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:TGWSG2HPOVXG6YRVQF2OW6HH3W","short_pith_number":"pith:TGWSG2HP","schema_version":"1.0","canonical_sha256":"99ad2368ef756e6f62358174eb78e7dd9834181554bbb2eec3fce175197eb2d7","source":{"kind":"arxiv","id":"1301.7355","version":3},"attestation_state":"computed","paper":{"title":"Protected edge modes without symmetry","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cond-mat.str-el","authors_text":"Michael Levin","submitted_at":"2013-01-30T20:51:38Z","abstract_excerpt":"We discuss the question of when a gapped 2D electron system without any symmetry has a protected gapless edge mode. While it is well known that systems with a nonzero thermal Hall conductance, $K_H \\neq 0$, support such modes, here we show that robust modes can also occur when $K_H = 0$ -- if the system has quasiparticles with fractional statistics. We show that some types of fractional statistics are compatible with a gapped edge, while others are fundamentally incompatible. More generally, we give a criterion for when an electron system with abelian statistics and $K_H = 0$ can support a gap"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1301.7355","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.str-el","submitted_at":"2013-01-30T20:51:38Z","cross_cats_sorted":[],"title_canon_sha256":"35bc25c8c4e88e10aee787d652fd7f17f341dba94bea8ae9c3a87cc54bd1196e","abstract_canon_sha256":"e611fdb557b152fb4e4135629419430fadfd30c53d7b3cc822be9b67d16189f5"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:21:54.730754Z","signature_b64":"QfrqNcaBFlMh3QqYA0IqfCwrkDumU/zjHqxWbNNYIHxfESuUk69DbOr4k8JDVyTcn8bJMgIGKu9d5TOmLuCkBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"99ad2368ef756e6f62358174eb78e7dd9834181554bbb2eec3fce175197eb2d7","last_reissued_at":"2026-05-18T03:21:54.730311Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:21:54.730311Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Protected edge modes without symmetry","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cond-mat.str-el","authors_text":"Michael Levin","submitted_at":"2013-01-30T20:51:38Z","abstract_excerpt":"We discuss the question of when a gapped 2D electron system without any symmetry has a protected gapless edge mode. While it is well known that systems with a nonzero thermal Hall conductance, $K_H \\neq 0$, support such modes, here we show that robust modes can also occur when $K_H = 0$ -- if the system has quasiparticles with fractional statistics. We show that some types of fractional statistics are compatible with a gapped edge, while others are fundamentally incompatible. More generally, we give a criterion for when an electron system with abelian statistics and $K_H = 0$ can support a gap"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.7355","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1301.7355","created_at":"2026-05-18T03:21:54.730381+00:00"},{"alias_kind":"arxiv_version","alias_value":"1301.7355v3","created_at":"2026-05-18T03:21:54.730381+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.7355","created_at":"2026-05-18T03:21:54.730381+00:00"},{"alias_kind":"pith_short_12","alias_value":"TGWSG2HPOVXG","created_at":"2026-05-18T12:28:02.375192+00:00"},{"alias_kind":"pith_short_16","alias_value":"TGWSG2HPOVXG6YRV","created_at":"2026-05-18T12:28:02.375192+00:00"},{"alias_kind":"pith_short_8","alias_value":"TGWSG2HP","created_at":"2026-05-18T12:28:02.375192+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":6,"internal_anchor_count":6,"sample":[{"citing_arxiv_id":"2301.05687","citing_title":"Mixed-state topological order and the errorfield double formulation of decoherence-induced transitions","ref_index":21,"is_internal_anchor":true},{"citing_arxiv_id":"2204.02407","citing_title":"Higher Gauging and Non-invertible Condensation Defects","ref_index":124,"is_internal_anchor":true},{"citing_arxiv_id":"2308.00747","citing_title":"What's Done Cannot Be Undone: TASI Lectures on Non-Invertible Symmetries","ref_index":265,"is_internal_anchor":true},{"citing_arxiv_id":"2312.16317","citing_title":"Non-Invertible Anyon Condensation and Level-Rank Dualities","ref_index":90,"is_internal_anchor":true},{"citing_arxiv_id":"2410.11942","citing_title":"Operator algebra and algorithmic construction of boundaries and defects in (2+1)D topological Pauli stabilizer codes","ref_index":101,"is_internal_anchor":true},{"citing_arxiv_id":"2508.08639","citing_title":"Extending fusion rules with finite subgroups: A general construction of $Z_{N}$ extended conformal field theories and their orbifoldings","ref_index":103,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/TGWSG2HPOVXG6YRVQF2OW6HH3W","json":"https://pith.science/pith/TGWSG2HPOVXG6YRVQF2OW6HH3W.json","graph_json":"https://pith.science/api/pith-number/TGWSG2HPOVXG6YRVQF2OW6HH3W/graph.json","events_json":"https://pith.science/api/pith-number/TGWSG2HPOVXG6YRVQF2OW6HH3W/events.json","paper":"https://pith.science/paper/TGWSG2HP"},"agent_actions":{"view_html":"https://pith.science/pith/TGWSG2HPOVXG6YRVQF2OW6HH3W","download_json":"https://pith.science/pith/TGWSG2HPOVXG6YRVQF2OW6HH3W.json","view_paper":"https://pith.science/paper/TGWSG2HP","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1301.7355&json=true","fetch_graph":"https://pith.science/api/pith-number/TGWSG2HPOVXG6YRVQF2OW6HH3W/graph.json","fetch_events":"https://pith.science/api/pith-number/TGWSG2HPOVXG6YRVQF2OW6HH3W/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/TGWSG2HPOVXG6YRVQF2OW6HH3W/action/timestamp_anchor","attest_storage":"https://pith.science/pith/TGWSG2HPOVXG6YRVQF2OW6HH3W/action/storage_attestation","attest_author":"https://pith.science/pith/TGWSG2HPOVXG6YRVQF2OW6HH3W/action/author_attestation","sign_citation":"https://pith.science/pith/TGWSG2HPOVXG6YRVQF2OW6HH3W/action/citation_signature","submit_replication":"https://pith.science/pith/TGWSG2HPOVXG6YRVQF2OW6HH3W/action/replication_record"}},"created_at":"2026-05-18T03:21:54.730381+00:00","updated_at":"2026-05-18T03:21:54.730381+00:00"}