{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:XKJ7VAXUB76Q5NDPRDW7UPKDTC","short_pith_number":"pith:XKJ7VAXU","schema_version":"1.0","canonical_sha256":"ba93fa82f40ffd0eb46f88edfa3d439889a0737a3ceab967b1043365cdb2b89d","source":{"kind":"arxiv","id":"1705.01557","version":2},"attestation_state":"computed","paper":{"title":"Gapless Symmetry Protected Topological Order","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech"],"primary_cat":"cond-mat.str-el","authors_text":"Daniel E. Parker, Romain Vasseur, Thomas Scaffidi","submitted_at":"2017-05-03T18:00:07Z","abstract_excerpt":"We introduce exactly solvable gapless quantum systems in $d$ dimensions that support symmetry protected topological (SPT) edge modes. Our construction leads to long-range entangled, critical points or phases that can be interpreted as critical condensates of domain walls \"decorated\" with dimension $(d-1)$ SPT systems. Using a combination of field theory and exact lattice results, we argue that such gapless SPT systems have symmetry-protected topological edge modes that can be either gapless or symmetry-broken, leading to unusual surface critical properties. Despite the absence of a bulk gap, t"},"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":"1705.01557","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.str-el","submitted_at":"2017-05-03T18:00:07Z","cross_cats_sorted":["cond-mat.stat-mech"],"title_canon_sha256":"3d7272aff72bc859d338501884731848523eb49fdb55d868c6924816f4f53241","abstract_canon_sha256":"febec7d95fb202203e8c4e20caf78a8ca59164918d34b5d4c03487b3475ee0fb"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:28:35.512733Z","signature_b64":"MjLeZCxzqMVMeZKeagwEzZE+ZOayQrJ5LJkL+m7R5iqxK/HzbCNw76nFS8pzrA7JspwADxxrEY9Y5HENN6XhCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ba93fa82f40ffd0eb46f88edfa3d439889a0737a3ceab967b1043365cdb2b89d","last_reissued_at":"2026-05-18T00:28:35.511901Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:28:35.511901Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Gapless Symmetry Protected Topological Order","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech"],"primary_cat":"cond-mat.str-el","authors_text":"Daniel E. Parker, Romain Vasseur, Thomas Scaffidi","submitted_at":"2017-05-03T18:00:07Z","abstract_excerpt":"We introduce exactly solvable gapless quantum systems in $d$ dimensions that support symmetry protected topological (SPT) edge modes. Our construction leads to long-range entangled, critical points or phases that can be interpreted as critical condensates of domain walls \"decorated\" with dimension $(d-1)$ SPT systems. Using a combination of field theory and exact lattice results, we argue that such gapless SPT systems have symmetry-protected topological edge modes that can be either gapless or symmetry-broken, leading to unusual surface critical properties. Despite the absence of a bulk gap, t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.01557","kind":"arxiv","version":2},"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":"1705.01557","created_at":"2026-05-18T00:28:35.512033+00:00"},{"alias_kind":"arxiv_version","alias_value":"1705.01557v2","created_at":"2026-05-18T00:28:35.512033+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.01557","created_at":"2026-05-18T00:28:35.512033+00:00"},{"alias_kind":"pith_short_12","alias_value":"XKJ7VAXUB76Q","created_at":"2026-05-18T12:31:56.362134+00:00"},{"alias_kind":"pith_short_16","alias_value":"XKJ7VAXUB76Q5NDP","created_at":"2026-05-18T12:31:56.362134+00:00"},{"alias_kind":"pith_short_8","alias_value":"XKJ7VAXU","created_at":"2026-05-18T12:31:56.362134+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":3,"internal_anchor_count":2,"sample":[{"citing_arxiv_id":"2605.07734","citing_title":"Characterizing bulk properties of gapped phases by smeared boundary conformal field theories: Role of duality in unusual ordering","ref_index":36,"is_internal_anchor":true},{"citing_arxiv_id":"2506.23155","citing_title":"Homomorphism, substructure, and ideal: Elementary but rigorous aspects of renormalization group or hierarchical structure of topological orders","ref_index":58,"is_internal_anchor":true},{"citing_arxiv_id":"2605.07734","citing_title":"Characterizing bulk properties of gapped phases by smeared boundary conformal field theories: Role of duality in unusual ordering","ref_index":36,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/XKJ7VAXUB76Q5NDPRDW7UPKDTC","json":"https://pith.science/pith/XKJ7VAXUB76Q5NDPRDW7UPKDTC.json","graph_json":"https://pith.science/api/pith-number/XKJ7VAXUB76Q5NDPRDW7UPKDTC/graph.json","events_json":"https://pith.science/api/pith-number/XKJ7VAXUB76Q5NDPRDW7UPKDTC/events.json","paper":"https://pith.science/paper/XKJ7VAXU"},"agent_actions":{"view_html":"https://pith.science/pith/XKJ7VAXUB76Q5NDPRDW7UPKDTC","download_json":"https://pith.science/pith/XKJ7VAXUB76Q5NDPRDW7UPKDTC.json","view_paper":"https://pith.science/paper/XKJ7VAXU","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1705.01557&json=true","fetch_graph":"https://pith.science/api/pith-number/XKJ7VAXUB76Q5NDPRDW7UPKDTC/graph.json","fetch_events":"https://pith.science/api/pith-number/XKJ7VAXUB76Q5NDPRDW7UPKDTC/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/XKJ7VAXUB76Q5NDPRDW7UPKDTC/action/timestamp_anchor","attest_storage":"https://pith.science/pith/XKJ7VAXUB76Q5NDPRDW7UPKDTC/action/storage_attestation","attest_author":"https://pith.science/pith/XKJ7VAXUB76Q5NDPRDW7UPKDTC/action/author_attestation","sign_citation":"https://pith.science/pith/XKJ7VAXUB76Q5NDPRDW7UPKDTC/action/citation_signature","submit_replication":"https://pith.science/pith/XKJ7VAXUB76Q5NDPRDW7UPKDTC/action/replication_record"}},"created_at":"2026-05-18T00:28:35.512033+00:00","updated_at":"2026-05-18T00:28:35.512033+00:00"}