{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:ND2LFQHCMAU3Z6WO4HRMQCIPQO","short_pith_number":"pith:ND2LFQHC","schema_version":"1.0","canonical_sha256":"68f4b2c0e26029bcfacee1e2c8090f838ea6450a304c34075c78058cf493c9c9","source":{"kind":"arxiv","id":"1909.01425","version":2},"attestation_state":"computed","paper":{"title":"Topological Transition on the Conformal Manifold","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th"],"primary_cat":"cond-mat.str-el","authors_text":"Shu-Heng Shao, Wenjie Ji, Xiao-Gang Wen","submitted_at":"2019-09-03T20:03:42Z","abstract_excerpt":"Despite great successes in the study of gapped phases, a comprehensive understanding of the gapless phases and their transitions is still under developments. In this paper, we study a general phenomenon in the space of (1+1)$d$ critical phases with fermionic degrees of freedom described by a continuous family of conformal field theories (CFT), a.k.a. the conformal manifold. Along a one-dimensional locus on the conformal manifold, there can be a transition point, across which the fermionic CFTs on the two sides differ by stacking an invertible fermionic topological order (IFTO), point-by-point "},"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":"1909.01425","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.str-el","submitted_at":"2019-09-03T20:03:42Z","cross_cats_sorted":["hep-th"],"title_canon_sha256":"3274e4646190b735b14644c5ee647bb0bc591863c61e2acd3bdf5424e689b794","abstract_canon_sha256":"16fb03e3f24bf5cfe57e39948dd5b907b0cc43441e15629402b81d8593d14626"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T01:30:49.004673Z","signature_b64":"yJpUobTgtgN8xUZypxLXUOFfglMfs9tR4rDDkHZiLIwcRNqTtUKjk8YbAEz9szHZ9F3ijILG8+QRJujpTdB7Cw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"68f4b2c0e26029bcfacee1e2c8090f838ea6450a304c34075c78058cf493c9c9","last_reissued_at":"2026-07-05T01:30:49.004304Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T01:30:49.004304Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Topological Transition on the Conformal Manifold","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th"],"primary_cat":"cond-mat.str-el","authors_text":"Shu-Heng Shao, Wenjie Ji, Xiao-Gang Wen","submitted_at":"2019-09-03T20:03:42Z","abstract_excerpt":"Despite great successes in the study of gapped phases, a comprehensive understanding of the gapless phases and their transitions is still under developments. In this paper, we study a general phenomenon in the space of (1+1)$d$ critical phases with fermionic degrees of freedom described by a continuous family of conformal field theories (CFT), a.k.a. the conformal manifold. Along a one-dimensional locus on the conformal manifold, there can be a transition point, across which the fermionic CFTs on the two sides differ by stacking an invertible fermionic topological order (IFTO), point-by-point "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1909.01425","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1909.01425/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"1909.01425","created_at":"2026-07-05T01:30:49.004380+00:00"},{"alias_kind":"arxiv_version","alias_value":"1909.01425v2","created_at":"2026-07-05T01:30:49.004380+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1909.01425","created_at":"2026-07-05T01:30:49.004380+00:00"},{"alias_kind":"pith_short_12","alias_value":"ND2LFQHCMAU3","created_at":"2026-07-05T01:30:49.004380+00:00"},{"alias_kind":"pith_short_16","alias_value":"ND2LFQHCMAU3Z6WO","created_at":"2026-07-05T01:30:49.004380+00:00"},{"alias_kind":"pith_short_8","alias_value":"ND2LFQHC","created_at":"2026-07-05T01:30:49.004380+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":10,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2607.07786","citing_title":"Chiral Tube Algebras I: Topological Defect Lines, Twisted Modules, and Finite Gauging","ref_index":91,"is_internal_anchor":true},{"citing_arxiv_id":"2605.07734","citing_title":"Characterizing gapped phases by smeared boundary conformal field theories: Duality in unusual ordering with spontaneously broken generalized symmetries","ref_index":109,"is_internal_anchor":false},{"citing_arxiv_id":"2204.02407","citing_title":"Higher Gauging and Non-invertible Condensation Defects","ref_index":11,"is_internal_anchor":false},{"citing_arxiv_id":"2111.01139","citing_title":"Non-Invertible Duality Defects in 3+1 Dimensions","ref_index":11,"is_internal_anchor":false},{"citing_arxiv_id":"2308.00747","citing_title":"What's Done Cannot Be Undone: TASI Lectures on Non-Invertible Symmetries","ref_index":30,"is_internal_anchor":false},{"citing_arxiv_id":"2205.09545","citing_title":"Snowmass White Paper: Generalized Symmetries in Quantum Field Theory and Beyond","ref_index":100,"is_internal_anchor":false},{"citing_arxiv_id":"2605.07734","citing_title":"Characterizing gapped phases by smeared boundary conformal field theories: Duality in unusual ordering with spontaneously broken generalized symmetries","ref_index":116,"is_internal_anchor":false},{"citing_arxiv_id":"2601.03879","citing_title":"Defects in N=1 minimal models and RG flows","ref_index":24,"is_internal_anchor":false},{"citing_arxiv_id":"2605.07734","citing_title":"Characterizing gapped phases by smeared boundary conformal field theories: Duality in unusual ordering with spontaneously broken generalized symmetries","ref_index":114,"is_internal_anchor":false},{"citing_arxiv_id":"2605.02883","citing_title":"de Sitter Vacua & pUniverses","ref_index":41,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/ND2LFQHCMAU3Z6WO4HRMQCIPQO","json":"https://pith.science/pith/ND2LFQHCMAU3Z6WO4HRMQCIPQO.json","graph_json":"https://pith.science/api/pith-number/ND2LFQHCMAU3Z6WO4HRMQCIPQO/graph.json","events_json":"https://pith.science/api/pith-number/ND2LFQHCMAU3Z6WO4HRMQCIPQO/events.json","paper":"https://pith.science/paper/ND2LFQHC"},"agent_actions":{"view_html":"https://pith.science/pith/ND2LFQHCMAU3Z6WO4HRMQCIPQO","download_json":"https://pith.science/pith/ND2LFQHCMAU3Z6WO4HRMQCIPQO.json","view_paper":"https://pith.science/paper/ND2LFQHC","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1909.01425&json=true","fetch_graph":"https://pith.science/api/pith-number/ND2LFQHCMAU3Z6WO4HRMQCIPQO/graph.json","fetch_events":"https://pith.science/api/pith-number/ND2LFQHCMAU3Z6WO4HRMQCIPQO/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ND2LFQHCMAU3Z6WO4HRMQCIPQO/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ND2LFQHCMAU3Z6WO4HRMQCIPQO/action/storage_attestation","attest_author":"https://pith.science/pith/ND2LFQHCMAU3Z6WO4HRMQCIPQO/action/author_attestation","sign_citation":"https://pith.science/pith/ND2LFQHCMAU3Z6WO4HRMQCIPQO/action/citation_signature","submit_replication":"https://pith.science/pith/ND2LFQHCMAU3Z6WO4HRMQCIPQO/action/replication_record"}},"created_at":"2026-07-05T01:30:49.004380+00:00","updated_at":"2026-07-05T01:30:49.004380+00:00"}