{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:ONJOXKWHUAKXODUO4UFCE5ZRIF","short_pith_number":"pith:ONJOXKWH","schema_version":"1.0","canonical_sha256":"7352ebaac7a015770e8ee50a22773141465dd543640e31024b565c34e258dedc","source":{"kind":"arxiv","id":"2605.13952","version":1},"attestation_state":"computed","paper":{"title":"Non-Invertible Symmetries and Boundaries for Two-Dimensional Fermions","license":"http://creativecommons.org/licenses/by/4.0/","headline":"Two free complex Weyl fermions have anomaly-free Z_k symmetries for each primitive Pythagorean triple, each producing a non-invertible defect that generates all U(1)^2-preserving conformal boundaries.","cross_cats":["cond-mat.str-el"],"primary_cat":"hep-th","authors_text":"Guillermo Arias-Tamargo, Maxwell L. Vel\\'asquez Cotini Hutt, Philip Boyle Smith, Rishi Mouland","submitted_at":"2026-05-13T18:00:00Z","abstract_excerpt":"We study the relation between boundary conditions and categorical symmetries of two-dimensional fermionic conformal field theories. We determine all anomaly-free invertible global symmetries of two free complex Weyl fermions, which take the form $\\mathbb{Z}_k$ for each primitive Pythagorean triple $a^2 + b^2 = k^2$. The theory is self-dual under gauging any of these symmetries, and so to each there is associated a non-invertible topological defect. We study the properties of these lines, and show that any conformal boundary condition of two Dirac fermions that preserves a $U(1)^2$ symmetry can"},"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":true,"formal_links_present":true},"canonical_record":{"source":{"id":"2605.13952","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-th","submitted_at":"2026-05-13T18:00:00Z","cross_cats_sorted":["cond-mat.str-el"],"title_canon_sha256":"858b8fac8d46e52b43701f15706b39efce9cc0d16bceae0e317a79eb8618ef46","abstract_canon_sha256":"1af71e433f0749915045deb901ae54571be81719fcb4506dec86e664b450042b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:39:13.719995Z","signature_b64":"E685N2N+Gc0/Q+13cX0KULvChdL2KP8c3rEPyd2pMvtTce4I4bZEEsH2SX5R/b3AoS5wF1NjXHE8x97JqhqyAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7352ebaac7a015770e8ee50a22773141465dd543640e31024b565c34e258dedc","last_reissued_at":"2026-05-17T23:39:13.719445Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:39:13.719445Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Non-Invertible Symmetries and Boundaries for Two-Dimensional Fermions","license":"http://creativecommons.org/licenses/by/4.0/","headline":"Two free complex Weyl fermions have anomaly-free Z_k symmetries for each primitive Pythagorean triple, each producing a non-invertible defect that generates all U(1)^2-preserving conformal boundaries.","cross_cats":["cond-mat.str-el"],"primary_cat":"hep-th","authors_text":"Guillermo Arias-Tamargo, Maxwell L. Vel\\'asquez Cotini Hutt, Philip Boyle Smith, Rishi Mouland","submitted_at":"2026-05-13T18:00:00Z","abstract_excerpt":"We study the relation between boundary conditions and categorical symmetries of two-dimensional fermionic conformal field theories. We determine all anomaly-free invertible global symmetries of two free complex Weyl fermions, which take the form $\\mathbb{Z}_k$ for each primitive Pythagorean triple $a^2 + b^2 = k^2$. The theory is self-dual under gauging any of these symmetries, and so to each there is associated a non-invertible topological defect. We study the properties of these lines, and show that any conformal boundary condition of two Dirac fermions that preserves a $U(1)^2$ symmetry can"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"We determine all anomaly-free invertible global symmetries of two free complex Weyl fermions, which take the form Z_k for each primitive Pythagorean triple a^2 + b^2 = k^2. ... any conformal boundary condition of two Dirac fermions that preserves a U(1)^2 symmetry can be found by dressing a trivial Dirichlet boundary with one of them.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The assumption that gauging any of these Z_k symmetries renders the theory self-dual, allowing the non-invertible defects to be well-defined and to generate all listed boundary conditions without additional anomalies or inconsistencies.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Z_k symmetries from Pythagorean triples in two free Weyl fermions yield non-invertible defects that generate all U(1)^2-preserving boundaries for two Dirac fermions.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Two free complex Weyl fermions have anomaly-free Z_k symmetries for each primitive Pythagorean triple, each producing a non-invertible defect that generates all U(1)^2-preserving conformal boundaries.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"94a029c48ab36543f9ab42f57801bf93ccb89ac64135b73770341dcabfdf34d6"},"source":{"id":"2605.13952","kind":"arxiv","version":1},"verdict":{"id":"3d10c23c-1d45-4a87-b1f3-1a14bc362b6e","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-15T02:42:47.833723Z","strongest_claim":"We determine all anomaly-free invertible global symmetries of two free complex Weyl fermions, which take the form Z_k for each primitive Pythagorean triple a^2 + b^2 = k^2. ... any conformal boundary condition of two Dirac fermions that preserves a U(1)^2 symmetry can be found by dressing a trivial Dirichlet boundary with one of them.","one_line_summary":"Z_k symmetries from Pythagorean triples in two free Weyl fermions yield non-invertible defects that generate all U(1)^2-preserving boundaries for two Dirac fermions.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The assumption that gauging any of these Z_k symmetries renders the theory self-dual, allowing the non-invertible defects to be well-defined and to generate all listed boundary conditions without additional anomalies or inconsistencies.","pith_extraction_headline":"Two free complex Weyl fermions have anomaly-free Z_k symmetries for each primitive Pythagorean triple, each producing a non-invertible defect that generates all U(1)^2-preserving conformal boundaries."},"references":{"count":58,"sample":[{"doi":"","year":2018,"title":"K. Jensen, E. Shaverin and A. Yarom,’t Hooft anomalies and boundaries,Journal of High Energy Physics2018(2018)","work_id":"43148e46-6935-4062-8736-e444a996ad89","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2021,"title":"R. Thorngren and Y. Wang,Anomalous symmetries end at the boundary,Journal of High Energy Physics2021(2021)","work_id":"248046c4-dff4-4836-93ed-7711a068cc04","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2017,"title":"Boundary conformal field theory and symmetry protected topological phases in $2+1$ dimensions","work_id":"f0a3a51d-1b9c-4493-9308-ed15528f311f","ref_index":3,"cited_arxiv_id":"1704.01193","is_internal_anchor":true},{"doi":"","year":2024,"title":"L. Li, C.-T. Hsieh, Y. Yao and M. Oshikawa,Boundary conditions and anomalies of conformal field theories in 1+1 dimensions,Phys. Rev. B110(2024) 045118 [2205.11190]","work_id":"bbf787b7-5fc1-4e59-8a30-dcac7203080b","ref_index":4,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2020,"title":"Boyle Smith and D","work_id":"324954ca-8172-433a-b6aa-88ce753dfbbf","ref_index":5,"cited_arxiv_id":"","is_internal_anchor":false}],"resolved_work":58,"snapshot_sha256":"b910e89ab18fd0c1b1a4d142b30257fecb63ca67b6a00aaa66efc282b62e4c08","internal_anchors":15},"formal_canon":{"evidence_count":2,"snapshot_sha256":"d4ac5f20893586d7e69329e1415eabec4504d92dbe7ed3bce20714af8007fee5"},"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":"2605.13952","created_at":"2026-05-17T23:39:13.719536+00:00"},{"alias_kind":"arxiv_version","alias_value":"2605.13952v1","created_at":"2026-05-17T23:39:13.719536+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.13952","created_at":"2026-05-17T23:39:13.719536+00:00"},{"alias_kind":"pith_short_12","alias_value":"ONJOXKWHUAKX","created_at":"2026-05-18T12:33:37.589309+00:00"},{"alias_kind":"pith_short_16","alias_value":"ONJOXKWHUAKXODUO","created_at":"2026-05-18T12:33:37.589309+00:00"},{"alias_kind":"pith_short_8","alias_value":"ONJOXKWH","created_at":"2026-05-18T12:33:37.589309+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2605.19363","citing_title":"Non-invertible Symmetries in Weyl Fermions, and Applications to Fermion-Boundary Scattering Problem","ref_index":33,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":2,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/ONJOXKWHUAKXODUO4UFCE5ZRIF","json":"https://pith.science/pith/ONJOXKWHUAKXODUO4UFCE5ZRIF.json","graph_json":"https://pith.science/api/pith-number/ONJOXKWHUAKXODUO4UFCE5ZRIF/graph.json","events_json":"https://pith.science/api/pith-number/ONJOXKWHUAKXODUO4UFCE5ZRIF/events.json","paper":"https://pith.science/paper/ONJOXKWH"},"agent_actions":{"view_html":"https://pith.science/pith/ONJOXKWHUAKXODUO4UFCE5ZRIF","download_json":"https://pith.science/pith/ONJOXKWHUAKXODUO4UFCE5ZRIF.json","view_paper":"https://pith.science/paper/ONJOXKWH","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2605.13952&json=true","fetch_graph":"https://pith.science/api/pith-number/ONJOXKWHUAKXODUO4UFCE5ZRIF/graph.json","fetch_events":"https://pith.science/api/pith-number/ONJOXKWHUAKXODUO4UFCE5ZRIF/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ONJOXKWHUAKXODUO4UFCE5ZRIF/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ONJOXKWHUAKXODUO4UFCE5ZRIF/action/storage_attestation","attest_author":"https://pith.science/pith/ONJOXKWHUAKXODUO4UFCE5ZRIF/action/author_attestation","sign_citation":"https://pith.science/pith/ONJOXKWHUAKXODUO4UFCE5ZRIF/action/citation_signature","submit_replication":"https://pith.science/pith/ONJOXKWHUAKXODUO4UFCE5ZRIF/action/replication_record"}},"created_at":"2026-05-17T23:39:13.719536+00:00","updated_at":"2026-05-17T23:39:13.719536+00:00"}