{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:2VBNOCRRPSBCB5BOV3Q67E324G","short_pith_number":"pith:2VBNOCRR","schema_version":"1.0","canonical_sha256":"d542d70a317c8220f42eaee1ef937ae1a958b2805ec3088d1073ee6a67302258","source":{"kind":"arxiv","id":"1908.02289","version":1},"attestation_state":"computed","paper":{"title":"Gauge Theory And Integrability, III","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech","math-ph","math.MP","nlin.SI"],"primary_cat":"hep-th","authors_text":"Kevin Costello, Masahito Yamazaki","submitted_at":"2019-08-06T18:00:00Z","abstract_excerpt":"We study two-dimensional integrable field theories from the viewpoint of the four-dimensional Chern-Simons-type gauge theory introduced recently. The integrable field theories are realized as effective theories for the four-dimensional theory coupled with two-dimensional surface defects, and we can systematically compute their Lagrangians and the Lax operators satisfying the zero-curvature condition. Our construction includes many known integrable field theories, such as Gross-Neveu models, principal chiral models with Wess-Zumino terms and symmetric-space coset sigma models. Moreover we obtai"},"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":"1908.02289","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2019-08-06T18:00:00Z","cross_cats_sorted":["cond-mat.stat-mech","math-ph","math.MP","nlin.SI"],"title_canon_sha256":"e650923a95c35d97a925ce5220c6ffbc0371ac6571194ef3eb91db1b6f63c6d2","abstract_canon_sha256":"872d94329497b36799ac7bb12e42e4378493ff5004041029f069ce70c8887806"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T23:52:07.149140Z","signature_b64":"pAI/f1ITY769jZls9vvwvB8UbMuXrmsg7dPlMyfjgoTXmddp2a3Tk58mtjvl3+uAO94wow6Dj+PUSusChRbEBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d542d70a317c8220f42eaee1ef937ae1a958b2805ec3088d1073ee6a67302258","last_reissued_at":"2026-07-04T23:52:07.148661Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T23:52:07.148661Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Gauge Theory And Integrability, III","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech","math-ph","math.MP","nlin.SI"],"primary_cat":"hep-th","authors_text":"Kevin Costello, Masahito Yamazaki","submitted_at":"2019-08-06T18:00:00Z","abstract_excerpt":"We study two-dimensional integrable field theories from the viewpoint of the four-dimensional Chern-Simons-type gauge theory introduced recently. The integrable field theories are realized as effective theories for the four-dimensional theory coupled with two-dimensional surface defects, and we can systematically compute their Lagrangians and the Lax operators satisfying the zero-curvature condition. Our construction includes many known integrable field theories, such as Gross-Neveu models, principal chiral models with Wess-Zumino terms and symmetric-space coset sigma models. Moreover we obtai"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.02289","kind":"arxiv","version":1},"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/1908.02289/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":"1908.02289","created_at":"2026-07-04T23:52:07.148716+00:00"},{"alias_kind":"arxiv_version","alias_value":"1908.02289v1","created_at":"2026-07-04T23:52:07.148716+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.02289","created_at":"2026-07-04T23:52:07.148716+00:00"},{"alias_kind":"pith_short_12","alias_value":"2VBNOCRRPSBC","created_at":"2026-07-04T23:52:07.148716+00:00"},{"alias_kind":"pith_short_16","alias_value":"2VBNOCRRPSBCB5BO","created_at":"2026-07-04T23:52:07.148716+00:00"},{"alias_kind":"pith_short_8","alias_value":"2VBNOCRR","created_at":"2026-07-04T23:52:07.148716+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":10,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2606.25660","citing_title":"Lattice non-invertible symmetry from non-commuting transfer matrices","ref_index":72,"is_internal_anchor":false},{"citing_arxiv_id":"2606.30717","citing_title":"The auxiliary-deformed Breitenlohner-Maison model: duality frames and higher-dimensional origin","ref_index":19,"is_internal_anchor":false},{"citing_arxiv_id":"2606.30717","citing_title":"The auxiliary-deformed Breitenlohner-Maison model: duality frames and higher-dimensional origin","ref_index":19,"is_internal_anchor":false},{"citing_arxiv_id":"2605.18213","citing_title":"The classical Yangian symmetry of Auxiliary Field Sigma Models","ref_index":92,"is_internal_anchor":false},{"citing_arxiv_id":"2507.01858","citing_title":"Infinite Dimensional Topological-Holomorphic Symmetry in Three-Dimensions","ref_index":30,"is_internal_anchor":false},{"citing_arxiv_id":"2509.20643","citing_title":"Non-Commutative Gauge Theory at the Beach","ref_index":24,"is_internal_anchor":false},{"citing_arxiv_id":"2602.11288","citing_title":"The Yang-Baxter Sigma Model from Twistor Space","ref_index":5,"is_internal_anchor":false},{"citing_arxiv_id":"2604.26452","citing_title":"Integrable Deformations of the Breitenlohner-Maison Model from 4d Chern-Simons Theory","ref_index":9,"is_internal_anchor":false},{"citing_arxiv_id":"2604.24864","citing_title":"On the structure of higher-dimensional integrable field theories","ref_index":19,"is_internal_anchor":false},{"citing_arxiv_id":"2604.09771","citing_title":"Towards a Carrollian Description of Yang-Mills","ref_index":58,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/2VBNOCRRPSBCB5BOV3Q67E324G","json":"https://pith.science/pith/2VBNOCRRPSBCB5BOV3Q67E324G.json","graph_json":"https://pith.science/api/pith-number/2VBNOCRRPSBCB5BOV3Q67E324G/graph.json","events_json":"https://pith.science/api/pith-number/2VBNOCRRPSBCB5BOV3Q67E324G/events.json","paper":"https://pith.science/paper/2VBNOCRR"},"agent_actions":{"view_html":"https://pith.science/pith/2VBNOCRRPSBCB5BOV3Q67E324G","download_json":"https://pith.science/pith/2VBNOCRRPSBCB5BOV3Q67E324G.json","view_paper":"https://pith.science/paper/2VBNOCRR","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1908.02289&json=true","fetch_graph":"https://pith.science/api/pith-number/2VBNOCRRPSBCB5BOV3Q67E324G/graph.json","fetch_events":"https://pith.science/api/pith-number/2VBNOCRRPSBCB5BOV3Q67E324G/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/2VBNOCRRPSBCB5BOV3Q67E324G/action/timestamp_anchor","attest_storage":"https://pith.science/pith/2VBNOCRRPSBCB5BOV3Q67E324G/action/storage_attestation","attest_author":"https://pith.science/pith/2VBNOCRRPSBCB5BOV3Q67E324G/action/author_attestation","sign_citation":"https://pith.science/pith/2VBNOCRRPSBCB5BOV3Q67E324G/action/citation_signature","submit_replication":"https://pith.science/pith/2VBNOCRRPSBCB5BOV3Q67E324G/action/replication_record"}},"created_at":"2026-07-04T23:52:07.148716+00:00","updated_at":"2026-07-04T23:52:07.148716+00:00"}