{"paper":{"title":"Exact results for the Hubbard model on bipartite lattices in spatial dimensions $d>1$: Seven theorems from the full [SU(2)$\\times$SU(2)$\\times$U(1)]/$\\mathbb{Z}_2^2$ symmetry","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"The Hubbard model on bipartite lattices in d>1 obeys seven exact theorems derived from its full [SU(2)×SU(2)×U(1)]/ℤ₂² symmetry.","cross_cats":[],"primary_cat":"cond-mat.str-el","authors_text":"J. M. P. Carmelo","submitted_at":"2026-04-28T14:41:14Z","abstract_excerpt":"There are few exact results for the Hubbard model on bipartite lattices of spatial dimension $d>1$. Nevertheless, the Hubbard model with transfer integral $t$ and onsite repulsion $U$ on bipartite lattices with $N_a$ sites, such as the square, honeycomb, cubic, body-centered cubic, face-centered cubic, and diamond lattices, provides the simplest toy model for describing electronic correlations in many condensed-matter systems and is therefore a quantum problem of considerable physical interest. Seven exact theorems that provide new physical insight into the model are established. Overall, the "},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"Seven exact theorems that provide new physical insight into the model are established. Overall, the exact framework based on physical spins and physical η-spins for the Hubbard model on bipartite lattices of spatial dimension d>1 introduced in this paper offers a robust foundation for future studies.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The full [SU(2)×SU(2)×U(1)]/Z₂² symmetry applies exactly to the Hubbard model on bipartite lattices in d>1 and generates the seven theorems without additional assumptions or approximations.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Seven exact theorems for the Hubbard model on bipartite lattices in d>1 are derived from its full [SU(2)×SU(2)×U(1)]/Z₂² symmetry, introducing a framework of physical spins and η-spins.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"The Hubbard model on bipartite lattices in d>1 obeys seven exact theorems derived from its full [SU(2)×SU(2)×U(1)]/ℤ₂² symmetry.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"05548ec774d540395b5dec0993331758da5dcc3f09d7e54e02fb97b7288855e0"},"source":{"id":"2604.25712","kind":"arxiv","version":2},"verdict":{"id":"e11cb85c-e802-44c9-9fda-9081c348c8c7","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-07T14:36:28.234328Z","strongest_claim":"Seven exact theorems that provide new physical insight into the model are established. Overall, the exact framework based on physical spins and physical η-spins for the Hubbard model on bipartite lattices of spatial dimension d>1 introduced in this paper offers a robust foundation for future studies.","one_line_summary":"Seven exact theorems for the Hubbard model on bipartite lattices in d>1 are derived from its full [SU(2)×SU(2)×U(1)]/Z₂² symmetry, introducing a framework of physical spins and η-spins.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The full [SU(2)×SU(2)×U(1)]/Z₂² symmetry applies exactly to the Hubbard model on bipartite lattices in d>1 and generates the seven theorems without additional assumptions or approximations.","pith_extraction_headline":"The Hubbard model on bipartite lattices in d>1 obeys seven exact theorems derived from its full [SU(2)×SU(2)×U(1)]/ℤ₂² symmetry."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2604.25712/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"doi_compliance","ran_at":"2026-05-19T20:51:32.990240Z","status":"completed","version":"1.0.0","findings_count":0}],"snapshot_sha256":"c7a20fa3e23d0dd52e76d90b0fe0d2738ead1fdda164f5bb3c18637999cc3846"},"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"}