{"paper":{"title":"$c=1$ strings as a matrix integral","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"The c=1 string's perturbative S-matrix is equivalently described by a double-scaled matrix integral with spectral curve x(z)=2√2 cos(z), y(z)=sin(z).","cross_cats":[],"primary_cat":"hep-th","authors_text":"Lorenz Eberhardt, Scott Collier, Victor A. Rodriguez","submitted_at":"2026-04-07T18:00:00Z","abstract_excerpt":"We study the perturbative $S$-matrix of the $c=1$ string and show that it admits a description in terms of a double-scaled (0+0)-dimensional matrix integral based on the spectral curve $\\mathsf{x}(z) = 2\\sqrt{2}\\cos(z)$, $\\mathsf{y}(z)=\\sin(z)$. Combined with the famous duality to matrix quantum mechanics, this establishes a triality between three formulations of the theory: the worldsheet description, matrix quantum mechanics, and a matrix integral.\n  Starting from the intersection number expressions for the complex Liouville string, we derive closed-form Feynman rule expressions for the $c=1"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"We study the perturbative S-matrix of the c=1 string and show that it admits a description in terms of a double-scaled (0+0)-dimensional matrix integral based on the spectral curve x(z) = 2√2 cos(z), y(z)=sin(z). Combined with the famous duality to matrix quantum mechanics, this establishes a triality between three formulations of the theory: the worldsheet description, matrix quantum mechanics, and a matrix integral.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The physical S-matrix elements are recovered by restriction to the first Brillouin zone followed by analytic continuation to Lorentzian kinematics from the intersection-number expressions that describe a discretized target space.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"The c=1 string perturbative S-matrix equals a double-scaled (0+0)-dimensional matrix integral on the spectral curve x(z)=2√2 cos(z), y(z)=sin(z), establishing triality with worldsheet and matrix quantum mechanics descriptions.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"The c=1 string's perturbative S-matrix is equivalently described by a double-scaled matrix integral with spectral curve x(z)=2√2 cos(z), y(z)=sin(z).","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"0082cdb49681b6f6da57f1d32407422864573b0248fdd2609b453904952ec3af"},"source":{"id":"2604.06301","kind":"arxiv","version":2},"verdict":{"id":"967e7f46-753f-4d12-b2d3-43449f5aa734","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-10T18:50:01.303301Z","strongest_claim":"We study the perturbative S-matrix of the c=1 string and show that it admits a description in terms of a double-scaled (0+0)-dimensional matrix integral based on the spectral curve x(z) = 2√2 cos(z), y(z)=sin(z). Combined with the famous duality to matrix quantum mechanics, this establishes a triality between three formulations of the theory: the worldsheet description, matrix quantum mechanics, and a matrix integral.","one_line_summary":"The c=1 string perturbative S-matrix equals a double-scaled (0+0)-dimensional matrix integral on the spectral curve x(z)=2√2 cos(z), y(z)=sin(z), establishing triality with worldsheet and matrix quantum mechanics descriptions.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The physical S-matrix elements are recovered by restriction to the first Brillouin zone followed by analytic continuation to Lorentzian kinematics from the intersection-number expressions that describe a discretized target space.","pith_extraction_headline":"The c=1 string's perturbative S-matrix is equivalently described by a double-scaled matrix integral with spectral curve x(z)=2√2 cos(z), y(z)=sin(z)."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2604.06301/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":2,"snapshot_sha256":"f1b9c8bd040b0f5bdb0f78ba7581a5bcf0a205c6d9ac89ba91a09caed99f120f"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}