{"paper":{"title":"Certified spectral functions from lattice Monte Carlo data","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.str-el","hep-th"],"primary_cat":"hep-lat","authors_text":"Antoine Tilloy, Sophie Mutzel","submitted_at":"2026-06-08T17:47:57Z","abstract_excerpt":"The Monte Carlo method, applied to lattice quantum field theory, gives access to Euclidean correlation functions with well-understood error bars. Recovering the observables one cares about, such as the spectral density, requires solving an ill-posed inverse problem, usually tackled with heuristics that lose rigorous control of the error. Instead of trying to find the ``best'' spectral density $\\rho(\\omega)$, we ask how small or large linear functionals $\\int_{\\mathbb{R}^+} G(\\omega) \\rho(\\omega) \\mathrm{d} \\omega$ of it can be, given the Monte Carlo data and the reflection positivity of the la"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.09791","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/2606.09791/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"}