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We compare this with Euclidean diffusion models, where such behavior requires an explicitly designed drift term, while in the Lie-group setting it arises naturally."},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"A specific noise schedule leads to a linear decay of the expectation value of the Wilson action as a function of diffusion time in diffusion processes on Lie groups.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The diffusion process is defined directly on the Lie group manifold with the chosen noise schedule, and the Wilson action remains a well-defined observable whose expectation value can be tracked linearly without additional corrections from the group structure or discretization.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"A specific noise schedule in Lie-group diffusion models yields linear decay of the Wilson action expectation value versus diffusion time, emerging naturally without an added drift term.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"A specific noise schedule in Lie group diffusion makes the Wilson action expectation decay linearly with time.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"34fbb5c099fa5f2030287aae97ef4ee16bd85a6df4f9d27c09cfc6829d81c84f"},"source":{"id":"2605.17326","kind":"arxiv","version":1},"verdict":{"id":"85011d3f-aad4-414f-9610-e4b20d6fa8e2","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-19T22:50:32.781243Z","strongest_claim":"A specific noise schedule leads to a linear decay of the expectation value of the Wilson action as a function of diffusion time in diffusion processes on Lie groups.","one_line_summary":"A specific noise schedule in Lie-group diffusion models yields linear decay of the Wilson action expectation value versus diffusion time, emerging naturally without an added drift term.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The diffusion process is defined directly on the Lie group manifold with the chosen noise schedule, and the Wilson action remains a well-defined observable whose expectation value can be tracked linearly without additional corrections from the group structure or discretization.","pith_extraction_headline":"A specific noise schedule in Lie group diffusion makes the Wilson action expectation decay linearly with time."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.17326/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"doi_compliance","ran_at":"2026-05-19T23:01:51.683931Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_title_agreement","ran_at":"2026-05-19T23:01:19.679959Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"claim_evidence","ran_at":"2026-05-19T21:41:57.813192Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"ai_meta_artifact","ran_at":"2026-05-19T21:33:23.746191Z","status":"skipped","version":"1.0.0","findings_count":0}],"snapshot_sha256":"999885a4b966f64a5d1da80243430ea8f104893ccc214caf3686fa14b85b79f7"},"references":{"count":11,"sample":[{"doi":"","year":1985,"title":"Gardiner, Crispin W. , title =. 1985 , edition =","work_id":"43b42b56-e03e-49fb-a603-d18c87ce22e9","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2020,"title":"Score-Based Generative Modeling through Stochastic Differential Equations","work_id":"d9110e53-a5d4-4794-a4c5-a575e91c31ad","ref_index":2,"cited_arxiv_id":"2011.13456","is_internal_anchor":true},{"doi":"","year":2020,"title":"Denoising Diffusion Probabilistic Models","work_id":"dc023f4e-7c79-471c-b713-deeb559ba010","ref_index":3,"cited_arxiv_id":"2006.11239","is_internal_anchor":true},{"doi":"","year":2022,"title":"Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow","work_id":"a1989e1b-d66d-4533-be3a-fb9c5fd62290","ref_index":4,"cited_arxiv_id":"2209.03003","is_internal_anchor":true},{"doi":"","year":2022,"title":"Flow Matching for Generative Modeling","work_id":"6edb71c4-5d64-40af-a394-9757ea051a36","ref_index":5,"cited_arxiv_id":"2210.02747","is_internal_anchor":true}],"resolved_work":11,"snapshot_sha256":"e4f4af36520456855e0b3c04717cad1701722558116d47dc9186dcff6bc0de8b","internal_anchors":5},"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"}