{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:YD6GZVTPBAB3MWU2TDRTAR7WJK","short_pith_number":"pith:YD6GZVTP","schema_version":"1.0","canonical_sha256":"c0fc6cd66f0803b65a9a98e33047f64a9986e7e3829a1ffb5a02c796bf3499a5","source":{"kind":"arxiv","id":"2605.17326","version":1},"attestation_state":"computed","paper":{"title":"Noise scheduling and linear dynamics in diffusion models on Lie groups","license":"http://creativecommons.org/licenses/by/4.0/","headline":"A specific noise schedule in Lie group diffusion makes the Wilson action expectation decay linearly with time.","cross_cats":[],"primary_cat":"hep-lat","authors_text":"Javad Komijani","submitted_at":"2026-05-17T08:34:31Z","abstract_excerpt":"We investigate the role of the noise schedule in diffusion processes on Lie groups, with particular emphasis on applications to lattice gauge theory. We show that a specific noise schedule leads to a linear decay of the expectation value of the Wilson action as a function of diffusion time. 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."},"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":true,"formal_links_present":false},"canonical_record":{"source":{"id":"2605.17326","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-lat","submitted_at":"2026-05-17T08:34:31Z","cross_cats_sorted":[],"title_canon_sha256":"8f0650f3da75ed613ff06334de416b0bd2b51eeaa8e2ec39f2d016d4afa7be7d","abstract_canon_sha256":"7e867cdaec8a4a4187ccf3aff645a8831932766659323518afcf18fb8ed9a235"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-20T00:03:52.248893Z","signature_b64":"3sUqptagdYsHQ1M83FaI/UMjRLjq2cg3NtIOz4lwstzeE2ZOkMGJZ3qkg0DX7CXpnqB3W5GWW7IivtniQ0wNDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c0fc6cd66f0803b65a9a98e33047f64a9986e7e3829a1ffb5a02c796bf3499a5","last_reissued_at":"2026-05-20T00:03:52.247980Z","signature_status":"signed_v1","first_computed_at":"2026-05-20T00:03:52.247980Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Noise scheduling and linear dynamics in diffusion models on Lie groups","license":"http://creativecommons.org/licenses/by/4.0/","headline":"A specific noise schedule in Lie group diffusion makes the Wilson action expectation decay linearly with time.","cross_cats":[],"primary_cat":"hep-lat","authors_text":"Javad Komijani","submitted_at":"2026-05-17T08:34:31Z","abstract_excerpt":"We investigate the role of the noise schedule in diffusion processes on Lie groups, with particular emphasis on applications to lattice gauge theory. We show that a specific noise schedule leads to a linear decay of the expectation value of the Wilson action as a function of diffusion time. 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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2605.17326","created_at":"2026-05-20T00:03:52.248113+00:00"},{"alias_kind":"arxiv_version","alias_value":"2605.17326v1","created_at":"2026-05-20T00:03:52.248113+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.17326","created_at":"2026-05-20T00:03:52.248113+00:00"},{"alias_kind":"pith_short_12","alias_value":"YD6GZVTPBAB3","created_at":"2026-05-20T00:03:52.248113+00:00"},{"alias_kind":"pith_short_16","alias_value":"YD6GZVTPBAB3MWU2","created_at":"2026-05-20T00:03:52.248113+00:00"},{"alias_kind":"pith_short_8","alias_value":"YD6GZVTP","created_at":"2026-05-20T00:03:52.248113+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/YD6GZVTPBAB3MWU2TDRTAR7WJK","json":"https://pith.science/pith/YD6GZVTPBAB3MWU2TDRTAR7WJK.json","graph_json":"https://pith.science/api/pith-number/YD6GZVTPBAB3MWU2TDRTAR7WJK/graph.json","events_json":"https://pith.science/api/pith-number/YD6GZVTPBAB3MWU2TDRTAR7WJK/events.json","paper":"https://pith.science/paper/YD6GZVTP"},"agent_actions":{"view_html":"https://pith.science/pith/YD6GZVTPBAB3MWU2TDRTAR7WJK","download_json":"https://pith.science/pith/YD6GZVTPBAB3MWU2TDRTAR7WJK.json","view_paper":"https://pith.science/paper/YD6GZVTP","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2605.17326&json=true","fetch_graph":"https://pith.science/api/pith-number/YD6GZVTPBAB3MWU2TDRTAR7WJK/graph.json","fetch_events":"https://pith.science/api/pith-number/YD6GZVTPBAB3MWU2TDRTAR7WJK/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/YD6GZVTPBAB3MWU2TDRTAR7WJK/action/timestamp_anchor","attest_storage":"https://pith.science/pith/YD6GZVTPBAB3MWU2TDRTAR7WJK/action/storage_attestation","attest_author":"https://pith.science/pith/YD6GZVTPBAB3MWU2TDRTAR7WJK/action/author_attestation","sign_citation":"https://pith.science/pith/YD6GZVTPBAB3MWU2TDRTAR7WJK/action/citation_signature","submit_replication":"https://pith.science/pith/YD6GZVTPBAB3MWU2TDRTAR7WJK/action/replication_record"}},"created_at":"2026-05-20T00:03:52.248113+00:00","updated_at":"2026-05-20T00:03:52.248113+00:00"}