{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2005:ZTOQAXRUTMWP4OABIDWD6BCMYR","short_pith_number":"pith:ZTOQAXRU","schema_version":"1.0","canonical_sha256":"ccdd005e349b2cfe380140ec3f044cc45a25868b1bed39165fd3c3ed78055b1c","source":{"kind":"arxiv","id":"hep-lat/0512021","version":1},"attestation_state":"computed","paper":{"title":"Stability of lattice QCD simulations and the thermodynamic limit","license":"","headline":"","cross_cats":[],"primary_cat":"hep-lat","authors_text":"L. Del Debbio, L. Giusti, M. L\\\"uscher, N. Tantalo, R. Petronzio","submitted_at":"2005-12-15T14:19:49Z","abstract_excerpt":"We study the spectral gap of the Wilson--Dirac operator in two-flavour lattice QCD as a function of the lattice spacing $a$, the space-time volume $V$ and the current-quark mass $m$. It turns out that the median of the probability distribution of the gap scales proportionally to $m$ and that its width is practically equal to $a/\\sqrt{V}$. In particular, numerical simulations are safe from accidental zero modes in the large-volume regime of QCD."},"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":false,"formal_links_present":false},"canonical_record":{"source":{"id":"hep-lat/0512021","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"hep-lat","submitted_at":"2005-12-15T14:19:49Z","cross_cats_sorted":[],"title_canon_sha256":"4472a819815241e67ffbd4cb346a876d934a2786f6fde4fc83a364b63048b044","abstract_canon_sha256":"c605b36cf5141d31b81986c85072ea952d3132376fe218b578506b0fdb4ab256"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T16:55:26.610374Z","signature_b64":"wIhhJxf08dpPKAqwzMHTNc5ZBPf3j2jw65ZLcLSMPCGAsrdTC4bVGAzzDeQPsFPy73NweAQIm/6lwlBovooEBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ccdd005e349b2cfe380140ec3f044cc45a25868b1bed39165fd3c3ed78055b1c","last_reissued_at":"2026-07-04T16:55:26.609950Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T16:55:26.609950Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Stability of lattice QCD simulations and the thermodynamic limit","license":"","headline":"","cross_cats":[],"primary_cat":"hep-lat","authors_text":"L. Del Debbio, L. Giusti, M. L\\\"uscher, N. Tantalo, R. Petronzio","submitted_at":"2005-12-15T14:19:49Z","abstract_excerpt":"We study the spectral gap of the Wilson--Dirac operator in two-flavour lattice QCD as a function of the lattice spacing $a$, the space-time volume $V$ and the current-quark mass $m$. It turns out that the median of the probability distribution of the gap scales proportionally to $m$ and that its width is practically equal to $a/\\sqrt{V}$. In particular, numerical simulations are safe from accidental zero modes in the large-volume regime of QCD."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"hep-lat/0512021","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/hep-lat/0512021/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"hep-lat/0512021","created_at":"2026-07-04T16:55:26.610014+00:00"},{"alias_kind":"arxiv_version","alias_value":"hep-lat/0512021v1","created_at":"2026-07-04T16:55:26.610014+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.hep-lat/0512021","created_at":"2026-07-04T16:55:26.610014+00:00"},{"alias_kind":"pith_short_12","alias_value":"ZTOQAXRUTMWP","created_at":"2026-07-04T16:55:26.610014+00:00"},{"alias_kind":"pith_short_16","alias_value":"ZTOQAXRUTMWP4OAB","created_at":"2026-07-04T16:55:26.610014+00:00"},{"alias_kind":"pith_short_8","alias_value":"ZTOQAXRU","created_at":"2026-07-04T16:55:26.610014+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/ZTOQAXRUTMWP4OABIDWD6BCMYR","json":"https://pith.science/pith/ZTOQAXRUTMWP4OABIDWD6BCMYR.json","graph_json":"https://pith.science/api/pith-number/ZTOQAXRUTMWP4OABIDWD6BCMYR/graph.json","events_json":"https://pith.science/api/pith-number/ZTOQAXRUTMWP4OABIDWD6BCMYR/events.json","paper":"https://pith.science/paper/ZTOQAXRU"},"agent_actions":{"view_html":"https://pith.science/pith/ZTOQAXRUTMWP4OABIDWD6BCMYR","download_json":"https://pith.science/pith/ZTOQAXRUTMWP4OABIDWD6BCMYR.json","view_paper":"https://pith.science/paper/ZTOQAXRU","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=hep-lat/0512021&json=true","fetch_graph":"https://pith.science/api/pith-number/ZTOQAXRUTMWP4OABIDWD6BCMYR/graph.json","fetch_events":"https://pith.science/api/pith-number/ZTOQAXRUTMWP4OABIDWD6BCMYR/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ZTOQAXRUTMWP4OABIDWD6BCMYR/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ZTOQAXRUTMWP4OABIDWD6BCMYR/action/storage_attestation","attest_author":"https://pith.science/pith/ZTOQAXRUTMWP4OABIDWD6BCMYR/action/author_attestation","sign_citation":"https://pith.science/pith/ZTOQAXRUTMWP4OABIDWD6BCMYR/action/citation_signature","submit_replication":"https://pith.science/pith/ZTOQAXRUTMWP4OABIDWD6BCMYR/action/replication_record"}},"created_at":"2026-07-04T16:55:26.610014+00:00","updated_at":"2026-07-04T16:55:26.610014+00:00"}