{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2005:ZTOQAXRUTMWP4OABIDWD6BCMYR","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"c605b36cf5141d31b81986c85072ea952d3132376fe218b578506b0fdb4ab256","cross_cats_sorted":[],"license":"","primary_cat":"hep-lat","submitted_at":"2005-12-15T14:19:49Z","title_canon_sha256":"4472a819815241e67ffbd4cb346a876d934a2786f6fde4fc83a364b63048b044"},"schema_version":"1.0","source":{"id":"hep-lat/0512021","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"hep-lat/0512021","created_at":"2026-07-04T16:55:26Z"},{"alias_kind":"arxiv_version","alias_value":"hep-lat/0512021v1","created_at":"2026-07-04T16:55:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.hep-lat/0512021","created_at":"2026-07-04T16:55:26Z"},{"alias_kind":"pith_short_12","alias_value":"ZTOQAXRUTMWP","created_at":"2026-07-04T16:55:26Z"},{"alias_kind":"pith_short_16","alias_value":"ZTOQAXRUTMWP4OAB","created_at":"2026-07-04T16:55:26Z"},{"alias_kind":"pith_short_8","alias_value":"ZTOQAXRU","created_at":"2026-07-04T16:55:26Z"}],"graph_snapshots":[{"event_id":"sha256:0a2f602f184dc29938bb0b6b00c2d96bd4c1a01bf04cb453a34d816d59288939","target":"graph","created_at":"2026-07-04T16:55:26Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/hep-lat/0512021/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"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.","authors_text":"L. Del Debbio, L. Giusti, M. L\\\"uscher, N. Tantalo, R. Petronzio","cross_cats":[],"headline":"","license":"","primary_cat":"hep-lat","submitted_at":"2005-12-15T14:19:49Z","title":"Stability of lattice QCD simulations and the thermodynamic limit"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"hep-lat/0512021","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:065202332173ffeec5855546e9961255daf45d4550edf1b97c49507b0de4d965","target":"record","created_at":"2026-07-04T16:55:26Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"c605b36cf5141d31b81986c85072ea952d3132376fe218b578506b0fdb4ab256","cross_cats_sorted":[],"license":"","primary_cat":"hep-lat","submitted_at":"2005-12-15T14:19:49Z","title_canon_sha256":"4472a819815241e67ffbd4cb346a876d934a2786f6fde4fc83a364b63048b044"},"schema_version":"1.0","source":{"id":"hep-lat/0512021","kind":"arxiv","version":1}},"canonical_sha256":"ccdd005e349b2cfe380140ec3f044cc45a25868b1bed39165fd3c3ed78055b1c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ccdd005e349b2cfe380140ec3f044cc45a25868b1bed39165fd3c3ed78055b1c","first_computed_at":"2026-07-04T16:55:26.609950Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T16:55:26.609950Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"wIhhJxf08dpPKAqwzMHTNc5ZBPf3j2jw65ZLcLSMPCGAsrdTC4bVGAzzDeQPsFPy73NweAQIm/6lwlBovooEBg==","signature_status":"signed_v1","signed_at":"2026-07-04T16:55:26.610374Z","signed_message":"canonical_sha256_bytes"},"source_id":"hep-lat/0512021","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:065202332173ffeec5855546e9961255daf45d4550edf1b97c49507b0de4d965","sha256:0a2f602f184dc29938bb0b6b00c2d96bd4c1a01bf04cb453a34d816d59288939"],"state_sha256":"ea2798d0c72ed94da999f7cae4eda58f1a2474e031c323b29e8887502d92e676"}