{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:TAJ4IWPH4TMX3J3PPOMS2ACMS3","short_pith_number":"pith:TAJ4IWPH","canonical_record":{"source":{"id":"1203.4847","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-lat","submitted_at":"2012-03-21T21:47:18Z","cross_cats_sorted":["hep-th"],"title_canon_sha256":"b2c4d7901879868e1cb1d83f59452b60abe878d0ba062f924ee9c12f73bef9af","abstract_canon_sha256":"71c7fb3143ed3cb6db8f219bde5b16e83adc9fad7c8c78f5e44adcdad8cf3509"},"schema_version":"1.0"},"canonical_sha256":"9813c459e7e4d97da76f7b992d004c96eeaa819e012801e58777a1caea4a9e73","source":{"kind":"arxiv","id":"1203.4847","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1203.4847","created_at":"2026-05-18T03:34:35Z"},{"alias_kind":"arxiv_version","alias_value":"1203.4847v3","created_at":"2026-05-18T03:34:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1203.4847","created_at":"2026-05-18T03:34:35Z"},{"alias_kind":"pith_short_12","alias_value":"TAJ4IWPH4TMX","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_16","alias_value":"TAJ4IWPH4TMX3J3P","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_8","alias_value":"TAJ4IWPH","created_at":"2026-05-18T12:27:23Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:TAJ4IWPH4TMX3J3PPOMS2ACMS3","target":"record","payload":{"canonical_record":{"source":{"id":"1203.4847","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-lat","submitted_at":"2012-03-21T21:47:18Z","cross_cats_sorted":["hep-th"],"title_canon_sha256":"b2c4d7901879868e1cb1d83f59452b60abe878d0ba062f924ee9c12f73bef9af","abstract_canon_sha256":"71c7fb3143ed3cb6db8f219bde5b16e83adc9fad7c8c78f5e44adcdad8cf3509"},"schema_version":"1.0"},"canonical_sha256":"9813c459e7e4d97da76f7b992d004c96eeaa819e012801e58777a1caea4a9e73","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:34:35.655829Z","signature_b64":"t34pfjDrVL7Nf0RvXOOzXwp9pjiF/juYovsrqLqmB471JI528bHYoyIWkAkc/hkint5HwCc65cmrn5WPxQegAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9813c459e7e4d97da76f7b992d004c96eeaa819e012801e58777a1caea4a9e73","last_reissued_at":"2026-05-18T03:34:35.655348Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:34:35.655348Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1203.4847","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:34:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nNg+p9Xg5sLInhIhMbmb9sLALnbojC8u1+i1ERWMIAkC7D2ybfK1sevso+iKDnooP5fKPyWijDcjBdOX4sE2DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T00:19:49.125072Z"},"content_sha256":"167567cb5dfcfe70602a3acd7b1b0bed46ac05c97ce43df70493a91e2ee5c3b8","schema_version":"1.0","event_id":"sha256:167567cb5dfcfe70602a3acd7b1b0bed46ac05c97ce43df70493a91e2ee5c3b8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:TAJ4IWPH4TMX3J3PPOMS2ACMS3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Enumerating Gribov copies on the lattice","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th"],"primary_cat":"hep-lat","authors_text":"Ciaran Hughes, Dhagash Mehta, Jon-Ivar Skullerud","submitted_at":"2012-03-21T21:47:18Z","abstract_excerpt":"In the modern formulation of lattice gauge-fixing, the gauge fixing condition is written in terms of the minima or stationary points (collectively called solutions) of a gauge-fixing functional. Due to the non-linearity of this functional, it usually has many solutions called Gribov copies. The dependence of the number of Gribov copies, n[U] on the different gauge orbits plays an important role in constructing the Faddeev-Popov procedure and hence in realising the BRST symmetry on the lattice. Here, we initiate a study of counting n[U] for different orbits using three complimentary methods: 1."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.4847","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:34:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NnIL+h+9ACFmuGWVom9oaqaUZ96GP+OyK/G9v5wbegLsE2hB28eBUBU2RIUycowYu2fmUBgGtlo55m0VxlZUAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T00:19:49.125449Z"},"content_sha256":"e46aff2ee4654846d14a8adb97d2c97dbc057ac9492b1a85ad03101617752318","schema_version":"1.0","event_id":"sha256:e46aff2ee4654846d14a8adb97d2c97dbc057ac9492b1a85ad03101617752318"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TAJ4IWPH4TMX3J3PPOMS2ACMS3/bundle.json","state_url":"https://pith.science/pith/TAJ4IWPH4TMX3J3PPOMS2ACMS3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TAJ4IWPH4TMX3J3PPOMS2ACMS3/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-27T00:19:49Z","links":{"resolver":"https://pith.science/pith/TAJ4IWPH4TMX3J3PPOMS2ACMS3","bundle":"https://pith.science/pith/TAJ4IWPH4TMX3J3PPOMS2ACMS3/bundle.json","state":"https://pith.science/pith/TAJ4IWPH4TMX3J3PPOMS2ACMS3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TAJ4IWPH4TMX3J3PPOMS2ACMS3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:TAJ4IWPH4TMX3J3PPOMS2ACMS3","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":"71c7fb3143ed3cb6db8f219bde5b16e83adc9fad7c8c78f5e44adcdad8cf3509","cross_cats_sorted":["hep-th"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-lat","submitted_at":"2012-03-21T21:47:18Z","title_canon_sha256":"b2c4d7901879868e1cb1d83f59452b60abe878d0ba062f924ee9c12f73bef9af"},"schema_version":"1.0","source":{"id":"1203.4847","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1203.4847","created_at":"2026-05-18T03:34:35Z"},{"alias_kind":"arxiv_version","alias_value":"1203.4847v3","created_at":"2026-05-18T03:34:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1203.4847","created_at":"2026-05-18T03:34:35Z"},{"alias_kind":"pith_short_12","alias_value":"TAJ4IWPH4TMX","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_16","alias_value":"TAJ4IWPH4TMX3J3P","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_8","alias_value":"TAJ4IWPH","created_at":"2026-05-18T12:27:23Z"}],"graph_snapshots":[{"event_id":"sha256:e46aff2ee4654846d14a8adb97d2c97dbc057ac9492b1a85ad03101617752318","target":"graph","created_at":"2026-05-18T03:34:35Z","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"},"paper":{"abstract_excerpt":"In the modern formulation of lattice gauge-fixing, the gauge fixing condition is written in terms of the minima or stationary points (collectively called solutions) of a gauge-fixing functional. Due to the non-linearity of this functional, it usually has many solutions called Gribov copies. The dependence of the number of Gribov copies, n[U] on the different gauge orbits plays an important role in constructing the Faddeev-Popov procedure and hence in realising the BRST symmetry on the lattice. Here, we initiate a study of counting n[U] for different orbits using three complimentary methods: 1.","authors_text":"Ciaran Hughes, Dhagash Mehta, Jon-Ivar Skullerud","cross_cats":["hep-th"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-lat","submitted_at":"2012-03-21T21:47:18Z","title":"Enumerating Gribov copies on the lattice"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.4847","kind":"arxiv","version":3},"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":"sha256:167567cb5dfcfe70602a3acd7b1b0bed46ac05c97ce43df70493a91e2ee5c3b8","target":"record","created_at":"2026-05-18T03:34:35Z","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":"71c7fb3143ed3cb6db8f219bde5b16e83adc9fad7c8c78f5e44adcdad8cf3509","cross_cats_sorted":["hep-th"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-lat","submitted_at":"2012-03-21T21:47:18Z","title_canon_sha256":"b2c4d7901879868e1cb1d83f59452b60abe878d0ba062f924ee9c12f73bef9af"},"schema_version":"1.0","source":{"id":"1203.4847","kind":"arxiv","version":3}},"canonical_sha256":"9813c459e7e4d97da76f7b992d004c96eeaa819e012801e58777a1caea4a9e73","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9813c459e7e4d97da76f7b992d004c96eeaa819e012801e58777a1caea4a9e73","first_computed_at":"2026-05-18T03:34:35.655348Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:34:35.655348Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"t34pfjDrVL7Nf0RvXOOzXwp9pjiF/juYovsrqLqmB471JI528bHYoyIWkAkc/hkint5HwCc65cmrn5WPxQegAg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:34:35.655829Z","signed_message":"canonical_sha256_bytes"},"source_id":"1203.4847","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:167567cb5dfcfe70602a3acd7b1b0bed46ac05c97ce43df70493a91e2ee5c3b8","sha256:e46aff2ee4654846d14a8adb97d2c97dbc057ac9492b1a85ad03101617752318"],"state_sha256":"8dfa8f669ca57451fbb1eb572a2dd00b15e6d89edb99ebfe119fa898cc42d1a1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HRgoPaofXbhlKIEwrwkXWddTf6UYnygEFSPHqqKGIEyZ1OQctWg6KzLC5MCQqg8aCBstVGZvNsnQh+mEjkALCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T00:19:49.128036Z","bundle_sha256":"188c95389010739503606ff139fa716706673a23d898bbf6284c6d20dc0c5642"}}