{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:1999:N2NAXJN65PHRGAMBN6JHREWDET","short_pith_number":"pith:N2NAXJN6","schema_version":"1.0","canonical_sha256":"6e9a0ba5beebcf1301816f927892c324c4a1cd14ee536aa507e66c484a438f10","source":{"kind":"arxiv","id":"hep-lat/9904007","version":2},"attestation_state":"computed","paper":{"title":"Relation $Tr \\gamma_{5}= 0$ and the index theorem in lattice gauge theory","license":"","headline":"","cross_cats":["hep-th"],"primary_cat":"hep-lat","authors_text":"Kazuo Fujikawa (Dept. of Physics, Univ. of Tokyo)","submitted_at":"1999-04-23T09:02:52Z","abstract_excerpt":"The relation $Tr \\gamma_{5}= 0$ implies the contribution to the trace from unphysical (would-be) species doublers in lattice gauge theory. This statement is also true for the Pauli-Villars regularization in continuum theory. If one insists on $Tr \\gamma_{5}= 0$, one thus inevitably includes unphysical states in the Hilbert space. If one truncates the trace to the contribution from physical species only, one obtains $\\tilde{T}r \\gamma_{5} = n_{+} - n_{-}$ which is equal to the Pontryagin index. A smooth continuum limit of $\\tilde{T}r \\gamma_{5} = Tr \\gamma_{5}(1-(a/2)D) = n_{+} - n_{-}$ for the"},"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/9904007","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"hep-lat","submitted_at":"1999-04-23T09:02:52Z","cross_cats_sorted":["hep-th"],"title_canon_sha256":"85537d7f5cf9a6a8daf923bdc4e73040a7ec1252270baa9770d97b35a34a385a","abstract_canon_sha256":"b46a9c4bbc5f59fb705825919006d3226f1abffc8806ac8fce67cfa3566b74aa"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T16:14:00.063710Z","signature_b64":"RpzIgrBfY4OP6BVkOr/IfgIQ+45WQRm17j7H8/XDKgoQooQj9D0QMMS8g+jyZCzzwou/ygnFYlqbZepFJ7IZAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6e9a0ba5beebcf1301816f927892c324c4a1cd14ee536aa507e66c484a438f10","last_reissued_at":"2026-07-04T16:14:00.063241Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T16:14:00.063241Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Relation $Tr \\gamma_{5}= 0$ and the index theorem in lattice gauge theory","license":"","headline":"","cross_cats":["hep-th"],"primary_cat":"hep-lat","authors_text":"Kazuo Fujikawa (Dept. of Physics, Univ. of Tokyo)","submitted_at":"1999-04-23T09:02:52Z","abstract_excerpt":"The relation $Tr \\gamma_{5}= 0$ implies the contribution to the trace from unphysical (would-be) species doublers in lattice gauge theory. This statement is also true for the Pauli-Villars regularization in continuum theory. If one insists on $Tr \\gamma_{5}= 0$, one thus inevitably includes unphysical states in the Hilbert space. If one truncates the trace to the contribution from physical species only, one obtains $\\tilde{T}r \\gamma_{5} = n_{+} - n_{-}$ which is equal to the Pontryagin index. A smooth continuum limit of $\\tilde{T}r \\gamma_{5} = Tr \\gamma_{5}(1-(a/2)D) = n_{+} - n_{-}$ for the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"hep-lat/9904007","kind":"arxiv","version":2},"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/9904007/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/9904007","created_at":"2026-07-04T16:14:00.063297+00:00"},{"alias_kind":"arxiv_version","alias_value":"hep-lat/9904007v2","created_at":"2026-07-04T16:14:00.063297+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.hep-lat/9904007","created_at":"2026-07-04T16:14:00.063297+00:00"},{"alias_kind":"pith_short_12","alias_value":"N2NAXJN65PHR","created_at":"2026-07-04T16:14:00.063297+00:00"},{"alias_kind":"pith_short_16","alias_value":"N2NAXJN65PHRGAMB","created_at":"2026-07-04T16:14:00.063297+00:00"},{"alias_kind":"pith_short_8","alias_value":"N2NAXJN6","created_at":"2026-07-04T16:14:00.063297+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2411.09886","citing_title":"Lattice Chiral Fermion without Hermiticity","ref_index":32,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/N2NAXJN65PHRGAMBN6JHREWDET","json":"https://pith.science/pith/N2NAXJN65PHRGAMBN6JHREWDET.json","graph_json":"https://pith.science/api/pith-number/N2NAXJN65PHRGAMBN6JHREWDET/graph.json","events_json":"https://pith.science/api/pith-number/N2NAXJN65PHRGAMBN6JHREWDET/events.json","paper":"https://pith.science/paper/N2NAXJN6"},"agent_actions":{"view_html":"https://pith.science/pith/N2NAXJN65PHRGAMBN6JHREWDET","download_json":"https://pith.science/pith/N2NAXJN65PHRGAMBN6JHREWDET.json","view_paper":"https://pith.science/paper/N2NAXJN6","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=hep-lat/9904007&json=true","fetch_graph":"https://pith.science/api/pith-number/N2NAXJN65PHRGAMBN6JHREWDET/graph.json","fetch_events":"https://pith.science/api/pith-number/N2NAXJN65PHRGAMBN6JHREWDET/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/N2NAXJN65PHRGAMBN6JHREWDET/action/timestamp_anchor","attest_storage":"https://pith.science/pith/N2NAXJN65PHRGAMBN6JHREWDET/action/storage_attestation","attest_author":"https://pith.science/pith/N2NAXJN65PHRGAMBN6JHREWDET/action/author_attestation","sign_citation":"https://pith.science/pith/N2NAXJN65PHRGAMBN6JHREWDET/action/citation_signature","submit_replication":"https://pith.science/pith/N2NAXJN65PHRGAMBN6JHREWDET/action/replication_record"}},"created_at":"2026-07-04T16:14:00.063297+00:00","updated_at":"2026-07-04T16:14:00.063297+00:00"}