{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:C353VRNJ7CLYBYEGJBXBNNEXJ7","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":"dc9fa9ad365bd0dbba523a785200ecc27cefe150c75054be720d815ee13e2708","cross_cats_sorted":["cond-mat.other","hep-lat","hep-ph","math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2017-10-10T02:21:20Z","title_canon_sha256":"8555cabe3d50a7ad036f2b28f0390efa06198ac27923f1aa4bd0779aeb2ece12"},"schema_version":"1.0","source":{"id":"1710.03379","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1710.03379","created_at":"2026-05-18T00:26:14Z"},{"alias_kind":"arxiv_version","alias_value":"1710.03379v2","created_at":"2026-05-18T00:26:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.03379","created_at":"2026-05-18T00:26:14Z"},{"alias_kind":"pith_short_12","alias_value":"C353VRNJ7CLY","created_at":"2026-05-18T12:31:08Z"},{"alias_kind":"pith_short_16","alias_value":"C353VRNJ7CLYBYEG","created_at":"2026-05-18T12:31:08Z"},{"alias_kind":"pith_short_8","alias_value":"C353VRNJ","created_at":"2026-05-18T12:31:08Z"}],"graph_snapshots":[{"event_id":"sha256:c1bfe219eed48659cbff51ba032c99ffceee630d56182163bd493f554cf24667","target":"graph","created_at":"2026-05-18T00:26:14Z","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":"The Atiyah-Patodi-Singer(APS) index theorem attracts attention for understanding physics on the surface of materials in topological phases. The mathematical set-up for this theorem is, however, not directly related to the physical fermion system, as it imposes on the fermion fields a non-local boundary condition known as the \"APS boundary condition\" by hand, which is unlikely to be realized in the materials. In this work, we attempt to reformulate the APS index in a \"physicist-friendly\" way for a simple set-up with $U(1)$ or $SU(N)$ gauge group on a flat four-dimensional Euclidean space. We fi","authors_text":"Hidenori Fukaya, Satoshi Yamaguchi, Tetsuya Onogi","cross_cats":["cond-mat.other","hep-lat","hep-ph","math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2017-10-10T02:21:20Z","title":"Atiyah-Patodi-Singer index from the domain-wall fermion Dirac operator"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.03379","kind":"arxiv","version":2},"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":"sha256:3fc54290d77234a2e5b9b89356ce8f7848e847cf15290ed13562633fb89d5f3a","target":"record","created_at":"2026-05-18T00:26:14Z","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":"dc9fa9ad365bd0dbba523a785200ecc27cefe150c75054be720d815ee13e2708","cross_cats_sorted":["cond-mat.other","hep-lat","hep-ph","math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2017-10-10T02:21:20Z","title_canon_sha256":"8555cabe3d50a7ad036f2b28f0390efa06198ac27923f1aa4bd0779aeb2ece12"},"schema_version":"1.0","source":{"id":"1710.03379","kind":"arxiv","version":2}},"canonical_sha256":"16fbbac5a9f89780e086486e16b4974fdaede34b84276e7c314fc4759e64fd3f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"16fbbac5a9f89780e086486e16b4974fdaede34b84276e7c314fc4759e64fd3f","first_computed_at":"2026-05-18T00:26:14.391417Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:26:14.391417Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"q5O1y4TFCSOozDCU3XD9NfTdFI9UXAW09CSAyXj0RLSwLsg7kX0Ek/dy8VM2v6iDXrbr5+3eg/ruYqbjdk3yBw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:26:14.392026Z","signed_message":"canonical_sha256_bytes"},"source_id":"1710.03379","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3fc54290d77234a2e5b9b89356ce8f7848e847cf15290ed13562633fb89d5f3a","sha256:c1bfe219eed48659cbff51ba032c99ffceee630d56182163bd493f554cf24667"],"state_sha256":"fc076d216af6f5420947beece247b1bd7b57990f2eb64a3605a6b161508601a5"}