{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:E2NIZND34VTA4LTAYF5L4YNNJ4","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":"5e5be5fe4e03db4d0e53321ea9a8036d3c34d6291366753f7c14e4fd37b98bef","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-05-02T20:16:24Z","title_canon_sha256":"c5904a8b592e9be2760a4cd1317fbd89705b2ee02b3461dbee12612e3077239e"},"schema_version":"1.0","source":{"id":"1205.0562","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1205.0562","created_at":"2026-05-18T03:56:33Z"},{"alias_kind":"arxiv_version","alias_value":"1205.0562v1","created_at":"2026-05-18T03:56:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.0562","created_at":"2026-05-18T03:56:33Z"},{"alias_kind":"pith_short_12","alias_value":"E2NIZND34VTA","created_at":"2026-05-18T12:27:04Z"},{"alias_kind":"pith_short_16","alias_value":"E2NIZND34VTA4LTA","created_at":"2026-05-18T12:27:04Z"},{"alias_kind":"pith_short_8","alias_value":"E2NIZND3","created_at":"2026-05-18T12:27:04Z"}],"graph_snapshots":[{"event_id":"sha256:f32d2a97f70b89d2a1973d92b5993360549ca530aca1aa6734a6fdc5da77d991","target":"graph","created_at":"2026-05-18T03:56:33Z","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 previous work, we introduced eta invariants for even dimensional manifolds. It plays the same role as the eta invariant of Atiyah-Patodi-Singer, which is for odd dimensional manifolds. It is associated to $K^1$ representatives on even dimensional manifolds and is closely related to the so called WZW theory in physics. In fact, it is an intrinsic interpretation of the Wess-Zumino term without passing to the bounding 3-manifold. Spectrally the eta invariant is defined on a finite cylinder, rather than on the manifold itself. Thus it is an interesting question to find an intrinsic spectral int","authors_text":"Weiping Zhang, Xianzhe Dai","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-05-02T20:16:24Z","title":"Eta invariant and holonomy, the even dimensional case"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.0562","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:c9e98995adb7754c044443620e7f14ea244e86007a548cf0143a52af0457972a","target":"record","created_at":"2026-05-18T03:56:33Z","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":"5e5be5fe4e03db4d0e53321ea9a8036d3c34d6291366753f7c14e4fd37b98bef","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-05-02T20:16:24Z","title_canon_sha256":"c5904a8b592e9be2760a4cd1317fbd89705b2ee02b3461dbee12612e3077239e"},"schema_version":"1.0","source":{"id":"1205.0562","kind":"arxiv","version":1}},"canonical_sha256":"269a8cb47be5660e2e60c17abe61ad4f368e39d60a957b07f7362b33bf0156d4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"269a8cb47be5660e2e60c17abe61ad4f368e39d60a957b07f7362b33bf0156d4","first_computed_at":"2026-05-18T03:56:33.639346Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:56:33.639346Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"SsOK4qgk/6Epif7A86Ue1gAdo0lj4dbhCmqUoFMTYtI4JtbSZXb898y+RP7w9pQTnCsoFcAkZSYs/RdLVeWICw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:56:33.639742Z","signed_message":"canonical_sha256_bytes"},"source_id":"1205.0562","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c9e98995adb7754c044443620e7f14ea244e86007a548cf0143a52af0457972a","sha256:f32d2a97f70b89d2a1973d92b5993360549ca530aca1aa6734a6fdc5da77d991"],"state_sha256":"ae73fdd14bcc742d57cebfd92793c5b55b33de50495dbc8d01c926eab88cfdb2"}