{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:1994:ZOEJD24QKB5FN66GUCDJDUMZWC","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":"4351a0d98a76fdf288ae344e20f14a8b22f3da9f0a8332d9fae8cdccfa861919","cross_cats_sorted":["math.DG"],"license":"","primary_cat":"hep-th","submitted_at":"1994-06-21T16:29:17Z","title_canon_sha256":"9cc3c47ac5b628adf8559277b59cf3cda06ff5cc2ff0aba9184b9f18266abcaa"},"schema_version":"1.0","source":{"id":"hep-th/9406140","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"hep-th/9406140","created_at":"2026-05-18T01:06:04Z"},{"alias_kind":"arxiv_version","alias_value":"hep-th/9406140v1","created_at":"2026-05-18T01:06:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.hep-th/9406140","created_at":"2026-05-18T01:06:04Z"},{"alias_kind":"pith_short_12","alias_value":"ZOEJD24QKB5F","created_at":"2026-05-18T12:25:47Z"},{"alias_kind":"pith_short_16","alias_value":"ZOEJD24QKB5FN66G","created_at":"2026-05-18T12:25:47Z"},{"alias_kind":"pith_short_8","alias_value":"ZOEJD24Q","created_at":"2026-05-18T12:25:47Z"}],"graph_snapshots":[{"event_id":"sha256:90126b077837b828a8d104065eceeeb0ecc16b02868d79259b8051932df5c82d","target":"graph","created_at":"2026-05-18T01:06:04Z","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":"This paper is essentially a short version of hep-th/9404046. We compute multiplicative anomaly det(AB)/(detA detB) =F(A,B) for elliptic pseudo-differential operators (PDOs) A, B on a closed manifold M in terms of their symbols. We prove that F(A,B)=1 for elliptic differential operators close to positive-definite ones on an odd-dimensional M. For such M we introduce a holomorphic determinant. Its monodromy lies in a finite group of roots of unity.\n  In general case, we relate the multiplicative anomaly with a central extension of the group of elliptic symbols and with an invariant quadratic for","authors_text":"Maxim Kontsevich, Simeon Vishik","cross_cats":["math.DG"],"headline":"","license":"","primary_cat":"hep-th","submitted_at":"1994-06-21T16:29:17Z","title":"Geometry of determinants of elliptic operators"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"hep-th/9406140","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:a7b1a2eb989d525c4aed7d31e20975f9d61a2d07e3ed22069296695121b0a885","target":"record","created_at":"2026-05-18T01:06:04Z","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":"4351a0d98a76fdf288ae344e20f14a8b22f3da9f0a8332d9fae8cdccfa861919","cross_cats_sorted":["math.DG"],"license":"","primary_cat":"hep-th","submitted_at":"1994-06-21T16:29:17Z","title_canon_sha256":"9cc3c47ac5b628adf8559277b59cf3cda06ff5cc2ff0aba9184b9f18266abcaa"},"schema_version":"1.0","source":{"id":"hep-th/9406140","kind":"arxiv","version":1}},"canonical_sha256":"cb8891eb90507a56fbc6a08691d199b0b5cc9e1fcbc3ab41a82305586984d0a2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cb8891eb90507a56fbc6a08691d199b0b5cc9e1fcbc3ab41a82305586984d0a2","first_computed_at":"2026-05-18T01:06:04.508544Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:06:04.508544Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+WqOrWE8dP/Uk3igU8kU3AQnMmqT63SiTaCeAlvk3ryz4iOmF4UE5YHrvrfxfzGXI+6qb16S/Z+qmU4291nmBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:06:04.509193Z","signed_message":"canonical_sha256_bytes"},"source_id":"hep-th/9406140","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a7b1a2eb989d525c4aed7d31e20975f9d61a2d07e3ed22069296695121b0a885","sha256:90126b077837b828a8d104065eceeeb0ecc16b02868d79259b8051932df5c82d"],"state_sha256":"8b7f32ab034cb7f4d56d52b8c2ab6f71b6f3e95f5658802af9516760663d1f90"}