{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:5ACCTXYPCCYLIN5OAQQW6QDO6Q","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":"c5d52c9257b7ed213cb3b1811703fb5ed297025118628645e7b5c844b1f3cd3b","cross_cats_sorted":["gr-qc","math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2010-12-07T18:17:58Z","title_canon_sha256":"0e373219451b604fe54aa7e28545fae746cf4be2deef61f3e15ee8a9196990ac"},"schema_version":"1.0","source":{"id":"1012.1571","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1012.1571","created_at":"2026-05-18T04:12:12Z"},{"alias_kind":"arxiv_version","alias_value":"1012.1571v2","created_at":"2026-05-18T04:12:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1012.1571","created_at":"2026-05-18T04:12:12Z"},{"alias_kind":"pith_short_12","alias_value":"5ACCTXYPCCYL","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_16","alias_value":"5ACCTXYPCCYLIN5O","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_8","alias_value":"5ACCTXYP","created_at":"2026-05-18T12:26:04Z"}],"graph_snapshots":[{"event_id":"sha256:cb10569fb606b95abb1fff73bff5ce10353416ca36ecd0c27cfcac3a16fab0de","target":"graph","created_at":"2026-05-18T04:12:12Z","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 functional determinant of a special second order quantum-mechanical operator is calculated with its zero mode gauged out by the method of the Faddeev-Popov gauge fixing procedure. This operator subject to periodic boundary conditions arises in applications of the early Universe theory and, in particular, determines the one-loop statistical sum in quantum cosmology generated by a conformal field theory (CFT). The calculation is done for a special case of a periodic zero mode of this operator having two roots (nodes) within the period range, which corresponds to the class of cosmological ins","authors_text":"A.O.Barvinsky, A.Yu.Kamenshchik","cross_cats":["gr-qc","math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2010-12-07T18:17:58Z","title":"On the functional determinant of a special operator with a zero mode in cosmology"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1012.1571","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":"sha256:8c4dc007dc4f60bcebedc45d406e31bd03d2c42a6056abb294bb22f226531e84","target":"record","created_at":"2026-05-18T04:12:12Z","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":"c5d52c9257b7ed213cb3b1811703fb5ed297025118628645e7b5c844b1f3cd3b","cross_cats_sorted":["gr-qc","math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2010-12-07T18:17:58Z","title_canon_sha256":"0e373219451b604fe54aa7e28545fae746cf4be2deef61f3e15ee8a9196990ac"},"schema_version":"1.0","source":{"id":"1012.1571","kind":"arxiv","version":2}},"canonical_sha256":"e80429df0f10b0b437ae04216f406ef4384f8373123c54a4e3e5cf31e33ed2fd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e80429df0f10b0b437ae04216f406ef4384f8373123c54a4e3e5cf31e33ed2fd","first_computed_at":"2026-05-18T04:12:12.020970Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:12:12.020970Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Ss8xFL1nt2vjpmebxtYqzFSnSI+OKPMewkTMrKN5/J07P0SCuoc9CaiieTYSDGxbpxfcqzXPqaFryFyBcsaZAA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:12:12.021467Z","signed_message":"canonical_sha256_bytes"},"source_id":"1012.1571","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8c4dc007dc4f60bcebedc45d406e31bd03d2c42a6056abb294bb22f226531e84","sha256:cb10569fb606b95abb1fff73bff5ce10353416ca36ecd0c27cfcac3a16fab0de"],"state_sha256":"f6be00c5fb0b747d3e80ad15f84c6b86ad9d100df34d44c2c6b1da8d0086d6de"}