{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2007:2UDYFA7DYPZVZOTPFUEQHG23NH","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":"10e399e8f2a710884ebe77538c70e72a99c3d1d72f055307a771dbc90a9a15ed","cross_cats_sorted":["hep-th","math.MP"],"license":"","primary_cat":"math-ph","submitted_at":"2007-09-08T20:20:09Z","title_canon_sha256":"1e66af7bfd8b754a6aa4153271e7ca60475feda733b49c0b6ad9890b0198bf3f"},"schema_version":"1.0","source":{"id":"0709.1232","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0709.1232","created_at":"2026-05-18T04:14:36Z"},{"alias_kind":"arxiv_version","alias_value":"0709.1232v1","created_at":"2026-05-18T04:14:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0709.1232","created_at":"2026-05-18T04:14:36Z"},{"alias_kind":"pith_short_12","alias_value":"2UDYFA7DYPZV","created_at":"2026-05-18T12:25:54Z"},{"alias_kind":"pith_short_16","alias_value":"2UDYFA7DYPZVZOTP","created_at":"2026-05-18T12:25:54Z"},{"alias_kind":"pith_short_8","alias_value":"2UDYFA7D","created_at":"2026-05-18T12:25:54Z"}],"graph_snapshots":[{"event_id":"sha256:a37e60920e1a3de97741ea90ae72e515c577342fe30ad66c433afb7977147212","target":"graph","created_at":"2026-05-18T04:14:36Z","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 this article we consider the zeta regularized determinant of Laplace-type operators on the generalized cone. For {\\it arbitrary} self-adjoint extensions of a matrix of singular ordinary differential operators modelled on the generalized cone, a closed expression for the determinant is given. The result involves a determinant of an endomorphism of a finite-dimensional vector space, the endomorphism encoding the self-adjoint extension chosen. For particular examples, like the Friedrich's extension, the answer is easily extracted from the general result. In combination with \\cite{BKD}, a close","authors_text":"Jinsung Park, Klaus Kirsten, Paul Loya","cross_cats":["hep-th","math.MP"],"headline":"","license":"","primary_cat":"math-ph","submitted_at":"2007-09-08T20:20:09Z","title":"Functional determinants for general self-adjoint extensions of Laplace-type operators resulting from the generalized cone"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0709.1232","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":"sha256:39b5d3d8166022186137c3fb39d7c1dbfe9869aa860e0b8fb08250f791bb9901","target":"record","created_at":"2026-05-18T04:14:36Z","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":"10e399e8f2a710884ebe77538c70e72a99c3d1d72f055307a771dbc90a9a15ed","cross_cats_sorted":["hep-th","math.MP"],"license":"","primary_cat":"math-ph","submitted_at":"2007-09-08T20:20:09Z","title_canon_sha256":"1e66af7bfd8b754a6aa4153271e7ca60475feda733b49c0b6ad9890b0198bf3f"},"schema_version":"1.0","source":{"id":"0709.1232","kind":"arxiv","version":1}},"canonical_sha256":"d5078283e3c3f35cba6f2d09039b5b69f9d56eeefbd443cd4cd1a86a78d9bcce","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d5078283e3c3f35cba6f2d09039b5b69f9d56eeefbd443cd4cd1a86a78d9bcce","first_computed_at":"2026-05-18T04:14:36.735534Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:14:36.735534Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"FrTzBUFZrZsnEZaR0FWQtHkJO9m1kJcteQd8WwftyQCD1PmfHoAz//xJec5hYR2QU5uXkl9L4atLw8afmOMyDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:14:36.735935Z","signed_message":"canonical_sha256_bytes"},"source_id":"0709.1232","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:39b5d3d8166022186137c3fb39d7c1dbfe9869aa860e0b8fb08250f791bb9901","sha256:a37e60920e1a3de97741ea90ae72e515c577342fe30ad66c433afb7977147212"],"state_sha256":"b9b1eae5b6a775023a57ed867325abd0786455417b498496c12515fb39b8755b"}