{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:LEOTKL4VBLQAH6YGS5NQHZDERR","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":"54bc923102453413734a3ddfd4df074a3f84fe60ac2bb7b7da9fe2c69ebf1418","cross_cats_sorted":["hep-th","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-11-01T13:10:16Z","title_canon_sha256":"27a838701540d5a0a42c0eb3c431ef3c15f5befa3dd6a7acc427783e9250134c"},"schema_version":"1.0","source":{"id":"1311.0174","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1311.0174","created_at":"2026-05-18T02:18:23Z"},{"alias_kind":"arxiv_version","alias_value":"1311.0174v1","created_at":"2026-05-18T02:18:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1311.0174","created_at":"2026-05-18T02:18:23Z"},{"alias_kind":"pith_short_12","alias_value":"LEOTKL4VBLQA","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_16","alias_value":"LEOTKL4VBLQAH6YG","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_8","alias_value":"LEOTKL4V","created_at":"2026-05-18T12:27:51Z"}],"graph_snapshots":[{"event_id":"sha256:69df8a4e708cee6241d79ad9d787ae9ba24f1d1f503fd297388c5e1f026db2ee","target":"graph","created_at":"2026-05-18T02:18:23Z","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 paper we provide a detailed analysis of the analytic continuation of the spectral zeta function associated with one-dimensional regular Sturm-Liouville problems endowed with self-adjoint separated and coupled boundary conditions. The spectral zeta function is represented in terms of a complex integral and the analytic continuation in the entire complex plane is achieved by using the Liouville-Green (or WKB) asymptotic expansion of the eigenfunctions associated with the problem. The analytically continued expression of the spectral zeta function is then used to compute the functional de","authors_text":"Curtis Graham, Guglielmo Fucci, Klaus Kirsten","cross_cats":["hep-th","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-11-01T13:10:16Z","title":"Spectral Functions for Regular Sturm-Liouville Problems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.0174","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":"sha256:6f4cc0b0973bdbc325ddf1e783952be88fd469d21d62bf668a4e4fed44800277","target":"record","created_at":"2026-05-18T02:18:23Z","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":"54bc923102453413734a3ddfd4df074a3f84fe60ac2bb7b7da9fe2c69ebf1418","cross_cats_sorted":["hep-th","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-11-01T13:10:16Z","title_canon_sha256":"27a838701540d5a0a42c0eb3c431ef3c15f5befa3dd6a7acc427783e9250134c"},"schema_version":"1.0","source":{"id":"1311.0174","kind":"arxiv","version":1}},"canonical_sha256":"591d352f950ae003fb06975b03e4648c77fb68589882607da70db0c75bee6d64","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"591d352f950ae003fb06975b03e4648c77fb68589882607da70db0c75bee6d64","first_computed_at":"2026-05-18T02:18:23.949111Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:18:23.949111Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"gCUsYRw2hyU2eYHPgJ+91KAznZUjkOe7z3k4xbIlxfzmJabNu0DaN4i53BgPtXw5E3j1gfYnr3yiVq/AwEn0AA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:18:23.949842Z","signed_message":"canonical_sha256_bytes"},"source_id":"1311.0174","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6f4cc0b0973bdbc325ddf1e783952be88fd469d21d62bf668a4e4fed44800277","sha256:69df8a4e708cee6241d79ad9d787ae9ba24f1d1f503fd297388c5e1f026db2ee"],"state_sha256":"98973057ed632d2aeb7ac64bb395d44a6d8d626cda183bc008e0b067d679b03e"}