{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2006:33GLJK33AOEJAUDHTK6VMCWVOC","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":"6ac2db2f37dfee08092b75daa30dfd9bd4bc582e40282c6176ea4462a56bfbd8","cross_cats_sorted":["cond-mat.mes-hall","math.MP","math.SP","quant-ph"],"license":"","primary_cat":"math-ph","submitted_at":"2006-10-25T14:24:01Z","title_canon_sha256":"1fa59a6f1759cb5c85faff6d120e1963dec2788846d62550e57105eff2eb854b"},"schema_version":"1.0","source":{"id":"math-ph/0610065","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math-ph/0610065","created_at":"2026-05-18T01:08:51Z"},{"alias_kind":"arxiv_version","alias_value":"math-ph/0610065v1","created_at":"2026-05-18T01:08:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math-ph/0610065","created_at":"2026-05-18T01:08:51Z"},{"alias_kind":"pith_short_12","alias_value":"33GLJK33AOEJ","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_16","alias_value":"33GLJK33AOEJAUDH","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_8","alias_value":"33GLJK33","created_at":"2026-05-18T12:25:53Z"}],"graph_snapshots":[{"event_id":"sha256:f12cbd54232ed6bf7eda8919e2b1c1810dc5548d6a3916e662be85411f61db25","target":"graph","created_at":"2026-05-18T01:08:51Z","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":"We discuss resonances for Schr\\\"odinger operators on metric graphs which consists of a finite compact part and a finite number of halflines attached to it; the vertex coupling is assumed to be of the $\\delta$-type or certain modifications of it. Using exterior complex scaling on the graph we show that the resolvent and scattering resonances coincide in this case.","authors_text":"Ji\\v{r}\\'i Lipovsk\\'y, Pavel Exner","cross_cats":["cond-mat.mes-hall","math.MP","math.SP","quant-ph"],"headline":"","license":"","primary_cat":"math-ph","submitted_at":"2006-10-25T14:24:01Z","title":"Equivalence of resolvent and scattering resonances on quantum graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math-ph/0610065","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":"sha256:28e2e91d75417e00cdd4414cdffff1aa0b67cec6156a43b6f5d8bbe18183ba39","target":"record","created_at":"2026-05-18T01:08:51Z","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":"6ac2db2f37dfee08092b75daa30dfd9bd4bc582e40282c6176ea4462a56bfbd8","cross_cats_sorted":["cond-mat.mes-hall","math.MP","math.SP","quant-ph"],"license":"","primary_cat":"math-ph","submitted_at":"2006-10-25T14:24:01Z","title_canon_sha256":"1fa59a6f1759cb5c85faff6d120e1963dec2788846d62550e57105eff2eb854b"},"schema_version":"1.0","source":{"id":"math-ph/0610065","kind":"arxiv","version":1}},"canonical_sha256":"deccb4ab7b03889050679abd560ad5708a5906052878aa79e460c888db832439","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"deccb4ab7b03889050679abd560ad5708a5906052878aa79e460c888db832439","first_computed_at":"2026-05-18T01:08:51.667005Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:08:51.667005Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"q/tarAmcEysOegymhl/m2P/YOWUGiyX3KaefdYNHKvG3mrPxqJHT8SQn9tu2bzqei9x3PkmvzKTYUeymT1kQDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:08:51.667597Z","signed_message":"canonical_sha256_bytes"},"source_id":"math-ph/0610065","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:28e2e91d75417e00cdd4414cdffff1aa0b67cec6156a43b6f5d8bbe18183ba39","sha256:f12cbd54232ed6bf7eda8919e2b1c1810dc5548d6a3916e662be85411f61db25"],"state_sha256":"d271303057620b4d4d13ae6c31572db69ce216a3e232d6e2a7ddd09427b0b7cc"}