{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:2LZEK7TFXUTKABU7L7I746ZO2C","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":"6cbcb62703b0789c75b0e59be881a6968773820304a9adc7a265b77ca21c27da","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-08-15T09:38:25Z","title_canon_sha256":"42e47454b87331d42c3bc4d8f2d51629ab1bdecd57e28a5dd276166fa3dbeb8e"},"schema_version":"1.0","source":{"id":"1208.3072","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1208.3072","created_at":"2026-05-18T01:55:15Z"},{"alias_kind":"arxiv_version","alias_value":"1208.3072v1","created_at":"2026-05-18T01:55:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1208.3072","created_at":"2026-05-18T01:55:15Z"},{"alias_kind":"pith_short_12","alias_value":"2LZEK7TFXUTK","created_at":"2026-05-18T12:26:50Z"},{"alias_kind":"pith_short_16","alias_value":"2LZEK7TFXUTKABU7","created_at":"2026-05-18T12:26:50Z"},{"alias_kind":"pith_short_8","alias_value":"2LZEK7TF","created_at":"2026-05-18T12:26:50Z"}],"graph_snapshots":[{"event_id":"sha256:c6ad4d4275844d14506156a994ec66bb94bd2bbd7ba6f5eb2c6d1807b042d99a","target":"graph","created_at":"2026-05-18T01:55:15Z","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 work explores the spectra of quantum graphs where the Schr\\\"odinger operator on the edges is equipped with a potential. The scattering approach, which was originally introduced for the potential free case, is extended to this case and used to derive a secular function whose zeros coincide with the eigenvalue spectrum. Exact trace formulas for both smooth and $\\delta$-potentials are derived, and an asymptotic semiclassical trace formula (for smooth potentials) is presented and discussed.","authors_text":"Ralf Rueckriemen, Uzy Smilansky","cross_cats":["math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-08-15T09:38:25Z","title":"Trace Formulae for quantum graphs with edge potentials"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.3072","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":"sha256:003adc89c1fa9bad4b6756e4d2f3fb6b0676f501cd4bcacb5c5ca764b0a7612a","target":"record","created_at":"2026-05-18T01:55:15Z","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":"6cbcb62703b0789c75b0e59be881a6968773820304a9adc7a265b77ca21c27da","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-08-15T09:38:25Z","title_canon_sha256":"42e47454b87331d42c3bc4d8f2d51629ab1bdecd57e28a5dd276166fa3dbeb8e"},"schema_version":"1.0","source":{"id":"1208.3072","kind":"arxiv","version":1}},"canonical_sha256":"d2f2457e65bd26a0069f5fd1fe7b2ed0a3f237b866a90df8b6bf184266e73d18","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d2f2457e65bd26a0069f5fd1fe7b2ed0a3f237b866a90df8b6bf184266e73d18","first_computed_at":"2026-05-18T01:55:15.727933Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:55:15.727933Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"eS1cLSv1YBl6I3SISSbUTKRZkrlf2lgdV5Mbx7fv4qVuwNwaXTeen2ZmzYsuuLkHkkssFFGokndcmnukIj0OAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:55:15.728385Z","signed_message":"canonical_sha256_bytes"},"source_id":"1208.3072","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:003adc89c1fa9bad4b6756e4d2f3fb6b0676f501cd4bcacb5c5ca764b0a7612a","sha256:c6ad4d4275844d14506156a994ec66bb94bd2bbd7ba6f5eb2c6d1807b042d99a"],"state_sha256":"531533a00dc0d020766aaa5bb66667a6353969bf49341ac673b26646e973a19c"}