{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:YQ3NO7JXWPLHMRWMEL2QGD5Z65","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":"af3c6d8b9a077523e9a8dc4d7b98c0d0c2d5b55cbd8cd9aa120357da4eab7f85","cross_cats_sorted":["math.MP","math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2014-02-07T02:40:12Z","title_canon_sha256":"fb4071235138809876b7be0ff896df4e2590173e15740479a5aeb567238f0518"},"schema_version":"1.0","source":{"id":"1402.1542","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1402.1542","created_at":"2026-05-18T01:44:46Z"},{"alias_kind":"arxiv_version","alias_value":"1402.1542v1","created_at":"2026-05-18T01:44:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1402.1542","created_at":"2026-05-18T01:44:46Z"},{"alias_kind":"pith_short_12","alias_value":"YQ3NO7JXWPLH","created_at":"2026-05-18T12:28:57Z"},{"alias_kind":"pith_short_16","alias_value":"YQ3NO7JXWPLHMRWM","created_at":"2026-05-18T12:28:57Z"},{"alias_kind":"pith_short_8","alias_value":"YQ3NO7JX","created_at":"2026-05-18T12:28:57Z"}],"graph_snapshots":[{"event_id":"sha256:2fa985f00c12b801680ee217d42231eefbfec17947a63d44d3196e82b56efc2a","target":"graph","created_at":"2026-05-18T01:44:46Z","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 spectral and scattering theory for 1-dimensional Dirac operators with mass $m$ and with zero-range interactions are fully investigated. Explicit expressions for the wave operators and for the scattering operator are provided. These new formulae take place in a representation which links, in a suitable way, the energies $-\\infty$ and $+\\infty$, and which emphasizes the role of $\\pm m$. Finally, a topological version of Levinson's theorem is deduced, with the threshold effects at $\\pm m$ automatically taken into account.","authors_text":"K. Pankrashkin, S. Richard","cross_cats":["math.MP","math.SP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2014-02-07T02:40:12Z","title":"One-dimensional Dirac operators with zero-range interactions: Spectral, scattering, and topological results"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.1542","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":"sha256:1d8378c3765e4d0c6a68d51287f952c6febc4f3b05d499b457bead65eb90bf40","target":"record","created_at":"2026-05-18T01:44:46Z","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":"af3c6d8b9a077523e9a8dc4d7b98c0d0c2d5b55cbd8cd9aa120357da4eab7f85","cross_cats_sorted":["math.MP","math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2014-02-07T02:40:12Z","title_canon_sha256":"fb4071235138809876b7be0ff896df4e2590173e15740479a5aeb567238f0518"},"schema_version":"1.0","source":{"id":"1402.1542","kind":"arxiv","version":1}},"canonical_sha256":"c436d77d37b3d67646cc22f5030fb9f76148410689b5498d66bd5a5331f72f19","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c436d77d37b3d67646cc22f5030fb9f76148410689b5498d66bd5a5331f72f19","first_computed_at":"2026-05-18T01:44:46.604696Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:44:46.604696Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"IFgv9L5QwvZuNWNtq6e3qKQWGJdLLfk7P1Lh5GSoT3NIjRHGgu5wpHVlJ0PQ7Yvj/H3jr5TwZTaDmpbsXtcGCw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:44:46.605210Z","signed_message":"canonical_sha256_bytes"},"source_id":"1402.1542","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1d8378c3765e4d0c6a68d51287f952c6febc4f3b05d499b457bead65eb90bf40","sha256:2fa985f00c12b801680ee217d42231eefbfec17947a63d44d3196e82b56efc2a"],"state_sha256":"0eb3f0f28e65c19a8c237cf0c2f7b7fe9d6e7ec30ef83f886df351a2830c42b8"}