{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:YQ3NO7JXWPLHMRWMEL2QGD5Z65","short_pith_number":"pith:YQ3NO7JX","schema_version":"1.0","canonical_sha256":"c436d77d37b3d67646cc22f5030fb9f76148410689b5498d66bd5a5331f72f19","source":{"kind":"arxiv","id":"1402.1542","version":1},"attestation_state":"computed","paper":{"title":"One-dimensional Dirac operators with zero-range interactions: Spectral, scattering, and topological results","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP","math.SP"],"primary_cat":"math-ph","authors_text":"K. Pankrashkin, S. Richard","submitted_at":"2014-02-07T02:40:12Z","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."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1402.1542","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2014-02-07T02:40:12Z","cross_cats_sorted":["math.MP","math.SP"],"title_canon_sha256":"fb4071235138809876b7be0ff896df4e2590173e15740479a5aeb567238f0518","abstract_canon_sha256":"af3c6d8b9a077523e9a8dc4d7b98c0d0c2d5b55cbd8cd9aa120357da4eab7f85"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:44:46.605210Z","signature_b64":"IFgv9L5QwvZuNWNtq6e3qKQWGJdLLfk7P1Lh5GSoT3NIjRHGgu5wpHVlJ0PQ7Yvj/H3jr5TwZTaDmpbsXtcGCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c436d77d37b3d67646cc22f5030fb9f76148410689b5498d66bd5a5331f72f19","last_reissued_at":"2026-05-18T01:44:46.604696Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:44:46.604696Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"One-dimensional Dirac operators with zero-range interactions: Spectral, scattering, and topological results","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP","math.SP"],"primary_cat":"math-ph","authors_text":"K. Pankrashkin, S. Richard","submitted_at":"2014-02-07T02:40:12Z","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."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.1542","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1402.1542","created_at":"2026-05-18T01:44:46.604767+00:00"},{"alias_kind":"arxiv_version","alias_value":"1402.1542v1","created_at":"2026-05-18T01:44:46.604767+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1402.1542","created_at":"2026-05-18T01:44:46.604767+00:00"},{"alias_kind":"pith_short_12","alias_value":"YQ3NO7JXWPLH","created_at":"2026-05-18T12:28:57.508820+00:00"},{"alias_kind":"pith_short_16","alias_value":"YQ3NO7JXWPLHMRWM","created_at":"2026-05-18T12:28:57.508820+00:00"},{"alias_kind":"pith_short_8","alias_value":"YQ3NO7JX","created_at":"2026-05-18T12:28:57.508820+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/YQ3NO7JXWPLHMRWMEL2QGD5Z65","json":"https://pith.science/pith/YQ3NO7JXWPLHMRWMEL2QGD5Z65.json","graph_json":"https://pith.science/api/pith-number/YQ3NO7JXWPLHMRWMEL2QGD5Z65/graph.json","events_json":"https://pith.science/api/pith-number/YQ3NO7JXWPLHMRWMEL2QGD5Z65/events.json","paper":"https://pith.science/paper/YQ3NO7JX"},"agent_actions":{"view_html":"https://pith.science/pith/YQ3NO7JXWPLHMRWMEL2QGD5Z65","download_json":"https://pith.science/pith/YQ3NO7JXWPLHMRWMEL2QGD5Z65.json","view_paper":"https://pith.science/paper/YQ3NO7JX","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1402.1542&json=true","fetch_graph":"https://pith.science/api/pith-number/YQ3NO7JXWPLHMRWMEL2QGD5Z65/graph.json","fetch_events":"https://pith.science/api/pith-number/YQ3NO7JXWPLHMRWMEL2QGD5Z65/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/YQ3NO7JXWPLHMRWMEL2QGD5Z65/action/timestamp_anchor","attest_storage":"https://pith.science/pith/YQ3NO7JXWPLHMRWMEL2QGD5Z65/action/storage_attestation","attest_author":"https://pith.science/pith/YQ3NO7JXWPLHMRWMEL2QGD5Z65/action/author_attestation","sign_citation":"https://pith.science/pith/YQ3NO7JXWPLHMRWMEL2QGD5Z65/action/citation_signature","submit_replication":"https://pith.science/pith/YQ3NO7JXWPLHMRWMEL2QGD5Z65/action/replication_record"}},"created_at":"2026-05-18T01:44:46.604767+00:00","updated_at":"2026-05-18T01:44:46.604767+00:00"}