{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:SZ4RHGY5RZCU6AI3YDCARDHZV4","short_pith_number":"pith:SZ4RHGY5","schema_version":"1.0","canonical_sha256":"9679139b1d8e454f011bc0c4088cf9af3f1fa3fcac77aa1a955b88e958d61688","source":{"kind":"arxiv","id":"2606.20965","version":1},"attestation_state":"computed","paper":{"title":"Localization and eigenvalue asymptotics for long-range discrete Dirac operators with Stark potential","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.SP","authors_text":"C\\'esar de Oliveira, Mariane Pigossi, Moacir Aloisio","submitted_at":"2026-06-18T22:02:15Z","abstract_excerpt":"We study long-range discrete Dirac operators with Stark potential, extending the theory of Stark localization from scalar lattice models to systems with internal spinorial structure. We initially investigate the local setting, where two distinct localization mechanisms arise. The standard local Dirac-Stark operator yields two Stark-type spectral ladders and exponentially localized spinorial eigenfunctions. Conversely, a related pure-shift local model exhibits an invariant block structure that leads to explicitly computable eigenvalues and exact localization, with eigenfunctions compactly suppo"},"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":"2606.20965","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2026-06-18T22:02:15Z","cross_cats_sorted":[],"title_canon_sha256":"cb65e752997d561c7db57bee67a04ce3eea10acb95b71ea1b972f7a4673311b0","abstract_canon_sha256":"103943918c0bcd330b24a2a1f4981dbf39dce0ed0ca67c760723a7f2d42c228a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-23T01:12:23.501469Z","signature_b64":"NOr6hzqiaNaRZDlyntzX5rews1ivS23LJkaJeqUqev2d+KD6rC663W97k+KWeKR/rJa7g3rASRCy7/CzhK2FAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9679139b1d8e454f011bc0c4088cf9af3f1fa3fcac77aa1a955b88e958d61688","last_reissued_at":"2026-06-23T01:12:23.500989Z","signature_status":"signed_v1","first_computed_at":"2026-06-23T01:12:23.500989Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Localization and eigenvalue asymptotics for long-range discrete Dirac operators with Stark potential","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.SP","authors_text":"C\\'esar de Oliveira, Mariane Pigossi, Moacir Aloisio","submitted_at":"2026-06-18T22:02:15Z","abstract_excerpt":"We study long-range discrete Dirac operators with Stark potential, extending the theory of Stark localization from scalar lattice models to systems with internal spinorial structure. We initially investigate the local setting, where two distinct localization mechanisms arise. The standard local Dirac-Stark operator yields two Stark-type spectral ladders and exponentially localized spinorial eigenfunctions. Conversely, a related pure-shift local model exhibits an invariant block structure that leads to explicitly computable eigenvalues and exact localization, with eigenfunctions compactly suppo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.20965","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.20965/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2606.20965","created_at":"2026-06-23T01:12:23.501083+00:00"},{"alias_kind":"arxiv_version","alias_value":"2606.20965v1","created_at":"2026-06-23T01:12:23.501083+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.20965","created_at":"2026-06-23T01:12:23.501083+00:00"},{"alias_kind":"pith_short_12","alias_value":"SZ4RHGY5RZCU","created_at":"2026-06-23T01:12:23.501083+00:00"},{"alias_kind":"pith_short_16","alias_value":"SZ4RHGY5RZCU6AI3","created_at":"2026-06-23T01:12:23.501083+00:00"},{"alias_kind":"pith_short_8","alias_value":"SZ4RHGY5","created_at":"2026-06-23T01:12:23.501083+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/SZ4RHGY5RZCU6AI3YDCARDHZV4","json":"https://pith.science/pith/SZ4RHGY5RZCU6AI3YDCARDHZV4.json","graph_json":"https://pith.science/api/pith-number/SZ4RHGY5RZCU6AI3YDCARDHZV4/graph.json","events_json":"https://pith.science/api/pith-number/SZ4RHGY5RZCU6AI3YDCARDHZV4/events.json","paper":"https://pith.science/paper/SZ4RHGY5"},"agent_actions":{"view_html":"https://pith.science/pith/SZ4RHGY5RZCU6AI3YDCARDHZV4","download_json":"https://pith.science/pith/SZ4RHGY5RZCU6AI3YDCARDHZV4.json","view_paper":"https://pith.science/paper/SZ4RHGY5","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2606.20965&json=true","fetch_graph":"https://pith.science/api/pith-number/SZ4RHGY5RZCU6AI3YDCARDHZV4/graph.json","fetch_events":"https://pith.science/api/pith-number/SZ4RHGY5RZCU6AI3YDCARDHZV4/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/SZ4RHGY5RZCU6AI3YDCARDHZV4/action/timestamp_anchor","attest_storage":"https://pith.science/pith/SZ4RHGY5RZCU6AI3YDCARDHZV4/action/storage_attestation","attest_author":"https://pith.science/pith/SZ4RHGY5RZCU6AI3YDCARDHZV4/action/author_attestation","sign_citation":"https://pith.science/pith/SZ4RHGY5RZCU6AI3YDCARDHZV4/action/citation_signature","submit_replication":"https://pith.science/pith/SZ4RHGY5RZCU6AI3YDCARDHZV4/action/replication_record"}},"created_at":"2026-06-23T01:12:23.501083+00:00","updated_at":"2026-06-23T01:12:23.501083+00:00"}