{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:B5XZMU2PQXZC5WW6ZKZB64REKX","short_pith_number":"pith:B5XZMU2P","schema_version":"1.0","canonical_sha256":"0f6f96534f85f22edadecab21f722455ca14810ecff87e2f77dd4a43290ca572","source":{"kind":"arxiv","id":"1711.01029","version":1},"attestation_state":"computed","paper":{"title":"On the Global Limiting Absorption Principle for Massless Dirac Operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.SP","authors_text":"Alan Carey, Denis Potapov, Fedor Sukochev, Fritz Gesztesy, Galina Levitina, Jens Kaad, Roger Nichols","submitted_at":"2017-11-03T05:10:13Z","abstract_excerpt":"We prove a global limiting absorption principle on the entire real line for free, massless Dirac operators $H_0 = \\alpha \\cdot (-i \\nabla)$ for all space dimensions $n \\in \\mathbb{N}$, $n \\geq 2$. This is a new result for all dimensions other than three, in particular, it applies to the two-dimensional case which is known to be of some relevance in applications to graphene.\n  We also prove an essential self-adjointness result for first-order matrix-valued differential operators with Lipschitz coefficients."},"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":"1711.01029","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2017-11-03T05:10:13Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"3961e2d6f9ffe75a09f85894b52b6cc6a98222fbae124c8633e230b48ed1cbd4","abstract_canon_sha256":"bec731cec6b42e55131db97192668c863fc545d6f96c076546ed813c2f9e58dc"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:09:30.429713Z","signature_b64":"RjKnqTJLKpnv0crKi+HO2xtrtE2EOxdWYqpsha0ZB9m+Gu/CGWhN0JImqr35rZ34Xl4QMQWt60YwCDxWrqPuCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0f6f96534f85f22edadecab21f722455ca14810ecff87e2f77dd4a43290ca572","last_reissued_at":"2026-05-18T00:09:30.428898Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:09:30.428898Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the Global Limiting Absorption Principle for Massless Dirac Operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.SP","authors_text":"Alan Carey, Denis Potapov, Fedor Sukochev, Fritz Gesztesy, Galina Levitina, Jens Kaad, Roger Nichols","submitted_at":"2017-11-03T05:10:13Z","abstract_excerpt":"We prove a global limiting absorption principle on the entire real line for free, massless Dirac operators $H_0 = \\alpha \\cdot (-i \\nabla)$ for all space dimensions $n \\in \\mathbb{N}$, $n \\geq 2$. This is a new result for all dimensions other than three, in particular, it applies to the two-dimensional case which is known to be of some relevance in applications to graphene.\n  We also prove an essential self-adjointness result for first-order matrix-valued differential operators with Lipschitz coefficients."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.01029","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":"1711.01029","created_at":"2026-05-18T00:09:30.429031+00:00"},{"alias_kind":"arxiv_version","alias_value":"1711.01029v1","created_at":"2026-05-18T00:09:30.429031+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1711.01029","created_at":"2026-05-18T00:09:30.429031+00:00"},{"alias_kind":"pith_short_12","alias_value":"B5XZMU2PQXZC","created_at":"2026-05-18T12:31:08.081275+00:00"},{"alias_kind":"pith_short_16","alias_value":"B5XZMU2PQXZC5WW6","created_at":"2026-05-18T12:31:08.081275+00:00"},{"alias_kind":"pith_short_8","alias_value":"B5XZMU2P","created_at":"2026-05-18T12:31:08.081275+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/B5XZMU2PQXZC5WW6ZKZB64REKX","json":"https://pith.science/pith/B5XZMU2PQXZC5WW6ZKZB64REKX.json","graph_json":"https://pith.science/api/pith-number/B5XZMU2PQXZC5WW6ZKZB64REKX/graph.json","events_json":"https://pith.science/api/pith-number/B5XZMU2PQXZC5WW6ZKZB64REKX/events.json","paper":"https://pith.science/paper/B5XZMU2P"},"agent_actions":{"view_html":"https://pith.science/pith/B5XZMU2PQXZC5WW6ZKZB64REKX","download_json":"https://pith.science/pith/B5XZMU2PQXZC5WW6ZKZB64REKX.json","view_paper":"https://pith.science/paper/B5XZMU2P","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1711.01029&json=true","fetch_graph":"https://pith.science/api/pith-number/B5XZMU2PQXZC5WW6ZKZB64REKX/graph.json","fetch_events":"https://pith.science/api/pith-number/B5XZMU2PQXZC5WW6ZKZB64REKX/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/B5XZMU2PQXZC5WW6ZKZB64REKX/action/timestamp_anchor","attest_storage":"https://pith.science/pith/B5XZMU2PQXZC5WW6ZKZB64REKX/action/storage_attestation","attest_author":"https://pith.science/pith/B5XZMU2PQXZC5WW6ZKZB64REKX/action/author_attestation","sign_citation":"https://pith.science/pith/B5XZMU2PQXZC5WW6ZKZB64REKX/action/citation_signature","submit_replication":"https://pith.science/pith/B5XZMU2PQXZC5WW6ZKZB64REKX/action/replication_record"}},"created_at":"2026-05-18T00:09:30.429031+00:00","updated_at":"2026-05-18T00:09:30.429031+00:00"}