{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:6GNK64STHM7XBQT4E5QRWR2OG3","short_pith_number":"pith:6GNK64ST","schema_version":"1.0","canonical_sha256":"f19aaf72533b3f70c27c27611b474e36c76b07f262c3356ac50f47dbafcddbe8","source":{"kind":"arxiv","id":"1706.06479","version":1},"attestation_state":"computed","paper":{"title":"On the cubic Dirac equation with potential and the Lochak--Majorana condition","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.AP","authors_text":"Mamoru Okamoto, Piero D'Ancona","submitted_at":"2017-06-19T15:10:51Z","abstract_excerpt":"We study a cubic Dirac equation on $\\mathbb{R}\\times\\mathbb{R}^{3}$ \\begin{equation*}\n  i \\partial _t u + \\mathcal{D} u + V(x) u =\n  \\langle \\beta u,u \\rangle \\beta u\n  \\end{equation*} perturbed by a large potential with almost critical regularity. We prove global existence and scattering for small initial data in $H^{1}$ with additional angular regularity. The main tool is an endpoint Strichartz estimate for the perturbed Dirac flow. In particular, the result covers the case of spherically symmetric data with small $H^{1}$ norm.\n  When the potential $V$ has a suitable structure, we prove glob"},"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":"1706.06479","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-06-19T15:10:51Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"33953efebdeefd1fbb672b0601710ecaac1ba0d9bd07db38539e793b7e2be9d9","abstract_canon_sha256":"031b30139dd39df0d068b508310126a8f776e3924b4527696aa22511f1313458"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:39:42.200436Z","signature_b64":"fbJGRFw7omwKYWufrwvVnZL/qT84ktwOaUKECQrmq5kEE+PFcNXvP2Khku5uuWOPw9ZIFBV5Z1U+TbwexSzoBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f19aaf72533b3f70c27c27611b474e36c76b07f262c3356ac50f47dbafcddbe8","last_reissued_at":"2026-05-17T23:39:42.199740Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:39:42.199740Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the cubic Dirac equation with potential and the Lochak--Majorana condition","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.AP","authors_text":"Mamoru Okamoto, Piero D'Ancona","submitted_at":"2017-06-19T15:10:51Z","abstract_excerpt":"We study a cubic Dirac equation on $\\mathbb{R}\\times\\mathbb{R}^{3}$ \\begin{equation*}\n  i \\partial _t u + \\mathcal{D} u + V(x) u =\n  \\langle \\beta u,u \\rangle \\beta u\n  \\end{equation*} perturbed by a large potential with almost critical regularity. We prove global existence and scattering for small initial data in $H^{1}$ with additional angular regularity. The main tool is an endpoint Strichartz estimate for the perturbed Dirac flow. In particular, the result covers the case of spherically symmetric data with small $H^{1}$ norm.\n  When the potential $V$ has a suitable structure, we prove glob"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.06479","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":"1706.06479","created_at":"2026-05-17T23:39:42.199862+00:00"},{"alias_kind":"arxiv_version","alias_value":"1706.06479v1","created_at":"2026-05-17T23:39:42.199862+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.06479","created_at":"2026-05-17T23:39:42.199862+00:00"},{"alias_kind":"pith_short_12","alias_value":"6GNK64STHM7X","created_at":"2026-05-18T12:31:03.183658+00:00"},{"alias_kind":"pith_short_16","alias_value":"6GNK64STHM7XBQT4","created_at":"2026-05-18T12:31:03.183658+00:00"},{"alias_kind":"pith_short_8","alias_value":"6GNK64ST","created_at":"2026-05-18T12:31:03.183658+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/6GNK64STHM7XBQT4E5QRWR2OG3","json":"https://pith.science/pith/6GNK64STHM7XBQT4E5QRWR2OG3.json","graph_json":"https://pith.science/api/pith-number/6GNK64STHM7XBQT4E5QRWR2OG3/graph.json","events_json":"https://pith.science/api/pith-number/6GNK64STHM7XBQT4E5QRWR2OG3/events.json","paper":"https://pith.science/paper/6GNK64ST"},"agent_actions":{"view_html":"https://pith.science/pith/6GNK64STHM7XBQT4E5QRWR2OG3","download_json":"https://pith.science/pith/6GNK64STHM7XBQT4E5QRWR2OG3.json","view_paper":"https://pith.science/paper/6GNK64ST","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1706.06479&json=true","fetch_graph":"https://pith.science/api/pith-number/6GNK64STHM7XBQT4E5QRWR2OG3/graph.json","fetch_events":"https://pith.science/api/pith-number/6GNK64STHM7XBQT4E5QRWR2OG3/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/6GNK64STHM7XBQT4E5QRWR2OG3/action/timestamp_anchor","attest_storage":"https://pith.science/pith/6GNK64STHM7XBQT4E5QRWR2OG3/action/storage_attestation","attest_author":"https://pith.science/pith/6GNK64STHM7XBQT4E5QRWR2OG3/action/author_attestation","sign_citation":"https://pith.science/pith/6GNK64STHM7XBQT4E5QRWR2OG3/action/citation_signature","submit_replication":"https://pith.science/pith/6GNK64STHM7XBQT4E5QRWR2OG3/action/replication_record"}},"created_at":"2026-05-17T23:39:42.199862+00:00","updated_at":"2026-05-17T23:39:42.199862+00:00"}