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Using Bourgain-type spaces defined through the spectral resolution of $D$, together with elementary $L^\\infty$ bounds for the Dirac flow and fractional Nemytskii estimates below the trace threshold, we prove local well-posedness for initial data \\[ \\psi_0\\in H_D^s(G)\\cap L^\\infty(G;\\math"},"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":"2607.09303","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2026-07-10T11:34:35Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"6bcd8bcd09feb40abb2f0abf4cb430b6cf28d6d2f2fbac809f091721fb3f79c6","abstract_canon_sha256":"03726c889e3276e4fd79a12fc9f167446305a40ed2f5e7e5c02a5e14c9acf102"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-13T01:18:59.998521Z","signature_b64":"IRZLLZnN1YjjvkaJEvQv17KmDiqs+8wXJt8o6raltOacBCAwAx3169fZa29KLIu/xR7SnINhhQyhfVHCdrb/Bw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"87b713e4679060f9b7074a5a1c3ce0ae6b26283d99d0ca13a45f8835568a5d20","last_reissued_at":"2026-07-13T01:18:59.997493Z","signature_status":"signed_v1","first_computed_at":"2026-07-13T01:18:59.997493Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Local well-posedness for nonlinear Dirac equation on $N$-star metric graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.AP","authors_text":"Huichao Xing, Zhipeng Yang","submitted_at":"2026-07-10T11:34:35Z","abstract_excerpt":"We consider the Cauchy problem for the nonlinear Dirac equation on a noncompact $N$-star metric graph $G$, \\[ \\mathrm{i}\\partial_t \\psi = D\\psi - |\\psi|^{p-2}\\psi, \\qquad \\psi(0)=\\psi_0, \\] where $p\\ge3$, $\\psi:\\mathbb{R}\\times G\\to\\mathbb{C}^2$ and $D$ denotes the self-adjoint Dirac-Kirchhoff operator on $G$. Using Bourgain-type spaces defined through the spectral resolution of $D$, together with elementary $L^\\infty$ bounds for the Dirac flow and fractional Nemytskii estimates below the trace threshold, we prove local well-posedness for initial data \\[ \\psi_0\\in H_D^s(G)\\cap L^\\infty(G;\\math"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.09303","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/2607.09303/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":"2607.09303","created_at":"2026-07-13T01:18:59.998014+00:00"},{"alias_kind":"arxiv_version","alias_value":"2607.09303v1","created_at":"2026-07-13T01:18:59.998014+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.09303","created_at":"2026-07-13T01:18:59.998014+00:00"},{"alias_kind":"pith_short_12","alias_value":"Q63RHZDHSBQP","created_at":"2026-07-13T01:18:59.998014+00:00"},{"alias_kind":"pith_short_16","alias_value":"Q63RHZDHSBQPTNYH","created_at":"2026-07-13T01:18:59.998014+00:00"},{"alias_kind":"pith_short_8","alias_value":"Q63RHZDH","created_at":"2026-07-13T01:18:59.998014+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/Q63RHZDHSBQPTNYHJJNBYPHAVZ","json":"https://pith.science/pith/Q63RHZDHSBQPTNYHJJNBYPHAVZ.json","graph_json":"https://pith.science/api/pith-number/Q63RHZDHSBQPTNYHJJNBYPHAVZ/graph.json","events_json":"https://pith.science/api/pith-number/Q63RHZDHSBQPTNYHJJNBYPHAVZ/events.json","paper":"https://pith.science/paper/Q63RHZDH"},"agent_actions":{"view_html":"https://pith.science/pith/Q63RHZDHSBQPTNYHJJNBYPHAVZ","download_json":"https://pith.science/pith/Q63RHZDHSBQPTNYHJJNBYPHAVZ.json","view_paper":"https://pith.science/paper/Q63RHZDH","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2607.09303&json=true","fetch_graph":"https://pith.science/api/pith-number/Q63RHZDHSBQPTNYHJJNBYPHAVZ/graph.json","fetch_events":"https://pith.science/api/pith-number/Q63RHZDHSBQPTNYHJJNBYPHAVZ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/Q63RHZDHSBQPTNYHJJNBYPHAVZ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/Q63RHZDHSBQPTNYHJJNBYPHAVZ/action/storage_attestation","attest_author":"https://pith.science/pith/Q63RHZDHSBQPTNYHJJNBYPHAVZ/action/author_attestation","sign_citation":"https://pith.science/pith/Q63RHZDHSBQPTNYHJJNBYPHAVZ/action/citation_signature","submit_replication":"https://pith.science/pith/Q63RHZDHSBQPTNYHJJNBYPHAVZ/action/replication_record"}},"created_at":"2026-07-13T01:18:59.998014+00:00","updated_at":"2026-07-13T01:18:59.998014+00:00"}