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The nonlinearity acts edgewise and is given by a bilinear interaction between the positive and negative spectral parts, \\[ \\mathcal N(\\psi)=\\mathcal B\\bigl(\\Pi_+\\psi,\\Pi_-\\psi\\bigr), \\] where $\\Pi_\\pm$ are the spectral projections of $D$ and $\\mathcal B$ is a fix"},"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":"2606.09429","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2026-06-08T12:40:27Z","cross_cats_sorted":[],"title_canon_sha256":"f0fccae2c1be6506a4947c3b851d97415b54df58825e7c8795cb2aeb1649e83d","abstract_canon_sha256":"9810008ee3c99a8d0f0b5893319caa520750ec7155f26616488338d0bdb1b640"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-09T02:08:47.879685Z","signature_b64":"jaftGkRdncPCN14XUu9wu1UctSm5I54+82KvdDsg4JXhGTH60EfCo5bPrYhWKtLsm184KdX2QFNWZQdGT91dCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f9449cd9d440a8165625f7a3104c56f4f19b548ea204d073193e688adb285457","last_reissued_at":"2026-06-09T02:08:47.878928Z","signature_status":"signed_v1","first_computed_at":"2026-06-09T02:08:47.878928Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Low-regularity well-posedness for a mixed-sign quadratic Dirac equation on $N$-star metric graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Huichao Xing, Zhipeng Yang","submitted_at":"2026-06-08T12:40:27Z","abstract_excerpt":"We study the Cauchy problem for a mixed-sign quadratic Dirac equation on a noncompact $N$-star metric graph $G$, \\[ \\mathrm{i}\\partial_t \\psi = D\\psi - \\mathcal N(\\psi), \\qquad \\psi(0)=\\psi_0, \\] where $\\psi=(\\psi_1,\\psi_2)^{\\mathsf T}:\\mathbb{R}\\times G\\to\\mathbb{C}^2$ and $D$ denotes the self-adjoint Dirac-Kirchhoff operator on $G$. 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