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Del Pezzo","submitted_at":"2012-03-18T19:10:03Z","abstract_excerpt":"In this paper we study the game $p-$Laplacian on a tree, that is, $$ u(x)=\\frac{\\alpha}2\\left\\{\\max_{y\\in \\S(x)}u(y) + \\min_{y\\in \\S(x)}u(y)\\right\\} + \\frac{\\beta}{m}\\sum_{y\\in \\S(x)} u(y), $$ here $x$ is a vertex of the tree and $S(x)$ is the set of successors of $x$.\n  We study the family of the subsets of the tree that enjoy the unique continuation property, that is, subsets $U$ such that $u\\mid_U=0$ implies $u \\equiv 0$."},"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":"1203.3989","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-03-18T19:10:03Z","cross_cats_sorted":[],"title_canon_sha256":"a0c9de3737c6f1cb6e7309dec7a07714843339909028f68bb71063c443d69b37","abstract_canon_sha256":"e1e7056094de096d0f0dbb8f47ddfe42f8fef6a5f16ba7b405daae608d644f3f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:28:29.584102Z","signature_b64":"SnywOp3fZpsCTrTOnDx9lNHeFQa6IA5KxWhQ4xj0TlBDegMtQyW+eecGqfeA/QNCV1Ut8R+Teuk1hduub8mkDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c12a0c867b2961f4af16370f9a8b18bd8c768f8cd608745b499e957ba7c00ed8","last_reissued_at":"2026-05-18T02:28:29.583630Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:28:29.583630Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The unique continuation property for a nonlinear equation on trees","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Carolina A. 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