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We will prove that this set is locally contractible. We will also define the notion of a Lorentzian Aubry set ${\\cal A}$ and prove that the inclusions ${\\cal NU}(M,g)\\hookrightarrow \\operatorname{Cut}_M\\hookrightarrow J^+\\backslash {\\cal A}$ are homot"},"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":"2507.22737","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2025-07-30T14:57:03Z","cross_cats_sorted":["math-ph","math.DG","math.MP"],"title_canon_sha256":"4775d3b9c880d5973bc914ddb58f5adea71037cd42891391d66e5f8853849e17","abstract_canon_sha256":"8d4f5312cb3bbbfa3822207d43df1e7e0f1f1448216513855750ad63a5c0febb"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:45:48.116040Z","signature_b64":"wn8Xj2THxpzjt01bEtB+OFlgrXxm3XIRv2jhdr5DPkRWV5sADVi/32qdnojQhLGYRF9GvojSUivrUALD2+AqAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cbe847848293f1dc221148701b509049fc26eded6672588421c62f3693a9f573","last_reissued_at":"2026-07-05T11:45:48.115415Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:45:48.115415Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the locus of multiple maximizing geodesics on a globally hyperbolic spacetime","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math-ph","math.DG","math.MP"],"primary_cat":"math.OC","authors_text":"Alec Metsch","submitted_at":"2025-07-30T14:57:03Z","abstract_excerpt":"Extending the recent work of Cannarsa, Cheng and Fathi, we investigate topological properties of the locus ${\\cal NU}(M,g)$ of multiple maximizing geodesics on a globally hyperbolic spacetime $(M,g)$, i.e.\\ the set of causally related pairs $(x,y)$ for which there exists more than one maximizing geodesic (up to reparametrization) from $x$ to $y$. 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