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We show that if $\\cX_R$ and $\\cY_R$ are log-regular, and at least one is semistable, then $\\Sk(\\cX_R\\times_R \\cY_R) \\simeq \\Sk(\\cX_R)\\times \\Sk(\\cY_R)$.\n  The essential skeleton $\\Sk(X_K)$, defined by Musta\\c{t}\\u{a} and Nicaise, is a birational invariant of $X_K$ and is independent of the choice o"},"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":"1712.07235","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-12-19T21:55:58Z","cross_cats_sorted":[],"title_canon_sha256":"f7f812ff3856abc0a3ba7815b905d1579ec26ee552addb13606b8bcf9363d684","abstract_canon_sha256":"8a5784342f8a262e808f7299bdb4ba8d96867dea810b4480292a54c3447c9e04"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:43:07.200557Z","signature_b64":"LDdlYVXMMPDbhQMKgm6gS8L58woiEmCVy87xp5ttIzeYmG74flhg0YuQwo/XDMtkOSDxu01/xiITSC1qMx9nBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"53dce603cfd32a196eca02e3aa3e52f1a3cbca6b8e6d7529af6926a5d3e7fd0b","last_reissued_at":"2026-05-17T23:43:07.200139Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:43:07.200139Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Essential Skeleton of a product of degenerations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Enrica Mazzon, Morgan Brown","submitted_at":"2017-12-19T21:55:58Z","abstract_excerpt":"We study the problem of how the dual complex of the special fiber of an snc degeneration $\\cX_R$ changes under products. 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