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We study this process on the 3-regular tree $\\mathbb{T}_3$, where it is known that the critical threshold $p_c$, below which $\\mathbb{P}_p$-a.s. all spins fixate to $-1$, is strictly less than $1/2$. Defining $\\theta(p)$ to be the $\\mathbb{P}_p$-probability that a vertex fixates to $+1$, we show that $\\theta$ is a c"},"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":"1904.11625","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2019-04-25T23:30:37Z","cross_cats_sorted":[],"title_canon_sha256":"3f9de24b07b92e71396d074feae751199cb1d4ad8995085c080104978dc78b8c","abstract_canon_sha256":"a7eff66e3da1e0473f4d7de3ab7070ca24424cc023101550459377fc1e6c1ad0"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:47:43.192948Z","signature_b64":"FAoN+rj6E4NJSGt7F1LIH2Y+AkrAe5LA2GUX7E96MN+kdYeza4dqI0Xem2tMnXUa8kS8X2609N/3dRzyrFC0DA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e4e6110cfc21f6eba85119ca8bed9830ca803fd828d23852c8d04c5375576948","last_reissued_at":"2026-05-17T23:47:43.192335Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:47:43.192335Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Zero-temperature Glauber dynamics on the 3-regular tree and the median process","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Arnab Sen, Michael Damron","submitted_at":"2019-04-25T23:30:37Z","abstract_excerpt":"In zero-temperature Glauber dynamics, vertices of a graph are given i.i.d.~initial spins $\\sigma_x(0)$ from $\\{-1,+1\\}$ with $\\mathbb{P}_p(\\sigma_x(0) = +1)=p$, and they update their spins at the arrival times of i.i.d. 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