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We show that with free boundary conditions, for k \\geq 3, some sites fixate for large times and some do not, whereas for k=2, all sites fixate. With periodic boundary conditions, for k \\geq 4, some sites fixate and others do not, while for k=2 and 3, all sites fixate."},"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":"1303.2505","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-03-11T13:05:54Z","cross_cats_sorted":[],"title_canon_sha256":"381aa20af2c45f67f46f39e35585258ddffc5eaa014012bcdf7ef5641b117f7f","abstract_canon_sha256":"a497fe3fc3516a64f6f0791c0b6aa20c6555a497e5bfadc7dbdd694f2a7d2a68"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:31:18.827163Z","signature_b64":"rOqhe5BFMCBEobpaNQC9yznTpACQD3U95ZlUixT/HuLIt7U+PGYO7cc0Dtvj9/Fa7Ub+KZWG2dUhXm2PaJ4YAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5fed379972f12f775856ca8399d4a2350fa2eab70fc9633f623d692bf4e39e89","last_reissued_at":"2026-05-18T03:31:18.826344Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:31:18.826344Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Coarsening in 2D slabs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Charles M. 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