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K\\v r\\'i\\v z showed that if there is a soluble group of symmetries of $X$ that acts transitively on $X$, then $X$ is Ramsey. Determining which sets are Ramsey is a major unsolved problem.\n  In this paper we show that if there is a finite group of isometries of $\\mathbb R^d$ that acts transitively on a set $X$, and also on a set $Y$, then the `prism' formed by $X$ and $Y$ in $\\mathbb R^{d+1}$ (meaning the ","authors_text":"Imre Leader, Maria-Romina Ivan, Mark Walters","cross_cats":["math.GR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2026-06-11T15:25:49Z","title":"Generalised Prisms and Euclidean Ramsey Theory"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.13472","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:2e1f6b284eabc2fbf588b1f932365ea0b60212070e2e2c4aa450456eedada9ad","target":"record","created_at":"2026-06-12T01:10:04Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"e40ea12565a244de853ad333e3e68e8ba06eb3ae79cf2e74ef85cd93f89cf840","cross_cats_sorted":["math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2026-06-11T15:25:49Z","title_canon_sha256":"5d50904c5a41128e4f3e74f071c54bde1979916f000bf700c83a6f12d8aca619"},"schema_version":"1.0","source":{"id":"2606.13472","kind":"arxiv","version":1}},"canonical_sha256":"2f071b46c6aaea13ffd650464555d302a77dba4ce39468f71e6efeb52a283d83","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2f071b46c6aaea13ffd650464555d302a77dba4ce39468f71e6efeb52a283d83","first_computed_at":"2026-06-12T01:10:04.310757Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-12T01:10:04.310757Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"DI4hTLmUSal1QqFNvcLtz5Rv7pSS/CabRY7oc3xbkoUvNd4+vEVgUyNZKHfsAWQQe6Us67o3I7jP1ToabTXpAQ==","signature_status":"signed_v1","signed_at":"2026-06-12T01:10:04.311594Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.13472","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2e1f6b284eabc2fbf588b1f932365ea0b60212070e2e2c4aa450456eedada9ad","sha256:08c617c7f72ed2d4202dc5e66f444c716af1d06dc75295c8ac1ad6cabd553261"],"state_sha256":"9b057ac362f60fb23ddeb8ca1dd50ce2066e629a0a1a175dc44788b48eed6f94"}