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We disprove this conjecture. For every vertex-transitive graph $G$, we construct a finitary upho poset $P(G,v_0)$ from walks starting at a fixed vertex $v_0$. Applying this construction to the Petersen graph, we show that multiplicability of $P(G,v_0)$ would force the automorphism group of $G$ to 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":"2606.17549","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2026-06-16T05:52:25Z","cross_cats_sorted":[],"title_canon_sha256":"aa95480f88e942aa2956ee97996ca64bb7d67f43958be68dae410a80f74c785b","abstract_canon_sha256":"fc204ae1bbed15bb599e083d0368ec927e9a1dc97ba341242b61859fbdee1a05"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-19T16:11:38.616790Z","signature_b64":"zqshuCB45L/U92YnEWPcbkWvVaZUP0G9tUj7CVOchEaveenJJ3Fk8EMGsjayJRh7jgnN/eIrOkV9GdLNU9RGBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5f0a560b6829d1b9e3de69490e3d596ac41770054945b863415f8a772de783bd","last_reissued_at":"2026-06-19T16:11:38.616426Z","signature_status":"signed_v1","first_computed_at":"2026-06-19T16:11:38.616426Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A Non-Multiplicable Upho Poset Constructed from the Petersen Graph","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Ryunosuke Matsuoka","submitted_at":"2026-06-16T05:52:25Z","abstract_excerpt":"An upper homogeneous (upho) poset is a poset whose every principal filter is isomorphic to the whole poset. 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