{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:L4FFMC3IFHI3TY66NFEQ4PKZNL","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"fc204ae1bbed15bb599e083d0368ec927e9a1dc97ba341242b61859fbdee1a05","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2026-06-16T05:52:25Z","title_canon_sha256":"aa95480f88e942aa2956ee97996ca64bb7d67f43958be68dae410a80f74c785b"},"schema_version":"1.0","source":{"id":"2606.17549","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.17549","created_at":"2026-06-19T16:11:38Z"},{"alias_kind":"arxiv_version","alias_value":"2606.17549v2","created_at":"2026-06-19T16:11:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.17549","created_at":"2026-06-19T16:11:38Z"},{"alias_kind":"pith_short_12","alias_value":"L4FFMC3IFHI3","created_at":"2026-06-19T16:11:38Z"},{"alias_kind":"pith_short_16","alias_value":"L4FFMC3IFHI3TY66","created_at":"2026-06-19T16:11:38Z"},{"alias_kind":"pith_short_8","alias_value":"L4FFMC3I","created_at":"2026-06-19T16:11:38Z"}],"graph_snapshots":[{"event_id":"sha256:c23eb2b00d6bba17995f8db8e5f56c1847ed00ac59b33f8613ad44cea3216f71","target":"graph","created_at":"2026-06-19T16:11:38Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2606.17549/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"An upper homogeneous (upho) poset is a poset whose every principal filter is isomorphic to the whole poset. Fu--Peng--Zhang conjectured that every finitary upho poset admits a compatible left-cancellative, invertible-free monoid structure whose left-divisibility order coincides with the given order. 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","authors_text":"Ryunosuke Matsuoka","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2026-06-16T05:52:25Z","title":"A Non-Multiplicable Upho Poset Constructed from the Petersen Graph"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.17549","kind":"arxiv","version":2},"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":"sha256:9ca1c4282f3b017eac391c9859e84bf1efb528644c4a8cce38915476e8cef596","target":"record","created_at":"2026-06-19T16:11:38Z","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":"fc204ae1bbed15bb599e083d0368ec927e9a1dc97ba341242b61859fbdee1a05","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2026-06-16T05:52:25Z","title_canon_sha256":"aa95480f88e942aa2956ee97996ca64bb7d67f43958be68dae410a80f74c785b"},"schema_version":"1.0","source":{"id":"2606.17549","kind":"arxiv","version":2}},"canonical_sha256":"5f0a560b6829d1b9e3de69490e3d596ac41770054945b863415f8a772de783bd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5f0a560b6829d1b9e3de69490e3d596ac41770054945b863415f8a772de783bd","first_computed_at":"2026-06-19T16:11:38.616426Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-19T16:11:38.616426Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"zqshuCB45L/U92YnEWPcbkWvVaZUP0G9tUj7CVOchEaveenJJ3Fk8EMGsjayJRh7jgnN/eIrOkV9GdLNU9RGBA==","signature_status":"signed_v1","signed_at":"2026-06-19T16:11:38.616790Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.17549","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9ca1c4282f3b017eac391c9859e84bf1efb528644c4a8cce38915476e8cef596","sha256:c23eb2b00d6bba17995f8db8e5f56c1847ed00ac59b33f8613ad44cea3216f71"],"state_sha256":"1009650ab6fb6ecfbf14bc7c94aca800419a596423dc0f71fa70f697fe8db1cb"}