{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:UDCBBOBW5FKGENXZG6OUTAB3XH","short_pith_number":"pith:UDCBBOBW","schema_version":"1.0","canonical_sha256":"a0c410b836e9546236f9379d49803bb9fb87e529f66a6262f4bff14a5de1e88d","source":{"kind":"arxiv","id":"1810.11555","version":1},"attestation_state":"computed","paper":{"title":"Coherent systems of probability measures on graphs for representations of free Frobenius towers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO","math.PR"],"primary_cat":"math.RT","authors_text":"Henry Kvinge","submitted_at":"2018-10-26T23:37:20Z","abstract_excerpt":"First formally defined by Borodin and Olshanski, a coherent system on a graded graph is a sequence of probability measures which respect the action of certain down/up transition functions between graded components. In one common example of such a construction, each measure is the Plancherel measure for the symmetric group $S_{n}$ and the down transition function is induced from the inclusions $S_{n} \\hookrightarrow S_{n+1}$.\n  In this paper we generalize the above framework to the case where $\\{A_n\\}_{n \\geq 0}$ is any free Frobenius tower and $A_n$ is no longer assumed to be semisimple. In pa"},"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":"1810.11555","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2018-10-26T23:37:20Z","cross_cats_sorted":["math.CO","math.PR"],"title_canon_sha256":"94dc04b03fc842e30ede97caeb6b7a0d95e4b7f3691f13f9956db97442fed997","abstract_canon_sha256":"4ef6692eca25ed54f5b967a30b06ae860234618ea11032d95fa296a6cb0db822"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:02:08.263110Z","signature_b64":"2b0pQe3uo9H04bMQZ+OkWHHKzim23rP83EI3GWhpLd7aCeRNwhIUKGY9JnLiglVx6XXP+4KANNqfESsoWt8yAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a0c410b836e9546236f9379d49803bb9fb87e529f66a6262f4bff14a5de1e88d","last_reissued_at":"2026-05-18T00:02:08.262368Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:02:08.262368Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Coherent systems of probability measures on graphs for representations of free Frobenius towers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO","math.PR"],"primary_cat":"math.RT","authors_text":"Henry Kvinge","submitted_at":"2018-10-26T23:37:20Z","abstract_excerpt":"First formally defined by Borodin and Olshanski, a coherent system on a graded graph is a sequence of probability measures which respect the action of certain down/up transition functions between graded components. In one common example of such a construction, each measure is the Plancherel measure for the symmetric group $S_{n}$ and the down transition function is induced from the inclusions $S_{n} \\hookrightarrow S_{n+1}$.\n  In this paper we generalize the above framework to the case where $\\{A_n\\}_{n \\geq 0}$ is any free Frobenius tower and $A_n$ is no longer assumed to be semisimple. In pa"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.11555","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1810.11555","created_at":"2026-05-18T00:02:08.262487+00:00"},{"alias_kind":"arxiv_version","alias_value":"1810.11555v1","created_at":"2026-05-18T00:02:08.262487+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.11555","created_at":"2026-05-18T00:02:08.262487+00:00"},{"alias_kind":"pith_short_12","alias_value":"UDCBBOBW5FKG","created_at":"2026-05-18T12:32:56.356000+00:00"},{"alias_kind":"pith_short_16","alias_value":"UDCBBOBW5FKGENXZ","created_at":"2026-05-18T12:32:56.356000+00:00"},{"alias_kind":"pith_short_8","alias_value":"UDCBBOBW","created_at":"2026-05-18T12:32:56.356000+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/UDCBBOBW5FKGENXZG6OUTAB3XH","json":"https://pith.science/pith/UDCBBOBW5FKGENXZG6OUTAB3XH.json","graph_json":"https://pith.science/api/pith-number/UDCBBOBW5FKGENXZG6OUTAB3XH/graph.json","events_json":"https://pith.science/api/pith-number/UDCBBOBW5FKGENXZG6OUTAB3XH/events.json","paper":"https://pith.science/paper/UDCBBOBW"},"agent_actions":{"view_html":"https://pith.science/pith/UDCBBOBW5FKGENXZG6OUTAB3XH","download_json":"https://pith.science/pith/UDCBBOBW5FKGENXZG6OUTAB3XH.json","view_paper":"https://pith.science/paper/UDCBBOBW","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1810.11555&json=true","fetch_graph":"https://pith.science/api/pith-number/UDCBBOBW5FKGENXZG6OUTAB3XH/graph.json","fetch_events":"https://pith.science/api/pith-number/UDCBBOBW5FKGENXZG6OUTAB3XH/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/UDCBBOBW5FKGENXZG6OUTAB3XH/action/timestamp_anchor","attest_storage":"https://pith.science/pith/UDCBBOBW5FKGENXZG6OUTAB3XH/action/storage_attestation","attest_author":"https://pith.science/pith/UDCBBOBW5FKGENXZG6OUTAB3XH/action/author_attestation","sign_citation":"https://pith.science/pith/UDCBBOBW5FKGENXZG6OUTAB3XH/action/citation_signature","submit_replication":"https://pith.science/pith/UDCBBOBW5FKGENXZG6OUTAB3XH/action/replication_record"}},"created_at":"2026-05-18T00:02:08.262487+00:00","updated_at":"2026-05-18T00:02:08.262487+00:00"}