{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:DSIWBQJGDST7VBB4U4V4IKSH5W","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":"c71df695e8277e1e5e7293288c79b885378da8a1e8c92a3761b665164e6829e3","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-02-25T05:10:51Z","title_canon_sha256":"e01cbba1561b55663ad5efd581fc793ad75fa0c27d6fce5728db12b8b2d286cb"},"schema_version":"1.0","source":{"id":"1102.5159","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1102.5159","created_at":"2026-05-18T04:27:56Z"},{"alias_kind":"arxiv_version","alias_value":"1102.5159v1","created_at":"2026-05-18T04:27:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1102.5159","created_at":"2026-05-18T04:27:56Z"},{"alias_kind":"pith_short_12","alias_value":"DSIWBQJGDST7","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_16","alias_value":"DSIWBQJGDST7VBB4","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_8","alias_value":"DSIWBQJG","created_at":"2026-05-18T12:26:26Z"}],"graph_snapshots":[{"event_id":"sha256:5b8c3c88c7377c8e9084fb4153f2061d35868986b7c4ca1d3992bcb4f6661893","target":"graph","created_at":"2026-05-18T04:27:56Z","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"},"paper":{"abstract_excerpt":"John Holte [16] introduced a family of \"amazing matrices\" which give the transition probabilities of \"carries\" when adding a list of numbers. It was subsequently shown that these same matrices arise in the combinatorics of the Veronese embedding of commutative algebra [4,6,7] and in the analysis of riffle shuffling [6,7]. We find that the left eigenvectors of these matrices form the Foulkes character table of the symmetric group and the right eigenvectors are the Eulerian idempotents introduced by Loday [20] in work on Hochschild homology. The connections give new closed formulae for Foulkes c","authors_text":"Jason Fulman, Persi Diaconis","cross_cats":["math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-02-25T05:10:51Z","title":"Foulkes Characters, Eulerian Idempotents, and an Amazing Matrix"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.5159","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":"sha256:61698ba0e0e7986da3d3cba1bc2c761946346477886a71353fa65a31b6c79e93","target":"record","created_at":"2026-05-18T04:27:56Z","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":"c71df695e8277e1e5e7293288c79b885378da8a1e8c92a3761b665164e6829e3","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-02-25T05:10:51Z","title_canon_sha256":"e01cbba1561b55663ad5efd581fc793ad75fa0c27d6fce5728db12b8b2d286cb"},"schema_version":"1.0","source":{"id":"1102.5159","kind":"arxiv","version":1}},"canonical_sha256":"1c9160c1261ca7fa843ca72bc42a47ed837c231b6f5531261c1c8c2f375c4b1f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1c9160c1261ca7fa843ca72bc42a47ed837c231b6f5531261c1c8c2f375c4b1f","first_computed_at":"2026-05-18T04:27:56.155594Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:27:56.155594Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"C8QCB6Yb0S3EYARxFXiyQy2MH+WjGIJ3aDraIG39giPLVDTZXAlXJo5geFyrb+Gb2ocTnKQ148FFLg6SD9/tDA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:27:56.156188Z","signed_message":"canonical_sha256_bytes"},"source_id":"1102.5159","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:61698ba0e0e7986da3d3cba1bc2c761946346477886a71353fa65a31b6c79e93","sha256:5b8c3c88c7377c8e9084fb4153f2061d35868986b7c4ca1d3992bcb4f6661893"],"state_sha256":"1ece69762df6d04cd65674adf4f736c8967fd283457a0ec81e59b3d3e41b49a4"}