{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:SFIRO2DYTVSSSEJ6CEJSEDKML5","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":"9f5a7e28cc717b8952508be66fa65e7f05adb779b5fb6ca7d7b6c57790a3de79","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2008-04-07T01:10:12Z","title_canon_sha256":"9bf18358055a824d282b112448ccc5a4211784c6a3711742b605d000364a3f86"},"schema_version":"1.0","source":{"id":"0804.0944","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0804.0944","created_at":"2026-05-18T01:00:10Z"},{"alias_kind":"arxiv_version","alias_value":"0804.0944v1","created_at":"2026-05-18T01:00:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0804.0944","created_at":"2026-05-18T01:00:10Z"},{"alias_kind":"pith_short_12","alias_value":"SFIRO2DYTVSS","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"SFIRO2DYTVSSSEJ6","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"SFIRO2DY","created_at":"2026-05-18T12:25:58Z"}],"graph_snapshots":[{"event_id":"sha256:c33b2eb2b5c2d055d18aecd6299c59747407f0be47b26fcb10a10f39f1b103a0","target":"graph","created_at":"2026-05-18T01:00:10Z","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":"We introduce non-commutative analogues of $k$-Schur functions of Lapointe-Lascoux and Morse. We give an explicit formulas for the expansions of non-commutive functions with one and two parameters in terms of these new functions. These results are similar to the conjectures existing in the commutative case.","authors_text":"F. Descouens, M. Zabrocki, N. Bergeron","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2008-04-07T01:10:12Z","title":"A non-commutative generalization of $k$-Schur functions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0804.0944","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":"sha256:1fe4381c662369a60bad31168c23787f8f2ff0b9d125bf39d22c925194e0759e","target":"record","created_at":"2026-05-18T01:00:10Z","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":"9f5a7e28cc717b8952508be66fa65e7f05adb779b5fb6ca7d7b6c57790a3de79","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2008-04-07T01:10:12Z","title_canon_sha256":"9bf18358055a824d282b112448ccc5a4211784c6a3711742b605d000364a3f86"},"schema_version":"1.0","source":{"id":"0804.0944","kind":"arxiv","version":1}},"canonical_sha256":"91511768789d6529113e1113220d4c5f78c825f1b2183b056c3dac63026f93a3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"91511768789d6529113e1113220d4c5f78c825f1b2183b056c3dac63026f93a3","first_computed_at":"2026-05-18T01:00:10.762694Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:00:10.762694Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"2vPVMED/2XknelDdXX0bdmJRVzshDPt0tUwsRBUGrOhBgd//j1sURBpsqM+5K/Ph9KYcqYl9Pjw2NgaCpmbcAA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:00:10.763388Z","signed_message":"canonical_sha256_bytes"},"source_id":"0804.0944","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1fe4381c662369a60bad31168c23787f8f2ff0b9d125bf39d22c925194e0759e","sha256:c33b2eb2b5c2d055d18aecd6299c59747407f0be47b26fcb10a10f39f1b103a0"],"state_sha256":"bfa992c823a7df13faab87b194d2be84ab6282f8a7c331c4a6c26bc4b66c006a"}