{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2007:FQT6VGTB43CFGTESYSCWMBICEX","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":"996b4da32aa4afc28a0fb1869d303ba7cba1945b4331e95e7625cc2898bb9fdd","cross_cats_sorted":[],"license":"","primary_cat":"math.CO","submitted_at":"2007-10-02T07:24:15Z","title_canon_sha256":"3e3a12e19ae7b172d789b85588b1ef20e016f7887d562192fde0dfa766b28016"},"schema_version":"1.0","source":{"id":"0710.0447","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0710.0447","created_at":"2026-05-18T03:34:12Z"},{"alias_kind":"arxiv_version","alias_value":"0710.0447v1","created_at":"2026-05-18T03:34:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0710.0447","created_at":"2026-05-18T03:34:12Z"},{"alias_kind":"pith_short_12","alias_value":"FQT6VGTB43CF","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_16","alias_value":"FQT6VGTB43CFGTES","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_8","alias_value":"FQT6VGTB","created_at":"2026-05-18T12:25:55Z"}],"graph_snapshots":[{"event_id":"sha256:278127caf18c6d55365d233cd2aa04761c4233d3bd48007434ce81bf0840a345","target":"graph","created_at":"2026-05-18T03:34:12Z","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 prove conjectures of the third author [L. Tevlin, Proc. FPSAC'07, Tianjin] on two new bases of noncommutative symmetric functions: the transition matrices from the ribbon basis have nonnegative integral coefficients. This is done by means of two composition-valued statistics on permutations and packed words, which generalize the combinatorics of Genocchi numbers.","authors_text":"Florent Hivert, Jean-Christophe Novelli, Jean-Yves Thibon, Lenny Tevlin","cross_cats":[],"headline":"","license":"","primary_cat":"math.CO","submitted_at":"2007-10-02T07:24:15Z","title":"Permutation statistics related to a class of noncommutative symmetric functions and generalizations of the Genocchi numbers"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0710.0447","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":"sha256:2893b58dab411d37b28d48131659333b598c6ab1778541d4f22661a9dded1caf","target":"record","created_at":"2026-05-18T03:34:12Z","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":"996b4da32aa4afc28a0fb1869d303ba7cba1945b4331e95e7625cc2898bb9fdd","cross_cats_sorted":[],"license":"","primary_cat":"math.CO","submitted_at":"2007-10-02T07:24:15Z","title_canon_sha256":"3e3a12e19ae7b172d789b85588b1ef20e016f7887d562192fde0dfa766b28016"},"schema_version":"1.0","source":{"id":"0710.0447","kind":"arxiv","version":1}},"canonical_sha256":"2c27ea9a61e6c4534c92c48566050225e62ea5872c12217760c61c4a9d40c8c1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2c27ea9a61e6c4534c92c48566050225e62ea5872c12217760c61c4a9d40c8c1","first_computed_at":"2026-05-18T03:34:12.585172Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:34:12.585172Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"CC4zNirnKytouaUkpvWxLUsT7dAPTclChc0Skd437mp2GE2X+yUjIgVDnsjM6BPNJcao3C0d5d2bFAbNr6p6AA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:34:12.585693Z","signed_message":"canonical_sha256_bytes"},"source_id":"0710.0447","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2893b58dab411d37b28d48131659333b598c6ab1778541d4f22661a9dded1caf","sha256:278127caf18c6d55365d233cd2aa04761c4233d3bd48007434ce81bf0840a345"],"state_sha256":"2dcf31e92228fbb0e409513cb8b231753173f85e53a8a855f5e1f1abcccf4faa"}