{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:EQAEPZ2BRJZE7HXZLYQPAYOK6M","short_pith_number":"pith:EQAEPZ2B","canonical_record":{"source":{"id":"1812.04450","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2018-12-11T15:04:42Z","cross_cats_sorted":[],"title_canon_sha256":"3fd2861c69c8708800cd4b89c9d97558313a139f4100f3b93ef3b6ba66c3587e","abstract_canon_sha256":"10dcb2ad00298c59fe3849e11373d6438a628504dd7fb7fddb17e82359fb500a"},"schema_version":"1.0"},"canonical_sha256":"240047e7418a724f9ef95e20f061caf336bf3a35400f04f9e2ff7eb21197333b","source":{"kind":"arxiv","id":"1812.04450","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1812.04450","created_at":"2026-05-17T23:58:32Z"},{"alias_kind":"arxiv_version","alias_value":"1812.04450v1","created_at":"2026-05-17T23:58:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1812.04450","created_at":"2026-05-17T23:58:32Z"},{"alias_kind":"pith_short_12","alias_value":"EQAEPZ2BRJZE","created_at":"2026-05-18T12:32:22Z"},{"alias_kind":"pith_short_16","alias_value":"EQAEPZ2BRJZE7HXZ","created_at":"2026-05-18T12:32:22Z"},{"alias_kind":"pith_short_8","alias_value":"EQAEPZ2B","created_at":"2026-05-18T12:32:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:EQAEPZ2BRJZE7HXZLYQPAYOK6M","target":"record","payload":{"canonical_record":{"source":{"id":"1812.04450","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2018-12-11T15:04:42Z","cross_cats_sorted":[],"title_canon_sha256":"3fd2861c69c8708800cd4b89c9d97558313a139f4100f3b93ef3b6ba66c3587e","abstract_canon_sha256":"10dcb2ad00298c59fe3849e11373d6438a628504dd7fb7fddb17e82359fb500a"},"schema_version":"1.0"},"canonical_sha256":"240047e7418a724f9ef95e20f061caf336bf3a35400f04f9e2ff7eb21197333b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:58:32.082718Z","signature_b64":"xQybjhtKOUJ14QaaMLuftErWWQO1VUkTw/opambvSdliC+y1NhnSVSpRlB6NF5MVfb0eltxNdvKQNL4Ut2fkDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"240047e7418a724f9ef95e20f061caf336bf3a35400f04f9e2ff7eb21197333b","last_reissued_at":"2026-05-17T23:58:32.082143Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:58:32.082143Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1812.04450","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:58:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PZgKUw+1MQuOIwsgzZV/bmagnN8H2Suq+oHaYzYVjOFR7BMv2KY3Ww0uJKQ0s3vu/h9zG2R2fKSyJ/T4dLCyBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T19:05:20.740579Z"},"content_sha256":"0190a1fe2ef5316a831276a0c1c1963cadbaf3c185e7c4529c5e57f2fdb8efb4","schema_version":"1.0","event_id":"sha256:0190a1fe2ef5316a831276a0c1c1963cadbaf3c185e7c4529c5e57f2fdb8efb4"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:EQAEPZ2BRJZE7HXZLYQPAYOK6M","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Nonassociative Solomon's descent algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"J. M. P\\'erez-Izquierdo","submitted_at":"2018-12-11T15:04:42Z","abstract_excerpt":"Descent algebras of graded bialgebras were introduced by F. Patras as a generalization of Solomon's descent algebras for Coxeter groups of type $A$, i.e. symmetric groups. The universal enveloping algebra of the free Lie algebra on a countable number of generators, its descent algebra and Solomon's descent algebra, with its outer product, for symmetric groups are isomorphic to the Hopf algebra of noncommutative symmetric functions, a free associative algebra on a countable number of generators. In this paper we prove a similar result for universal enveloping algebras of relatively free Sabinin"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.04450","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:58:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"N5HH7iItinmgzqD03Nfu5IVcQSNbCpj6ucOyKjGM6Tjh4JyodCB04oQ2PBcKPFMY5NaZspatLRdpatiMhO/GCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T19:05:20.740931Z"},"content_sha256":"8c4caffa688d293ba2a8f7cb388389ff94835ba107e3452f3975035fb0d64e97","schema_version":"1.0","event_id":"sha256:8c4caffa688d293ba2a8f7cb388389ff94835ba107e3452f3975035fb0d64e97"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/EQAEPZ2BRJZE7HXZLYQPAYOK6M/bundle.json","state_url":"https://pith.science/pith/EQAEPZ2BRJZE7HXZLYQPAYOK6M/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/EQAEPZ2BRJZE7HXZLYQPAYOK6M/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-23T19:05:20Z","links":{"resolver":"https://pith.science/pith/EQAEPZ2BRJZE7HXZLYQPAYOK6M","bundle":"https://pith.science/pith/EQAEPZ2BRJZE7HXZLYQPAYOK6M/bundle.json","state":"https://pith.science/pith/EQAEPZ2BRJZE7HXZLYQPAYOK6M/state.json","well_known_bundle":"https://pith.science/.well-known/pith/EQAEPZ2BRJZE7HXZLYQPAYOK6M/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:EQAEPZ2BRJZE7HXZLYQPAYOK6M","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":"10dcb2ad00298c59fe3849e11373d6438a628504dd7fb7fddb17e82359fb500a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2018-12-11T15:04:42Z","title_canon_sha256":"3fd2861c69c8708800cd4b89c9d97558313a139f4100f3b93ef3b6ba66c3587e"},"schema_version":"1.0","source":{"id":"1812.04450","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1812.04450","created_at":"2026-05-17T23:58:32Z"},{"alias_kind":"arxiv_version","alias_value":"1812.04450v1","created_at":"2026-05-17T23:58:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1812.04450","created_at":"2026-05-17T23:58:32Z"},{"alias_kind":"pith_short_12","alias_value":"EQAEPZ2BRJZE","created_at":"2026-05-18T12:32:22Z"},{"alias_kind":"pith_short_16","alias_value":"EQAEPZ2BRJZE7HXZ","created_at":"2026-05-18T12:32:22Z"},{"alias_kind":"pith_short_8","alias_value":"EQAEPZ2B","created_at":"2026-05-18T12:32:22Z"}],"graph_snapshots":[{"event_id":"sha256:8c4caffa688d293ba2a8f7cb388389ff94835ba107e3452f3975035fb0d64e97","target":"graph","created_at":"2026-05-17T23:58:32Z","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":"Descent algebras of graded bialgebras were introduced by F. Patras as a generalization of Solomon's descent algebras for Coxeter groups of type $A$, i.e. symmetric groups. The universal enveloping algebra of the free Lie algebra on a countable number of generators, its descent algebra and Solomon's descent algebra, with its outer product, for symmetric groups are isomorphic to the Hopf algebra of noncommutative symmetric functions, a free associative algebra on a countable number of generators. In this paper we prove a similar result for universal enveloping algebras of relatively free Sabinin","authors_text":"J. M. P\\'erez-Izquierdo","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2018-12-11T15:04:42Z","title":"Nonassociative Solomon's descent algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.04450","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":"sha256:0190a1fe2ef5316a831276a0c1c1963cadbaf3c185e7c4529c5e57f2fdb8efb4","target":"record","created_at":"2026-05-17T23:58:32Z","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":"10dcb2ad00298c59fe3849e11373d6438a628504dd7fb7fddb17e82359fb500a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2018-12-11T15:04:42Z","title_canon_sha256":"3fd2861c69c8708800cd4b89c9d97558313a139f4100f3b93ef3b6ba66c3587e"},"schema_version":"1.0","source":{"id":"1812.04450","kind":"arxiv","version":1}},"canonical_sha256":"240047e7418a724f9ef95e20f061caf336bf3a35400f04f9e2ff7eb21197333b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"240047e7418a724f9ef95e20f061caf336bf3a35400f04f9e2ff7eb21197333b","first_computed_at":"2026-05-17T23:58:32.082143Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:58:32.082143Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"xQybjhtKOUJ14QaaMLuftErWWQO1VUkTw/opambvSdliC+y1NhnSVSpRlB6NF5MVfb0eltxNdvKQNL4Ut2fkDw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:58:32.082718Z","signed_message":"canonical_sha256_bytes"},"source_id":"1812.04450","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0190a1fe2ef5316a831276a0c1c1963cadbaf3c185e7c4529c5e57f2fdb8efb4","sha256:8c4caffa688d293ba2a8f7cb388389ff94835ba107e3452f3975035fb0d64e97"],"state_sha256":"ed386e3c2a723783eaa9a2df889648fcc3c00accc0c8f56cfd640d6a7a5f883b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OSlsSXMR+YFTasfhvtwe3E2gn9ktPlvYlRz2qDtujLAg1xaYJGuw9Nkii1lQTbj4V+n3EJChuGQJ/F4TK204DQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T19:05:20.742893Z","bundle_sha256":"ae8f684c27e6797e12f4430bb38cdbedc1ab18613dca775130517c7d128a47ee"}}