{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:MHPMR3CISDLO6O4FVISBFJOH3E","short_pith_number":"pith:MHPMR3CI","canonical_record":{"source":{"id":"1907.04411","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2019-07-09T20:57:09Z","cross_cats_sorted":["math.AT","math.CO"],"title_canon_sha256":"ad9e0b04fb033a44970a8c14a81bc93f5c138cf40786d7344c1c42cd01ba7824","abstract_canon_sha256":"70b521a00794b0629d2231d5bdd759d4020843c1c3dc7c3c021eee82d698ee5d"},"schema_version":"1.0"},"canonical_sha256":"61dec8ec4890d6ef3b85aa2412a5c7d9229e94b2ebe69ded90e7d83b06ff0140","source":{"kind":"arxiv","id":"1907.04411","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1907.04411","created_at":"2026-05-17T23:41:01Z"},{"alias_kind":"arxiv_version","alias_value":"1907.04411v1","created_at":"2026-05-17T23:41:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1907.04411","created_at":"2026-05-17T23:41:01Z"},{"alias_kind":"pith_short_12","alias_value":"MHPMR3CISDLO","created_at":"2026-05-18T12:33:21Z"},{"alias_kind":"pith_short_16","alias_value":"MHPMR3CISDLO6O4F","created_at":"2026-05-18T12:33:21Z"},{"alias_kind":"pith_short_8","alias_value":"MHPMR3CI","created_at":"2026-05-18T12:33:21Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:MHPMR3CISDLO6O4FVISBFJOH3E","target":"record","payload":{"canonical_record":{"source":{"id":"1907.04411","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2019-07-09T20:57:09Z","cross_cats_sorted":["math.AT","math.CO"],"title_canon_sha256":"ad9e0b04fb033a44970a8c14a81bc93f5c138cf40786d7344c1c42cd01ba7824","abstract_canon_sha256":"70b521a00794b0629d2231d5bdd759d4020843c1c3dc7c3c021eee82d698ee5d"},"schema_version":"1.0"},"canonical_sha256":"61dec8ec4890d6ef3b85aa2412a5c7d9229e94b2ebe69ded90e7d83b06ff0140","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:41:01.829587Z","signature_b64":"K0OsLYfgfQiMhc/6QgmSI5IRlTfYfJWBkFrAdOUaa/11xMCQFP+U5j9boWqXZJyNqiituThUwr/lizuvLN7QCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"61dec8ec4890d6ef3b85aa2412a5c7d9229e94b2ebe69ded90e7d83b06ff0140","last_reissued_at":"2026-05-17T23:41:01.828938Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:41:01.828938Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1907.04411","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":"2026-05-17T23:41:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cBCwPencLbQINx5Tn5lQTu0VHslNlsprWofNSpwG6aC2XkLymZyVvxCoITwBbCFOXax5L4FGzXRj+eptc5JWDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T01:41:47.093359Z"},"content_sha256":"5a2a97a348c7cd0d03266486d263ab0af5fd278c0c0862c305312b70095959dd","schema_version":"1.0","event_id":"sha256:5a2a97a348c7cd0d03266486d263ab0af5fd278c0c0862c305312b70095959dd"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:MHPMR3CISDLO6O4FVISBFJOH3E","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Split Hopf algebras, quasi-shuffle algebras, and the cohomology of Omega Sigma X","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT","math.CO"],"primary_cat":"math.RA","authors_text":"Nicholas J. Kuhn","submitted_at":"2019-07-09T20:57:09Z","abstract_excerpt":"Let A and B be two connected graded commutative k-algebras of finite type, where k is a perfect field of positive characteristic p. We prove that the quasi--shuffle algebras generated by A and B are isomorphic as Hopf algebras if and only if A and B are isomorphic as graded k-vector spaces equipped with a Frobenius (pth-power) map.\n  For the hardest part of this analysis, we work with the dual construction, and are led to study connected graded cocommutative Hopf algebras H with two additional properties: H is free as an associative algebra, and the projection onto the indecomposables is split"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.04411","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":"2026-05-17T23:41:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hyYc8v8F4w5JkKnCoNEWlLa8TQC+YqhR2SAmIu8oyZX9xNL+DTP8+Lrz0VBdxHa1jWGo5xa1b+wJW2YvlV8XCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T01:41:47.094115Z"},"content_sha256":"2c62f318042e6312cae027c9466126380f41417527ea872fdd5804127a1b833a","schema_version":"1.0","event_id":"sha256:2c62f318042e6312cae027c9466126380f41417527ea872fdd5804127a1b833a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MHPMR3CISDLO6O4FVISBFJOH3E/bundle.json","state_url":"https://pith.science/pith/MHPMR3CISDLO6O4FVISBFJOH3E/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MHPMR3CISDLO6O4FVISBFJOH3E/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":"2026-05-26T01:41:47Z","links":{"resolver":"https://pith.science/pith/MHPMR3CISDLO6O4FVISBFJOH3E","bundle":"https://pith.science/pith/MHPMR3CISDLO6O4FVISBFJOH3E/bundle.json","state":"https://pith.science/pith/MHPMR3CISDLO6O4FVISBFJOH3E/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MHPMR3CISDLO6O4FVISBFJOH3E/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:MHPMR3CISDLO6O4FVISBFJOH3E","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":"70b521a00794b0629d2231d5bdd759d4020843c1c3dc7c3c021eee82d698ee5d","cross_cats_sorted":["math.AT","math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2019-07-09T20:57:09Z","title_canon_sha256":"ad9e0b04fb033a44970a8c14a81bc93f5c138cf40786d7344c1c42cd01ba7824"},"schema_version":"1.0","source":{"id":"1907.04411","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1907.04411","created_at":"2026-05-17T23:41:01Z"},{"alias_kind":"arxiv_version","alias_value":"1907.04411v1","created_at":"2026-05-17T23:41:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1907.04411","created_at":"2026-05-17T23:41:01Z"},{"alias_kind":"pith_short_12","alias_value":"MHPMR3CISDLO","created_at":"2026-05-18T12:33:21Z"},{"alias_kind":"pith_short_16","alias_value":"MHPMR3CISDLO6O4F","created_at":"2026-05-18T12:33:21Z"},{"alias_kind":"pith_short_8","alias_value":"MHPMR3CI","created_at":"2026-05-18T12:33:21Z"}],"graph_snapshots":[{"event_id":"sha256:2c62f318042e6312cae027c9466126380f41417527ea872fdd5804127a1b833a","target":"graph","created_at":"2026-05-17T23:41:01Z","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":"Let A and B be two connected graded commutative k-algebras of finite type, where k is a perfect field of positive characteristic p. We prove that the quasi--shuffle algebras generated by A and B are isomorphic as Hopf algebras if and only if A and B are isomorphic as graded k-vector spaces equipped with a Frobenius (pth-power) map.\n  For the hardest part of this analysis, we work with the dual construction, and are led to study connected graded cocommutative Hopf algebras H with two additional properties: H is free as an associative algebra, and the projection onto the indecomposables is split","authors_text":"Nicholas J. Kuhn","cross_cats":["math.AT","math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2019-07-09T20:57:09Z","title":"Split Hopf algebras, quasi-shuffle algebras, and the cohomology of Omega Sigma X"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.04411","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":"sha256:5a2a97a348c7cd0d03266486d263ab0af5fd278c0c0862c305312b70095959dd","target":"record","created_at":"2026-05-17T23:41:01Z","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":"70b521a00794b0629d2231d5bdd759d4020843c1c3dc7c3c021eee82d698ee5d","cross_cats_sorted":["math.AT","math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2019-07-09T20:57:09Z","title_canon_sha256":"ad9e0b04fb033a44970a8c14a81bc93f5c138cf40786d7344c1c42cd01ba7824"},"schema_version":"1.0","source":{"id":"1907.04411","kind":"arxiv","version":1}},"canonical_sha256":"61dec8ec4890d6ef3b85aa2412a5c7d9229e94b2ebe69ded90e7d83b06ff0140","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"61dec8ec4890d6ef3b85aa2412a5c7d9229e94b2ebe69ded90e7d83b06ff0140","first_computed_at":"2026-05-17T23:41:01.828938Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:41:01.828938Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"K0OsLYfgfQiMhc/6QgmSI5IRlTfYfJWBkFrAdOUaa/11xMCQFP+U5j9boWqXZJyNqiituThUwr/lizuvLN7QCg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:41:01.829587Z","signed_message":"canonical_sha256_bytes"},"source_id":"1907.04411","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5a2a97a348c7cd0d03266486d263ab0af5fd278c0c0862c305312b70095959dd","sha256:2c62f318042e6312cae027c9466126380f41417527ea872fdd5804127a1b833a"],"state_sha256":"236d086624232f61f0cf52ec849223010b6551862c9f1dedc2311386f2d851c0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HH3H+uDoujjnAdV/uG77JJ4/KEsqgCGXDYwsJxL+bfPSToved5Z/sMfipwbwhTBcF2angYeuf0dyv3A0RBwkDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T01:41:47.098154Z","bundle_sha256":"2f16a5a32cfb245681334ff6bbf4d4a7be8057ea2ff7f2a32b932e8283ce6690"}}