{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:37SS4ABUHPJV77ER4MCN45LFSX","short_pith_number":"pith:37SS4ABU","canonical_record":{"source":{"id":"1801.04239","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2018-01-12T17:09:06Z","cross_cats_sorted":["math.AC"],"title_canon_sha256":"b3a05837298b3fdbdd55cdc05aa02c946df010fca1a6120fff4c983642038161","abstract_canon_sha256":"ab8508be77adc9766f12be3952b41e897637a5a08dc4613a141df25a66862b70"},"schema_version":"1.0"},"canonical_sha256":"dfe52e00343bd35ffc91e304de756595dbb1e825bcc8877cb0344366a5650610","source":{"kind":"arxiv","id":"1801.04239","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1801.04239","created_at":"2026-05-18T00:26:09Z"},{"alias_kind":"arxiv_version","alias_value":"1801.04239v1","created_at":"2026-05-18T00:26:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1801.04239","created_at":"2026-05-18T00:26:09Z"},{"alias_kind":"pith_short_12","alias_value":"37SS4ABUHPJV","created_at":"2026-05-18T12:32:02Z"},{"alias_kind":"pith_short_16","alias_value":"37SS4ABUHPJV77ER","created_at":"2026-05-18T12:32:02Z"},{"alias_kind":"pith_short_8","alias_value":"37SS4ABU","created_at":"2026-05-18T12:32:02Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:37SS4ABUHPJV77ER4MCN45LFSX","target":"record","payload":{"canonical_record":{"source":{"id":"1801.04239","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2018-01-12T17:09:06Z","cross_cats_sorted":["math.AC"],"title_canon_sha256":"b3a05837298b3fdbdd55cdc05aa02c946df010fca1a6120fff4c983642038161","abstract_canon_sha256":"ab8508be77adc9766f12be3952b41e897637a5a08dc4613a141df25a66862b70"},"schema_version":"1.0"},"canonical_sha256":"dfe52e00343bd35ffc91e304de756595dbb1e825bcc8877cb0344366a5650610","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:26:09.405767Z","signature_b64":"5g0JCpfyqSGMR+vIL5qwLMzldrrPu9La/DcuLTrpC5TKntlgTNOyuaa7Vb/BbSMLamEWEXLjkjjZWaCx1eKtDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"dfe52e00343bd35ffc91e304de756595dbb1e825bcc8877cb0344366a5650610","last_reissued_at":"2026-05-18T00:26:09.405228Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:26:09.405228Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1801.04239","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":"2026-05-18T00:26:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EST61iCoklRtTZXHLOLkt4R/mu26xSg/e7G6ZbNntfehDEBDALZxVRtscrSn4rjJtC0YGyjHqrMfrlgIBtqoDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T20:21:35.618525Z"},"content_sha256":"acf122d07c064b94f5193476681694d03b98f18e85f96279177dda626b001f83","schema_version":"1.0","event_id":"sha256:acf122d07c064b94f5193476681694d03b98f18e85f96279177dda626b001f83"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:37SS4ABUHPJV77ER4MCN45LFSX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Commutative modified Rota-Baxter algebras, shuffle products and Hopf algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC"],"primary_cat":"math.RA","authors_text":"Li Guo, Xigou Zhang, Xing Gao","submitted_at":"2018-01-12T17:09:06Z","abstract_excerpt":"In this paper, we begin a systematic study of modified Rota-Baxter algebras, as an associative analogue of the modified classical Yang-Baxter equation. We construct free commutative modified Rota-Baxter algebras by a variation of the shuffle product and describe the structure both recursively and explicitly. We then provide these algebras with a Hopf algebra structure by applying a Hochschild cocycle."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.04239","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":"2026-05-18T00:26:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6W0Z1sK0It8MJBrXdHFRd++ZUcmidJ6+Bfyl7WTS74uBPi0RnsZ/napE/BcD3hr/V4sOcfhd7MPcKRn+6T/HBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T20:21:35.618872Z"},"content_sha256":"46c6aa83d1b7aeda71ed68a6e828d48076acfedd2cd45ee406366b6765a9664e","schema_version":"1.0","event_id":"sha256:46c6aa83d1b7aeda71ed68a6e828d48076acfedd2cd45ee406366b6765a9664e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/37SS4ABUHPJV77ER4MCN45LFSX/bundle.json","state_url":"https://pith.science/pith/37SS4ABUHPJV77ER4MCN45LFSX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/37SS4ABUHPJV77ER4MCN45LFSX/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":"2026-06-04T20:21:35Z","links":{"resolver":"https://pith.science/pith/37SS4ABUHPJV77ER4MCN45LFSX","bundle":"https://pith.science/pith/37SS4ABUHPJV77ER4MCN45LFSX/bundle.json","state":"https://pith.science/pith/37SS4ABUHPJV77ER4MCN45LFSX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/37SS4ABUHPJV77ER4MCN45LFSX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:37SS4ABUHPJV77ER4MCN45LFSX","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":"ab8508be77adc9766f12be3952b41e897637a5a08dc4613a141df25a66862b70","cross_cats_sorted":["math.AC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2018-01-12T17:09:06Z","title_canon_sha256":"b3a05837298b3fdbdd55cdc05aa02c946df010fca1a6120fff4c983642038161"},"schema_version":"1.0","source":{"id":"1801.04239","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1801.04239","created_at":"2026-05-18T00:26:09Z"},{"alias_kind":"arxiv_version","alias_value":"1801.04239v1","created_at":"2026-05-18T00:26:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1801.04239","created_at":"2026-05-18T00:26:09Z"},{"alias_kind":"pith_short_12","alias_value":"37SS4ABUHPJV","created_at":"2026-05-18T12:32:02Z"},{"alias_kind":"pith_short_16","alias_value":"37SS4ABUHPJV77ER","created_at":"2026-05-18T12:32:02Z"},{"alias_kind":"pith_short_8","alias_value":"37SS4ABU","created_at":"2026-05-18T12:32:02Z"}],"graph_snapshots":[{"event_id":"sha256:46c6aa83d1b7aeda71ed68a6e828d48076acfedd2cd45ee406366b6765a9664e","target":"graph","created_at":"2026-05-18T00:26:09Z","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":"In this paper, we begin a systematic study of modified Rota-Baxter algebras, as an associative analogue of the modified classical Yang-Baxter equation. We construct free commutative modified Rota-Baxter algebras by a variation of the shuffle product and describe the structure both recursively and explicitly. We then provide these algebras with a Hopf algebra structure by applying a Hochschild cocycle.","authors_text":"Li Guo, Xigou Zhang, Xing Gao","cross_cats":["math.AC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2018-01-12T17:09:06Z","title":"Commutative modified Rota-Baxter algebras, shuffle products and Hopf algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.04239","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:acf122d07c064b94f5193476681694d03b98f18e85f96279177dda626b001f83","target":"record","created_at":"2026-05-18T00:26:09Z","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":"ab8508be77adc9766f12be3952b41e897637a5a08dc4613a141df25a66862b70","cross_cats_sorted":["math.AC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2018-01-12T17:09:06Z","title_canon_sha256":"b3a05837298b3fdbdd55cdc05aa02c946df010fca1a6120fff4c983642038161"},"schema_version":"1.0","source":{"id":"1801.04239","kind":"arxiv","version":1}},"canonical_sha256":"dfe52e00343bd35ffc91e304de756595dbb1e825bcc8877cb0344366a5650610","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"dfe52e00343bd35ffc91e304de756595dbb1e825bcc8877cb0344366a5650610","first_computed_at":"2026-05-18T00:26:09.405228Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:26:09.405228Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5g0JCpfyqSGMR+vIL5qwLMzldrrPu9La/DcuLTrpC5TKntlgTNOyuaa7Vb/BbSMLamEWEXLjkjjZWaCx1eKtDw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:26:09.405767Z","signed_message":"canonical_sha256_bytes"},"source_id":"1801.04239","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:acf122d07c064b94f5193476681694d03b98f18e85f96279177dda626b001f83","sha256:46c6aa83d1b7aeda71ed68a6e828d48076acfedd2cd45ee406366b6765a9664e"],"state_sha256":"d1d3e0a6fb29c1e7552ccb335c7b2873fd975dde3439a3f8aca07e95d1035989"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5LSw3xKJJdKs3LEgM2USPDR6Q+UkuFB0i8k7Jo+RQpQvP4uUN2w+CXMiEcQ4TgJga4UVvZmMpCZWNdwfSZKNBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T20:21:35.620818Z","bundle_sha256":"60b696852268afa85439e2f23f536d6af5e33107272a48bb24958a46c1f18894"}}