{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:QFXNMAFMDJGNBXTYNUEL2RRTUZ","short_pith_number":"pith:QFXNMAFM","canonical_record":{"source":{"id":"1503.02606","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math.AC","submitted_at":"2015-03-09T18:32:05Z","cross_cats_sorted":["math.RA"],"title_canon_sha256":"0fa3de6c56235002ddcdd72c72d3362c905db28c3754d876507e89f501d4ddea","abstract_canon_sha256":"e3cb6ff98fd047d7bb95467597fdffb8f5d799e4e683f85b6c1a73b9e72c2901"},"schema_version":"1.0"},"canonical_sha256":"816ed600ac1a4cd0de786d08bd4633a67ba4d2e7083632258a0007f133be0214","source":{"kind":"arxiv","id":"1503.02606","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.02606","created_at":"2026-05-18T02:14:16Z"},{"alias_kind":"arxiv_version","alias_value":"1503.02606v2","created_at":"2026-05-18T02:14:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.02606","created_at":"2026-05-18T02:14:16Z"},{"alias_kind":"pith_short_12","alias_value":"QFXNMAFMDJGN","created_at":"2026-05-18T12:29:37Z"},{"alias_kind":"pith_short_16","alias_value":"QFXNMAFMDJGNBXTY","created_at":"2026-05-18T12:29:37Z"},{"alias_kind":"pith_short_8","alias_value":"QFXNMAFM","created_at":"2026-05-18T12:29:37Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:QFXNMAFMDJGNBXTYNUEL2RRTUZ","target":"record","payload":{"canonical_record":{"source":{"id":"1503.02606","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math.AC","submitted_at":"2015-03-09T18:32:05Z","cross_cats_sorted":["math.RA"],"title_canon_sha256":"0fa3de6c56235002ddcdd72c72d3362c905db28c3754d876507e89f501d4ddea","abstract_canon_sha256":"e3cb6ff98fd047d7bb95467597fdffb8f5d799e4e683f85b6c1a73b9e72c2901"},"schema_version":"1.0"},"canonical_sha256":"816ed600ac1a4cd0de786d08bd4633a67ba4d2e7083632258a0007f133be0214","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:14:16.701014Z","signature_b64":"LT6LQbrA5B20nCSr/hq6nK3LDy/DBUKrMhqUNnzzqbHdja4byCL+3S43Kfyw/s97VSNpyTwhy32pVTycVjZFBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"816ed600ac1a4cd0de786d08bd4633a67ba4d2e7083632258a0007f133be0214","last_reissued_at":"2026-05-18T02:14:16.700300Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:14:16.700300Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1503.02606","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:14:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"C1hVPm8NGSydgrvAkpVgnxGDQuT6YELMCWwXcEozEcFnMTDdF+TAY1kKr7iSBErJyJd6R3qVHwg+1Pno9sYqAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T22:56:24.190662Z"},"content_sha256":"c11ffdf18703bf0877eba79d722b17c6702115e8eabe91bd3f3e3dc8c0d9cb65","schema_version":"1.0","event_id":"sha256:c11ffdf18703bf0877eba79d722b17c6702115e8eabe91bd3f3e3dc8c0d9cb65"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:QFXNMAFMDJGNBXTYNUEL2RRTUZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Classification of monomial Rota-Baxter operators on k[x]","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","headline":"","cross_cats":["math.RA"],"primary_cat":"math.AC","authors_text":"Houyi Yu","submitted_at":"2015-03-09T18:32:05Z","abstract_excerpt":"Rota-Baxter operators were introduced to solve certain analytic and combinatorial problems and then applied to many fields in mathematics and mathematical physics. The polynomial algebra $\\mathbf{k}[x]$ plays a central role both in analysis and algebra. In this paper, we explicitly classified all monomial Rota-Baxter operators on $\\mathbf{k}[x]$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.02606","kind":"arxiv","version":2},"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":"2026-05-18T02:14:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sytAuW5Biqv4nkzNiq56qT2U4AomvlEo24FoXmfQY39WE+TCbbZ75xzY1T3YOHO68aj/fvAptzItcUodNHWDAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T22:56:24.191260Z"},"content_sha256":"97b9708a08a47af1d15efcc796b176c21606bca83a85897d681b90c262418c72","schema_version":"1.0","event_id":"sha256:97b9708a08a47af1d15efcc796b176c21606bca83a85897d681b90c262418c72"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QFXNMAFMDJGNBXTYNUEL2RRTUZ/bundle.json","state_url":"https://pith.science/pith/QFXNMAFMDJGNBXTYNUEL2RRTUZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QFXNMAFMDJGNBXTYNUEL2RRTUZ/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":"2026-06-04T22:56:24Z","links":{"resolver":"https://pith.science/pith/QFXNMAFMDJGNBXTYNUEL2RRTUZ","bundle":"https://pith.science/pith/QFXNMAFMDJGNBXTYNUEL2RRTUZ/bundle.json","state":"https://pith.science/pith/QFXNMAFMDJGNBXTYNUEL2RRTUZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QFXNMAFMDJGNBXTYNUEL2RRTUZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:QFXNMAFMDJGNBXTYNUEL2RRTUZ","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":"e3cb6ff98fd047d7bb95467597fdffb8f5d799e4e683f85b6c1a73b9e72c2901","cross_cats_sorted":["math.RA"],"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math.AC","submitted_at":"2015-03-09T18:32:05Z","title_canon_sha256":"0fa3de6c56235002ddcdd72c72d3362c905db28c3754d876507e89f501d4ddea"},"schema_version":"1.0","source":{"id":"1503.02606","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.02606","created_at":"2026-05-18T02:14:16Z"},{"alias_kind":"arxiv_version","alias_value":"1503.02606v2","created_at":"2026-05-18T02:14:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.02606","created_at":"2026-05-18T02:14:16Z"},{"alias_kind":"pith_short_12","alias_value":"QFXNMAFMDJGN","created_at":"2026-05-18T12:29:37Z"},{"alias_kind":"pith_short_16","alias_value":"QFXNMAFMDJGNBXTY","created_at":"2026-05-18T12:29:37Z"},{"alias_kind":"pith_short_8","alias_value":"QFXNMAFM","created_at":"2026-05-18T12:29:37Z"}],"graph_snapshots":[{"event_id":"sha256:97b9708a08a47af1d15efcc796b176c21606bca83a85897d681b90c262418c72","target":"graph","created_at":"2026-05-18T02:14:16Z","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":"Rota-Baxter operators were introduced to solve certain analytic and combinatorial problems and then applied to many fields in mathematics and mathematical physics. The polynomial algebra $\\mathbf{k}[x]$ plays a central role both in analysis and algebra. In this paper, we explicitly classified all monomial Rota-Baxter operators on $\\mathbf{k}[x]$.","authors_text":"Houyi Yu","cross_cats":["math.RA"],"headline":"","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math.AC","submitted_at":"2015-03-09T18:32:05Z","title":"Classification of monomial Rota-Baxter operators on k[x]"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.02606","kind":"arxiv","version":2},"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:c11ffdf18703bf0877eba79d722b17c6702115e8eabe91bd3f3e3dc8c0d9cb65","target":"record","created_at":"2026-05-18T02:14:16Z","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":"e3cb6ff98fd047d7bb95467597fdffb8f5d799e4e683f85b6c1a73b9e72c2901","cross_cats_sorted":["math.RA"],"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math.AC","submitted_at":"2015-03-09T18:32:05Z","title_canon_sha256":"0fa3de6c56235002ddcdd72c72d3362c905db28c3754d876507e89f501d4ddea"},"schema_version":"1.0","source":{"id":"1503.02606","kind":"arxiv","version":2}},"canonical_sha256":"816ed600ac1a4cd0de786d08bd4633a67ba4d2e7083632258a0007f133be0214","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"816ed600ac1a4cd0de786d08bd4633a67ba4d2e7083632258a0007f133be0214","first_computed_at":"2026-05-18T02:14:16.700300Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:14:16.700300Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"LT6LQbrA5B20nCSr/hq6nK3LDy/DBUKrMhqUNnzzqbHdja4byCL+3S43Kfyw/s97VSNpyTwhy32pVTycVjZFBA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:14:16.701014Z","signed_message":"canonical_sha256_bytes"},"source_id":"1503.02606","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c11ffdf18703bf0877eba79d722b17c6702115e8eabe91bd3f3e3dc8c0d9cb65","sha256:97b9708a08a47af1d15efcc796b176c21606bca83a85897d681b90c262418c72"],"state_sha256":"94e05d8edc4624c9383cf0885441cff4677ce8a61ec8f98efa81ab21aa6073f1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4i+GrCHIOycxhu5ON0l652B20scfCv0INm/4ksxFLfi7yTknzX09FS4WXUXwEjhjQCZvdnnBdJYHy3ClJLDbCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T22:56:24.194938Z","bundle_sha256":"7117fc3ab773c423d773c7d5075181ecf0b3948fb10aaa9ed641e34f07eb8fe5"}}