{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:3XIBOC7RCND5EABUAXJI77355P","short_pith_number":"pith:3XIBOC7R","canonical_record":{"source":{"id":"1503.05073","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2015-03-17T14:33:15Z","cross_cats_sorted":[],"title_canon_sha256":"580b47719e7d9c0d6b8e342e9281a4e3932550d52dec1cd1d2d53a0b2621f6ef","abstract_canon_sha256":"d66ff8890116f13a54e825d8896a476bd9a86055c7b1503601fd70a61df15c6f"},"schema_version":"1.0"},"canonical_sha256":"ddd0170bf11347d2003405d28fff7debc3ef9b4297e436af79528595559698d3","source":{"kind":"arxiv","id":"1503.05073","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.05073","created_at":"2026-05-18T02:22:20Z"},{"alias_kind":"arxiv_version","alias_value":"1503.05073v1","created_at":"2026-05-18T02:22:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.05073","created_at":"2026-05-18T02:22:20Z"},{"alias_kind":"pith_short_12","alias_value":"3XIBOC7RCND5","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_16","alias_value":"3XIBOC7RCND5EABU","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_8","alias_value":"3XIBOC7R","created_at":"2026-05-18T12:29:02Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:3XIBOC7RCND5EABUAXJI77355P","target":"record","payload":{"canonical_record":{"source":{"id":"1503.05073","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2015-03-17T14:33:15Z","cross_cats_sorted":[],"title_canon_sha256":"580b47719e7d9c0d6b8e342e9281a4e3932550d52dec1cd1d2d53a0b2621f6ef","abstract_canon_sha256":"d66ff8890116f13a54e825d8896a476bd9a86055c7b1503601fd70a61df15c6f"},"schema_version":"1.0"},"canonical_sha256":"ddd0170bf11347d2003405d28fff7debc3ef9b4297e436af79528595559698d3","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:22:20.514353Z","signature_b64":"pfWwmcr37oD4nlWdOv36++SQ7kGqW0ew53InmcGlMyN3QUMt42dWMSs4pD2L0s18UXrAGrAwMJU0nmL1aS9RBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ddd0170bf11347d2003405d28fff7debc3ef9b4297e436af79528595559698d3","last_reissued_at":"2026-05-18T02:22:20.513633Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:22:20.513633Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1503.05073","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":"2026-05-18T02:22:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KdgKo/ylxfumwUz/PacE7tr7sE7oBzwGaE8O/w+0kNn221DuHcUwUPep3wM5cMxx18oKvwjAWvWoXz/OZM5DCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T23:02:45.882758Z"},"content_sha256":"42de34f861d2e33223682cacffbc665aa3cf38b6e02ef3146fab82581a59c2f5","schema_version":"1.0","event_id":"sha256:42de34f861d2e33223682cacffbc665aa3cf38b6e02ef3146fab82581a59c2f5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:3XIBOC7RCND5EABUAXJI77355P","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Rota-Baxter systems, dendriform algebras and covariant bialgebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.QA","authors_text":"Tomasz Brzezi\\'nski","submitted_at":"2015-03-17T14:33:15Z","abstract_excerpt":"A generalisation of the notion of a Rota-Baxter operator is proposed. This generalisation consists of two operators acting on an associative algebra and satisfying equations similar to the Rota-Baxter equation. Rota-Baxter operators of any weights and twisted Rota-Baxter operators are solutions of the proposed system. It is shown that dendriform algebra structures of a particular kind are equivalent to Rota-Baxter systems. It is shown further that a Rota-Baxter system induces a weak peudotwistor [F. Panaite & F. Van Oystaeyen, Twisted algebras, twisted bialgebras and Rota-Baxter operators, arX"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.05073","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":"2026-05-18T02:22:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"btvHqQi0ZO8VaSyPmWV5UUmbMrVinD/QeZgbDULAarMS/S04FIZ0Q3zezVyCNn7va2W0uoicH09M7rszkVCrAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T23:02:45.883502Z"},"content_sha256":"fac0b15fbf91cac2da5774de879fb3580917515171ecaf346c03ff94209a26d2","schema_version":"1.0","event_id":"sha256:fac0b15fbf91cac2da5774de879fb3580917515171ecaf346c03ff94209a26d2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3XIBOC7RCND5EABUAXJI77355P/bundle.json","state_url":"https://pith.science/pith/3XIBOC7RCND5EABUAXJI77355P/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3XIBOC7RCND5EABUAXJI77355P/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":"2026-06-11T23:02:45Z","links":{"resolver":"https://pith.science/pith/3XIBOC7RCND5EABUAXJI77355P","bundle":"https://pith.science/pith/3XIBOC7RCND5EABUAXJI77355P/bundle.json","state":"https://pith.science/pith/3XIBOC7RCND5EABUAXJI77355P/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3XIBOC7RCND5EABUAXJI77355P/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:3XIBOC7RCND5EABUAXJI77355P","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":"d66ff8890116f13a54e825d8896a476bd9a86055c7b1503601fd70a61df15c6f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2015-03-17T14:33:15Z","title_canon_sha256":"580b47719e7d9c0d6b8e342e9281a4e3932550d52dec1cd1d2d53a0b2621f6ef"},"schema_version":"1.0","source":{"id":"1503.05073","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.05073","created_at":"2026-05-18T02:22:20Z"},{"alias_kind":"arxiv_version","alias_value":"1503.05073v1","created_at":"2026-05-18T02:22:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.05073","created_at":"2026-05-18T02:22:20Z"},{"alias_kind":"pith_short_12","alias_value":"3XIBOC7RCND5","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_16","alias_value":"3XIBOC7RCND5EABU","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_8","alias_value":"3XIBOC7R","created_at":"2026-05-18T12:29:02Z"}],"graph_snapshots":[{"event_id":"sha256:fac0b15fbf91cac2da5774de879fb3580917515171ecaf346c03ff94209a26d2","target":"graph","created_at":"2026-05-18T02:22:20Z","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":"A generalisation of the notion of a Rota-Baxter operator is proposed. This generalisation consists of two operators acting on an associative algebra and satisfying equations similar to the Rota-Baxter equation. Rota-Baxter operators of any weights and twisted Rota-Baxter operators are solutions of the proposed system. It is shown that dendriform algebra structures of a particular kind are equivalent to Rota-Baxter systems. It is shown further that a Rota-Baxter system induces a weak peudotwistor [F. Panaite & F. Van Oystaeyen, Twisted algebras, twisted bialgebras and Rota-Baxter operators, arX","authors_text":"Tomasz Brzezi\\'nski","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2015-03-17T14:33:15Z","title":"Rota-Baxter systems, dendriform algebras and covariant bialgebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.05073","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":"sha256:42de34f861d2e33223682cacffbc665aa3cf38b6e02ef3146fab82581a59c2f5","target":"record","created_at":"2026-05-18T02:22:20Z","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":"d66ff8890116f13a54e825d8896a476bd9a86055c7b1503601fd70a61df15c6f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2015-03-17T14:33:15Z","title_canon_sha256":"580b47719e7d9c0d6b8e342e9281a4e3932550d52dec1cd1d2d53a0b2621f6ef"},"schema_version":"1.0","source":{"id":"1503.05073","kind":"arxiv","version":1}},"canonical_sha256":"ddd0170bf11347d2003405d28fff7debc3ef9b4297e436af79528595559698d3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ddd0170bf11347d2003405d28fff7debc3ef9b4297e436af79528595559698d3","first_computed_at":"2026-05-18T02:22:20.513633Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:22:20.513633Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"pfWwmcr37oD4nlWdOv36++SQ7kGqW0ew53InmcGlMyN3QUMt42dWMSs4pD2L0s18UXrAGrAwMJU0nmL1aS9RBw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:22:20.514353Z","signed_message":"canonical_sha256_bytes"},"source_id":"1503.05073","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:42de34f861d2e33223682cacffbc665aa3cf38b6e02ef3146fab82581a59c2f5","sha256:fac0b15fbf91cac2da5774de879fb3580917515171ecaf346c03ff94209a26d2"],"state_sha256":"6fe233a0e4be0f06737f79857cc92b243bc0a50ab4b20095f7b5a8343bd31673"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VQTClB7TqkxtT/NKZu9uJwed1w4/HgRPINHV0EIJKMzf+ImOb+mbRiEVm2ZNVdOqYHRH7X17OgUY36DuqdQTDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T23:02:45.887907Z","bundle_sha256":"7ca423254794a41341ad385c4636f8bfde8a36a27e07a58ab2e6def9e4a8cfa6"}}