{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2023:W3QE6TUBCSS2R4GS5IOHCMP6LU","short_pith_number":"pith:W3QE6TUB","canonical_record":{"source":{"id":"2304.00538","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2023-04-02T13:50:55Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"f9cef9a2692126dcd9ebe8b7e7d03d3475b79d53a420af1e9205ebf3eea690e9","abstract_canon_sha256":"80213248a99967e5c69900c2ee03de959742eab837709aa4e07153b4e3100f33"},"schema_version":"1.0"},"canonical_sha256":"b6e04f4e8114a5a8f0d2ea1c7131fe5d3de940f8b8e65bce2527ff178ff3bc36","source":{"kind":"arxiv","id":"2304.00538","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2304.00538","created_at":"2026-07-05T05:59:24Z"},{"alias_kind":"arxiv_version","alias_value":"2304.00538v2","created_at":"2026-07-05T05:59:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2304.00538","created_at":"2026-07-05T05:59:24Z"},{"alias_kind":"pith_short_12","alias_value":"W3QE6TUBCSS2","created_at":"2026-07-05T05:59:24Z"},{"alias_kind":"pith_short_16","alias_value":"W3QE6TUBCSS2R4GS","created_at":"2026-07-05T05:59:24Z"},{"alias_kind":"pith_short_8","alias_value":"W3QE6TUB","created_at":"2026-07-05T05:59:24Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2023:W3QE6TUBCSS2R4GS5IOHCMP6LU","target":"record","payload":{"canonical_record":{"source":{"id":"2304.00538","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2023-04-02T13:50:55Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"f9cef9a2692126dcd9ebe8b7e7d03d3475b79d53a420af1e9205ebf3eea690e9","abstract_canon_sha256":"80213248a99967e5c69900c2ee03de959742eab837709aa4e07153b4e3100f33"},"schema_version":"1.0"},"canonical_sha256":"b6e04f4e8114a5a8f0d2ea1c7131fe5d3de940f8b8e65bce2527ff178ff3bc36","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T05:59:24.120082Z","signature_b64":"VUL8kSGpFXV6Dy/TKh+vS9uhRWtnvqQJvOqdX97Av4oiErXGHv8g53J/OkFj8qmbsF15YLry8PyJwvLmCmHTAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b6e04f4e8114a5a8f0d2ea1c7131fe5d3de940f8b8e65bce2527ff178ff3bc36","last_reissued_at":"2026-07-05T05:59:24.119660Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T05:59:24.119660Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2304.00538","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":"2026-07-05T05:59:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UZpZkOXPhchRfoF0AFBOE1+qG68jze39YWYU1m8aXQWjXAPATDtlycJhwnXk5ri0NO6BnYATPWCRFybtcnHPAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-09T03:39:46.492129Z"},"content_sha256":"a6098193012266339a4907dd4a11e88117e8d17825a8d513353e3b64442ba438","schema_version":"1.0","event_id":"sha256:a6098193012266339a4907dd4a11e88117e8d17825a8d513353e3b64442ba438"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2023:W3QE6TUBCSS2R4GS5IOHCMP6LU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Deformations and cohomology theory of $\\Omega$-family Rota-Baxter algebras of arbitrary weight","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.RA","authors_text":"Chao Song, Kai Wang, Yuanyuan Zhang","submitted_at":"2023-04-02T13:50:55Z","abstract_excerpt":"In this paper, we firstly construct an $L_\\infty[1]$-algebra via the method of higher derived brackets, whose Maurer-Cartan elements correspond to relative $\\Omega$-family Rota-Baxter algebras structures of weight $\\lambda$. For a relative $\\Omega$-family Rota-Baxter algebra of weight $\\lambda$, the corresponding twisted $ L_{\\infty}[1] $-algebra controls its deformations, which leads to the cohomology theory of relative $\\Omega$-family Rota-Baxter algebras of weight $\\lambda$. Moreover, we also obtain the corresponding results for absolute $\\Omega$-family Rota-Baxter algebras of weight $\\lamb"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2304.00538","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2304.00538/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T05:59:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XLBeo0/Z56VxvGjQaAQwjdAshF347TOUX8vBGum6sjznT7AZqN9FNtiPPrWytUYS3UXSsMz6FesuGN0OpoetBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-09T03:39:46.492526Z"},"content_sha256":"706c36d831ebbc28b1ea1870bc2d463cfffc1d1e18c0ea22bf1de8d4d986a175","schema_version":"1.0","event_id":"sha256:706c36d831ebbc28b1ea1870bc2d463cfffc1d1e18c0ea22bf1de8d4d986a175"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/W3QE6TUBCSS2R4GS5IOHCMP6LU/bundle.json","state_url":"https://pith.science/pith/W3QE6TUBCSS2R4GS5IOHCMP6LU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/W3QE6TUBCSS2R4GS5IOHCMP6LU/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":"2026-07-09T03:39:46Z","links":{"resolver":"https://pith.science/pith/W3QE6TUBCSS2R4GS5IOHCMP6LU","bundle":"https://pith.science/pith/W3QE6TUBCSS2R4GS5IOHCMP6LU/bundle.json","state":"https://pith.science/pith/W3QE6TUBCSS2R4GS5IOHCMP6LU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/W3QE6TUBCSS2R4GS5IOHCMP6LU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:W3QE6TUBCSS2R4GS5IOHCMP6LU","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":"80213248a99967e5c69900c2ee03de959742eab837709aa4e07153b4e3100f33","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2023-04-02T13:50:55Z","title_canon_sha256":"f9cef9a2692126dcd9ebe8b7e7d03d3475b79d53a420af1e9205ebf3eea690e9"},"schema_version":"1.0","source":{"id":"2304.00538","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2304.00538","created_at":"2026-07-05T05:59:24Z"},{"alias_kind":"arxiv_version","alias_value":"2304.00538v2","created_at":"2026-07-05T05:59:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2304.00538","created_at":"2026-07-05T05:59:24Z"},{"alias_kind":"pith_short_12","alias_value":"W3QE6TUBCSS2","created_at":"2026-07-05T05:59:24Z"},{"alias_kind":"pith_short_16","alias_value":"W3QE6TUBCSS2R4GS","created_at":"2026-07-05T05:59:24Z"},{"alias_kind":"pith_short_8","alias_value":"W3QE6TUB","created_at":"2026-07-05T05:59:24Z"}],"graph_snapshots":[{"event_id":"sha256:706c36d831ebbc28b1ea1870bc2d463cfffc1d1e18c0ea22bf1de8d4d986a175","target":"graph","created_at":"2026-07-05T05:59:24Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2304.00538/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we firstly construct an $L_\\infty[1]$-algebra via the method of higher derived brackets, whose Maurer-Cartan elements correspond to relative $\\Omega$-family Rota-Baxter algebras structures of weight $\\lambda$. For a relative $\\Omega$-family Rota-Baxter algebra of weight $\\lambda$, the corresponding twisted $ L_{\\infty}[1] $-algebra controls its deformations, which leads to the cohomology theory of relative $\\Omega$-family Rota-Baxter algebras of weight $\\lambda$. Moreover, we also obtain the corresponding results for absolute $\\Omega$-family Rota-Baxter algebras of weight $\\lamb","authors_text":"Chao Song, Kai Wang, Yuanyuan Zhang","cross_cats":["math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2023-04-02T13:50:55Z","title":"Deformations and cohomology theory of $\\Omega$-family Rota-Baxter algebras of arbitrary weight"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2304.00538","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:a6098193012266339a4907dd4a11e88117e8d17825a8d513353e3b64442ba438","target":"record","created_at":"2026-07-05T05:59:24Z","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":"80213248a99967e5c69900c2ee03de959742eab837709aa4e07153b4e3100f33","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2023-04-02T13:50:55Z","title_canon_sha256":"f9cef9a2692126dcd9ebe8b7e7d03d3475b79d53a420af1e9205ebf3eea690e9"},"schema_version":"1.0","source":{"id":"2304.00538","kind":"arxiv","version":2}},"canonical_sha256":"b6e04f4e8114a5a8f0d2ea1c7131fe5d3de940f8b8e65bce2527ff178ff3bc36","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b6e04f4e8114a5a8f0d2ea1c7131fe5d3de940f8b8e65bce2527ff178ff3bc36","first_computed_at":"2026-07-05T05:59:24.119660Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T05:59:24.119660Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"VUL8kSGpFXV6Dy/TKh+vS9uhRWtnvqQJvOqdX97Av4oiErXGHv8g53J/OkFj8qmbsF15YLry8PyJwvLmCmHTAw==","signature_status":"signed_v1","signed_at":"2026-07-05T05:59:24.120082Z","signed_message":"canonical_sha256_bytes"},"source_id":"2304.00538","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a6098193012266339a4907dd4a11e88117e8d17825a8d513353e3b64442ba438","sha256:706c36d831ebbc28b1ea1870bc2d463cfffc1d1e18c0ea22bf1de8d4d986a175"],"state_sha256":"ad6f40a600a1d43cc7b2e3d176fd2e834869d31ec6e75f33a0998daf51629885"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1K+/m3QUUKXg9vmYjtjAlWrZbU5zZRByZy+pfK7PCLY3EQD5WPyZ7czY33EYOZ0MESX6EDQBKj0vuKa85+GTAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-09T03:39:46.494492Z","bundle_sha256":"10542b3a7e28ff4cb007518f2d8c81d30bdcb8163cf5c39a4392c9960c607dd1"}}