{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2022:XFFQWLF4QUMHOSGKWGV5SEQ3ZF","short_pith_number":"pith:XFFQWLF4","canonical_record":{"source":{"id":"2211.02986","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.QA","submitted_at":"2022-11-05T22:22:16Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"5f071fd1ebb54d2e5ed0a5b26546610fe8bf9d345c3048e2fec13f6cd950c656","abstract_canon_sha256":"5f128bae0c2f3f1c32e5f01f2478543b7da141e062511c3c230765bba602189a"},"schema_version":"1.0"},"canonical_sha256":"b94b0b2cbc85187748cab1abd9121bc963797a0d7bd0f4e62de6bcb72e99cb4f","source":{"kind":"arxiv","id":"2211.02986","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2211.02986","created_at":"2026-07-05T06:12:38Z"},{"alias_kind":"arxiv_version","alias_value":"2211.02986v1","created_at":"2026-07-05T06:12:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2211.02986","created_at":"2026-07-05T06:12:38Z"},{"alias_kind":"pith_short_12","alias_value":"XFFQWLF4QUMH","created_at":"2026-07-05T06:12:38Z"},{"alias_kind":"pith_short_16","alias_value":"XFFQWLF4QUMHOSGK","created_at":"2026-07-05T06:12:38Z"},{"alias_kind":"pith_short_8","alias_value":"XFFQWLF4","created_at":"2026-07-05T06:12:38Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2022:XFFQWLF4QUMHOSGKWGV5SEQ3ZF","target":"record","payload":{"canonical_record":{"source":{"id":"2211.02986","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.QA","submitted_at":"2022-11-05T22:22:16Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"5f071fd1ebb54d2e5ed0a5b26546610fe8bf9d345c3048e2fec13f6cd950c656","abstract_canon_sha256":"5f128bae0c2f3f1c32e5f01f2478543b7da141e062511c3c230765bba602189a"},"schema_version":"1.0"},"canonical_sha256":"b94b0b2cbc85187748cab1abd9121bc963797a0d7bd0f4e62de6bcb72e99cb4f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T06:12:38.730443Z","signature_b64":"wXlgRxVZ77WyadNQ8LMMRp/cVAO/yZN//+r1nBMW9knVAM9n4gqZ4hVxQ0nz5AzYh32MWZtePJmOm3mMEJ4wCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b94b0b2cbc85187748cab1abd9121bc963797a0d7bd0f4e62de6bcb72e99cb4f","last_reissued_at":"2026-07-05T06:12:38.729955Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T06:12:38.729955Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2211.02986","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":"2026-07-05T06:12:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"12VX1qOz3RzTD1Lf+9KrFXRCe0TqL5GlMu5EXX/ZRjpTAEp4pfZ+HQgzQRz1SR1mzB9zHGqvpSqVNewtmkQZDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-05T18:31:16.901542Z"},"content_sha256":"2e00fc59fc701c44b6c64f9240e91d7aff596c1c6ee5bcab3819f93d5ac41cb5","schema_version":"1.0","event_id":"sha256:2e00fc59fc701c44b6c64f9240e91d7aff596c1c6ee5bcab3819f93d5ac41cb5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2022:XFFQWLF4QUMHOSGKWGV5SEQ3ZF","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Braided Hopf algebras and gauge transformations II: $*$-structures and examples","license":"http://creativecommons.org/licenses/by-sa/4.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.QA","authors_text":"Chiara Pagani, Giovanni Landi, Paolo Aschieri","submitted_at":"2022-11-05T22:22:16Z","abstract_excerpt":"We consider noncommutative principal bundles which are equivariant under a triangular Hopf algebra. We present explicit examples of infinite dimensional braided Lie and Hopf algebras of infinitesimal gauge transformations of bundles on noncommutative spheres. The braiding of these algebras is implemented by the triangular structure of the symmetry Hopf algebra. We present a systematic analysis of compatible $*$-structures, encompassing the quasitriangular case."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2211.02986","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2211.02986/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":"2026-07-05T06:12:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Z/IbFIf5UnXhH9Qey9pX22Pfj9bZx4/6ojRucJDTHNji7YCKhZlqrPeud9U2c0NYghzxZeqqBMPoRl/e5C28AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-05T18:31:16.901832Z"},"content_sha256":"0f0566cbf6b224740b9b82d9d765ae71af9648ca52b41d5de40058df03ce2a97","schema_version":"1.0","event_id":"sha256:0f0566cbf6b224740b9b82d9d765ae71af9648ca52b41d5de40058df03ce2a97"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XFFQWLF4QUMHOSGKWGV5SEQ3ZF/bundle.json","state_url":"https://pith.science/pith/XFFQWLF4QUMHOSGKWGV5SEQ3ZF/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XFFQWLF4QUMHOSGKWGV5SEQ3ZF/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":"2026-08-05T18:31:16Z","links":{"resolver":"https://pith.science/pith/XFFQWLF4QUMHOSGKWGV5SEQ3ZF","bundle":"https://pith.science/pith/XFFQWLF4QUMHOSGKWGV5SEQ3ZF/bundle.json","state":"https://pith.science/pith/XFFQWLF4QUMHOSGKWGV5SEQ3ZF/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XFFQWLF4QUMHOSGKWGV5SEQ3ZF/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:XFFQWLF4QUMHOSGKWGV5SEQ3ZF","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":"5f128bae0c2f3f1c32e5f01f2478543b7da141e062511c3c230765bba602189a","cross_cats_sorted":["math-ph","math.MP"],"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.QA","submitted_at":"2022-11-05T22:22:16Z","title_canon_sha256":"5f071fd1ebb54d2e5ed0a5b26546610fe8bf9d345c3048e2fec13f6cd950c656"},"schema_version":"1.0","source":{"id":"2211.02986","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2211.02986","created_at":"2026-07-05T06:12:38Z"},{"alias_kind":"arxiv_version","alias_value":"2211.02986v1","created_at":"2026-07-05T06:12:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2211.02986","created_at":"2026-07-05T06:12:38Z"},{"alias_kind":"pith_short_12","alias_value":"XFFQWLF4QUMH","created_at":"2026-07-05T06:12:38Z"},{"alias_kind":"pith_short_16","alias_value":"XFFQWLF4QUMHOSGK","created_at":"2026-07-05T06:12:38Z"},{"alias_kind":"pith_short_8","alias_value":"XFFQWLF4","created_at":"2026-07-05T06:12:38Z"}],"graph_snapshots":[{"event_id":"sha256:0f0566cbf6b224740b9b82d9d765ae71af9648ca52b41d5de40058df03ce2a97","target":"graph","created_at":"2026-07-05T06:12:38Z","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/2211.02986/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We consider noncommutative principal bundles which are equivariant under a triangular Hopf algebra. We present explicit examples of infinite dimensional braided Lie and Hopf algebras of infinitesimal gauge transformations of bundles on noncommutative spheres. The braiding of these algebras is implemented by the triangular structure of the symmetry Hopf algebra. We present a systematic analysis of compatible $*$-structures, encompassing the quasitriangular case.","authors_text":"Chiara Pagani, Giovanni Landi, Paolo Aschieri","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.QA","submitted_at":"2022-11-05T22:22:16Z","title":"Braided Hopf algebras and gauge transformations II: $*$-structures and examples"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2211.02986","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":"sha256:2e00fc59fc701c44b6c64f9240e91d7aff596c1c6ee5bcab3819f93d5ac41cb5","target":"record","created_at":"2026-07-05T06:12:38Z","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":"5f128bae0c2f3f1c32e5f01f2478543b7da141e062511c3c230765bba602189a","cross_cats_sorted":["math-ph","math.MP"],"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.QA","submitted_at":"2022-11-05T22:22:16Z","title_canon_sha256":"5f071fd1ebb54d2e5ed0a5b26546610fe8bf9d345c3048e2fec13f6cd950c656"},"schema_version":"1.0","source":{"id":"2211.02986","kind":"arxiv","version":1}},"canonical_sha256":"b94b0b2cbc85187748cab1abd9121bc963797a0d7bd0f4e62de6bcb72e99cb4f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b94b0b2cbc85187748cab1abd9121bc963797a0d7bd0f4e62de6bcb72e99cb4f","first_computed_at":"2026-07-05T06:12:38.729955Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T06:12:38.729955Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"wXlgRxVZ77WyadNQ8LMMRp/cVAO/yZN//+r1nBMW9knVAM9n4gqZ4hVxQ0nz5AzYh32MWZtePJmOm3mMEJ4wCQ==","signature_status":"signed_v1","signed_at":"2026-07-05T06:12:38.730443Z","signed_message":"canonical_sha256_bytes"},"source_id":"2211.02986","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2e00fc59fc701c44b6c64f9240e91d7aff596c1c6ee5bcab3819f93d5ac41cb5","sha256:0f0566cbf6b224740b9b82d9d765ae71af9648ca52b41d5de40058df03ce2a97"],"state_sha256":"662015add45821638c96971c83f6f7e0306b6ba0a8b300b116aa5e32ba3f4dd2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"aDyHWIDp22KrzkMbwY0zOeY64C4B/OajpIQ5UfAnDAboZq/QBK3dkXvMJndT63GIxvugP6qYvrUotJ3jKsptDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-05T18:31:16.905074Z","bundle_sha256":"c0ca2a1e48657c1a0228804e6baf9b6bdd3ef7e53d45aeb174fe8d444ba7fd2d"}}