{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:SED3ORYX4UVCUOVO6PMS6CKINU","short_pith_number":"pith:SED3ORYX","canonical_record":{"source":{"id":"1006.1857","kind":"arxiv","version":6},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2010-06-09T17:14:22Z","cross_cats_sorted":["math.RA"],"title_canon_sha256":"3fc06f6d3994bb01dddfbb319886ea321fc3f76787b6e72699771075719144a1","abstract_canon_sha256":"22bba5add80090ea545d46b0deff70964058c00aeebb4a9b435700022e9b1547"},"schema_version":"1.0"},"canonical_sha256":"9107b74717e52a2a3aaef3d92f09486d389acb97afadd1dcbec2579465c2f1f3","source":{"kind":"arxiv","id":"1006.1857","version":6},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1006.1857","created_at":"2026-05-18T04:10:57Z"},{"alias_kind":"arxiv_version","alias_value":"1006.1857v6","created_at":"2026-05-18T04:10:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1006.1857","created_at":"2026-05-18T04:10:57Z"},{"alias_kind":"pith_short_12","alias_value":"SED3ORYX4UVC","created_at":"2026-05-18T12:26:13Z"},{"alias_kind":"pith_short_16","alias_value":"SED3ORYX4UVCUOVO","created_at":"2026-05-18T12:26:13Z"},{"alias_kind":"pith_short_8","alias_value":"SED3ORYX","created_at":"2026-05-18T12:26:13Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:SED3ORYX4UVCUOVO6PMS6CKINU","target":"record","payload":{"canonical_record":{"source":{"id":"1006.1857","kind":"arxiv","version":6},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2010-06-09T17:14:22Z","cross_cats_sorted":["math.RA"],"title_canon_sha256":"3fc06f6d3994bb01dddfbb319886ea321fc3f76787b6e72699771075719144a1","abstract_canon_sha256":"22bba5add80090ea545d46b0deff70964058c00aeebb4a9b435700022e9b1547"},"schema_version":"1.0"},"canonical_sha256":"9107b74717e52a2a3aaef3d92f09486d389acb97afadd1dcbec2579465c2f1f3","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:10:57.167435Z","signature_b64":"aH83fGMH6iHeKe5kDncsn2LI3yGsoGkmBprWweiCvP5xAngwGYleOJZZEGiKqngPIwfoiwOba0oZthz92t4gAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9107b74717e52a2a3aaef3d92f09486d389acb97afadd1dcbec2579465c2f1f3","last_reissued_at":"2026-05-18T04:10:57.166796Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:10:57.166796Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1006.1857","source_version":6,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:10:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LZmnTLoi2glbrG7wFrclKSxRjySVFHc/qNjWTCCu36cP03dkk2zuqGZo8K1RpQ9e1zUA8v4JA1EBXTaOCSUOAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T10:21:33.298803Z"},"content_sha256":"f17d0a1ecb6951d4479b625a553935c71713ff3ffcad0e243406ba8a34a2da2c","schema_version":"1.0","event_id":"sha256:f17d0a1ecb6951d4479b625a553935c71713ff3ffcad0e243406ba8a34a2da2c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:SED3ORYX4UVCUOVO6PMS6CKINU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Representations of the category of modules over pointed Hopf algebras over S_3 and S_4","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RA"],"primary_cat":"math.QA","authors_text":"Agust\\'in Garc\\'ia Iglesias, Mart\\'in Mombelli","submitted_at":"2010-06-09T17:14:22Z","abstract_excerpt":"We classify exact indecomposable module categories over the representation category of all non-trivial Hopf algebras with coradical S_3 and S_4. As a byproduct, we compute all its Hopf-Galois extensions and we show that these Hopf algebras are cocycle deformations of their graded versions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1006.1857","kind":"arxiv","version":6},"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":"2026-05-18T04:10:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3w8T30ymKisdiANHXi1SXaMgjGnpzwiZ7OGsc3paPx7KhmLqQBqYyJdtmuA3uRjn9W80DBgVLHE6rvDOADz/DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T10:21:33.299476Z"},"content_sha256":"79bbbc86a00c6cf838bb1f7a58dbfecf145b847d87ea0cf951d621a5f0b3ed59","schema_version":"1.0","event_id":"sha256:79bbbc86a00c6cf838bb1f7a58dbfecf145b847d87ea0cf951d621a5f0b3ed59"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SED3ORYX4UVCUOVO6PMS6CKINU/bundle.json","state_url":"https://pith.science/pith/SED3ORYX4UVCUOVO6PMS6CKINU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SED3ORYX4UVCUOVO6PMS6CKINU/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":"2026-05-31T10:21:33Z","links":{"resolver":"https://pith.science/pith/SED3ORYX4UVCUOVO6PMS6CKINU","bundle":"https://pith.science/pith/SED3ORYX4UVCUOVO6PMS6CKINU/bundle.json","state":"https://pith.science/pith/SED3ORYX4UVCUOVO6PMS6CKINU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SED3ORYX4UVCUOVO6PMS6CKINU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:SED3ORYX4UVCUOVO6PMS6CKINU","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":"22bba5add80090ea545d46b0deff70964058c00aeebb4a9b435700022e9b1547","cross_cats_sorted":["math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2010-06-09T17:14:22Z","title_canon_sha256":"3fc06f6d3994bb01dddfbb319886ea321fc3f76787b6e72699771075719144a1"},"schema_version":"1.0","source":{"id":"1006.1857","kind":"arxiv","version":6}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1006.1857","created_at":"2026-05-18T04:10:57Z"},{"alias_kind":"arxiv_version","alias_value":"1006.1857v6","created_at":"2026-05-18T04:10:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1006.1857","created_at":"2026-05-18T04:10:57Z"},{"alias_kind":"pith_short_12","alias_value":"SED3ORYX4UVC","created_at":"2026-05-18T12:26:13Z"},{"alias_kind":"pith_short_16","alias_value":"SED3ORYX4UVCUOVO","created_at":"2026-05-18T12:26:13Z"},{"alias_kind":"pith_short_8","alias_value":"SED3ORYX","created_at":"2026-05-18T12:26:13Z"}],"graph_snapshots":[{"event_id":"sha256:79bbbc86a00c6cf838bb1f7a58dbfecf145b847d87ea0cf951d621a5f0b3ed59","target":"graph","created_at":"2026-05-18T04:10:57Z","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":"We classify exact indecomposable module categories over the representation category of all non-trivial Hopf algebras with coradical S_3 and S_4. As a byproduct, we compute all its Hopf-Galois extensions and we show that these Hopf algebras are cocycle deformations of their graded versions.","authors_text":"Agust\\'in Garc\\'ia Iglesias, Mart\\'in Mombelli","cross_cats":["math.RA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2010-06-09T17:14:22Z","title":"Representations of the category of modules over pointed Hopf algebras over S_3 and S_4"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1006.1857","kind":"arxiv","version":6},"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:f17d0a1ecb6951d4479b625a553935c71713ff3ffcad0e243406ba8a34a2da2c","target":"record","created_at":"2026-05-18T04:10:57Z","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":"22bba5add80090ea545d46b0deff70964058c00aeebb4a9b435700022e9b1547","cross_cats_sorted":["math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2010-06-09T17:14:22Z","title_canon_sha256":"3fc06f6d3994bb01dddfbb319886ea321fc3f76787b6e72699771075719144a1"},"schema_version":"1.0","source":{"id":"1006.1857","kind":"arxiv","version":6}},"canonical_sha256":"9107b74717e52a2a3aaef3d92f09486d389acb97afadd1dcbec2579465c2f1f3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9107b74717e52a2a3aaef3d92f09486d389acb97afadd1dcbec2579465c2f1f3","first_computed_at":"2026-05-18T04:10:57.166796Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:10:57.166796Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"aH83fGMH6iHeKe5kDncsn2LI3yGsoGkmBprWweiCvP5xAngwGYleOJZZEGiKqngPIwfoiwOba0oZthz92t4gAg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:10:57.167435Z","signed_message":"canonical_sha256_bytes"},"source_id":"1006.1857","source_kind":"arxiv","source_version":6}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f17d0a1ecb6951d4479b625a553935c71713ff3ffcad0e243406ba8a34a2da2c","sha256:79bbbc86a00c6cf838bb1f7a58dbfecf145b847d87ea0cf951d621a5f0b3ed59"],"state_sha256":"7045b91abccd26175de372ef0c5f33315ca6a76c38cb233564753b205fe1116d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0thqBmJ8VXAaIhZio+I446290QGMvbs5bGa1K+wdOKl+261FhKoDS3SB0fjloJ7IKKtrIro6xo5Cj9A4MCOBCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T10:21:33.301889Z","bundle_sha256":"09619fa57b302811c0144bf0d96b7425927087198197e52d3dd0cdf531050f15"}}