{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:VRRM7NX6EQOYXM5EP7MJL3W64U","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":"03e091f99bcd0a67a1b729c00b212ef3dd7907903d8f0f90cec7a7ba5df1d757","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2011-11-07T15:13:14Z","title_canon_sha256":"7ab2c15c929b326e661912839cd613892528c10bc0fc101b45d387d8fbe5d45c"},"schema_version":"1.0","source":{"id":"1111.1610","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1111.1610","created_at":"2026-05-18T03:58:26Z"},{"alias_kind":"arxiv_version","alias_value":"1111.1610v2","created_at":"2026-05-18T03:58:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1111.1610","created_at":"2026-05-18T03:58:26Z"},{"alias_kind":"pith_short_12","alias_value":"VRRM7NX6EQOY","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_16","alias_value":"VRRM7NX6EQOYXM5E","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_8","alias_value":"VRRM7NX6","created_at":"2026-05-18T12:26:44Z"}],"graph_snapshots":[{"event_id":"sha256:3523bfd4b76c9661b9fba4af32d3e84c2f0d7b4301d061a2996070f7b718d675","target":"graph","created_at":"2026-05-18T03:58:26Z","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":"Let H be a finite-dimensional Hopf algebra. We give a description of the tensor product of bimodule categories over Rep(H). When the bimodule categories are invertible this description can be given explicitly. We present some consequences of this description in the case H is a pointed Hopf algebra.","authors_text":"Martin Mombelli","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2011-11-07T15:13:14Z","title":"On the tensor product of bimodule categories over Hopf algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.1610","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":"sha256:02db94bfacfa9227660f6ee5a27d68f806b0434878d8e4e30d0679a2b094dd5d","target":"record","created_at":"2026-05-18T03:58:26Z","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":"03e091f99bcd0a67a1b729c00b212ef3dd7907903d8f0f90cec7a7ba5df1d757","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2011-11-07T15:13:14Z","title_canon_sha256":"7ab2c15c929b326e661912839cd613892528c10bc0fc101b45d387d8fbe5d45c"},"schema_version":"1.0","source":{"id":"1111.1610","kind":"arxiv","version":2}},"canonical_sha256":"ac62cfb6fe241d8bb3a47fd895eedee505d30e607d54dc30c7931f7f21acbd08","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ac62cfb6fe241d8bb3a47fd895eedee505d30e607d54dc30c7931f7f21acbd08","first_computed_at":"2026-05-18T03:58:26.277414Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:58:26.277414Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"fm6pA9pK7jnlLcgdoDPOVqMDT4Pat8SlxLn+EM/A+B56gXlqdU79QxAquc+KpFACtHsHnfeZEmzIsQqpWBAZBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:58:26.278111Z","signed_message":"canonical_sha256_bytes"},"source_id":"1111.1610","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:02db94bfacfa9227660f6ee5a27d68f806b0434878d8e4e30d0679a2b094dd5d","sha256:3523bfd4b76c9661b9fba4af32d3e84c2f0d7b4301d061a2996070f7b718d675"],"state_sha256":"d2263f4d223c944c96da7769d6ac6dd9a25f8fb6a195c09f46efb783ef241734"}