{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:DQN46V7NMVSAYEG6SMETUHXL32","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":"12b8c4ed0f6e32d5cb1c4d73da79a4c0a1254acce60bf1faf0aae3b09d02d661","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2013-11-12T11:01:05Z","title_canon_sha256":"599c2d71e19542776a9ca45eec86f11c664040992e9984e6d7da723f4f710bef"},"schema_version":"1.0","source":{"id":"1311.2730","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1311.2730","created_at":"2026-05-18T02:56:43Z"},{"alias_kind":"arxiv_version","alias_value":"1311.2730v2","created_at":"2026-05-18T02:56:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1311.2730","created_at":"2026-05-18T02:56:43Z"},{"alias_kind":"pith_short_12","alias_value":"DQN46V7NMVSA","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_16","alias_value":"DQN46V7NMVSAYEG6","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_8","alias_value":"DQN46V7N","created_at":"2026-05-18T12:27:43Z"}],"graph_snapshots":[{"event_id":"sha256:04af783b958d69d9d21d23bf60e6f9ef538318a61d635511d253ba6472bba6a7","target":"graph","created_at":"2026-05-18T02:56:43Z","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":"This is a sequel paper of arXiv:1306.1466 in which we study the comodules over a regular weak multiplier bialgebra over a field, with a full comultiplication. Replacing the usual notion of coassociative coaction over a (weak) bialgebra, a comodule is defined via a pair of compatible linear maps. Both the total algebra and the base (co)algebra of a regular weak multiplier bialgebra with a full comultiplication are shown to carry comodule structures. Kahng and Van Daele's integrals are interpreted as comodule maps from the total to the base algebra. Generalizing the counitality of a comodule to ","authors_text":"Gabriella B\\\"ohm","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2013-11-12T11:01:05Z","title":"Comodules over weak multiplier bialgebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.2730","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:e975033fc25a3a9f47e21fc6fc9bb6c061bd850f8463612d2ee1431ae1b125b4","target":"record","created_at":"2026-05-18T02:56:43Z","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":"12b8c4ed0f6e32d5cb1c4d73da79a4c0a1254acce60bf1faf0aae3b09d02d661","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2013-11-12T11:01:05Z","title_canon_sha256":"599c2d71e19542776a9ca45eec86f11c664040992e9984e6d7da723f4f710bef"},"schema_version":"1.0","source":{"id":"1311.2730","kind":"arxiv","version":2}},"canonical_sha256":"1c1bcf57ed65640c10de93093a1eebde977e2057e4073e9db952d2c08be20055","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1c1bcf57ed65640c10de93093a1eebde977e2057e4073e9db952d2c08be20055","first_computed_at":"2026-05-18T02:56:43.764061Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:56:43.764061Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"GUpwd2xKF//WR5KSjudKY3bMa9EMcDlTF8fhIIPByEwUTViiPBOUIzUsOszAuxHpX4QHbg4dK+olTAb9aYCSCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:56:43.764490Z","signed_message":"canonical_sha256_bytes"},"source_id":"1311.2730","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e975033fc25a3a9f47e21fc6fc9bb6c061bd850f8463612d2ee1431ae1b125b4","sha256:04af783b958d69d9d21d23bf60e6f9ef538318a61d635511d253ba6472bba6a7"],"state_sha256":"6216292c019fce944a12bb7dc250600beb6d3ea7868253c696b65805d1b3798f"}