{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:6EM7YMYYPWA6WWRSLAUYM6ZBZ5","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":"9e4143299d23947c55cf5c556bba9ab94117f707b3d2f65b239aed57a427572c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2010-04-06T11:16:51Z","title_canon_sha256":"bc77da50a284b5d49ba779052cbbaa402f787f4e79f247f4558ecadd86efff0d"},"schema_version":"1.0","source":{"id":"1004.0824","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1004.0824","created_at":"2026-05-18T03:16:17Z"},{"alias_kind":"arxiv_version","alias_value":"1004.0824v1","created_at":"2026-05-18T03:16:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1004.0824","created_at":"2026-05-18T03:16:17Z"},{"alias_kind":"pith_short_12","alias_value":"6EM7YMYYPWA6","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_16","alias_value":"6EM7YMYYPWA6WWRS","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_8","alias_value":"6EM7YMYY","created_at":"2026-05-18T12:26:04Z"}],"graph_snapshots":[{"event_id":"sha256:e6a6bdca3764d6522208a60d70cc823e1bb3c742cb5ab2d174e6530d0e1177fe","target":"graph","created_at":"2026-05-18T03:16:17Z","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":"A theory of Galois co-objects for von Neumann bialgebras is introduced. This concept is closely related to the notion of comonoidal W*-Morita equivalence between von Neumann bialgebras, which is a Morita equivalence taking the comultiplication structure into account. We show that the property of `being a von Neumann algebraic quantum group' (i.e. `having invariant weights') is preserved under this equivalence relation. We also introduce the notion of a projective corepresentation for a von Neumann bialgebra, and show how it leads to a construction method for Galois co-objects and comonoidal W*","authors_text":"Kenny De Commer","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2010-04-06T11:16:51Z","title":"Comonoidal W*-Morita equivalence for von Neumann bialgebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1004.0824","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:b7515a59baaa316487d70221b99dcd4a26df8f16f1d53c6bb4968a4ba8629d4e","target":"record","created_at":"2026-05-18T03:16:17Z","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":"9e4143299d23947c55cf5c556bba9ab94117f707b3d2f65b239aed57a427572c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2010-04-06T11:16:51Z","title_canon_sha256":"bc77da50a284b5d49ba779052cbbaa402f787f4e79f247f4558ecadd86efff0d"},"schema_version":"1.0","source":{"id":"1004.0824","kind":"arxiv","version":1}},"canonical_sha256":"f119fc33187d81eb5a325829867b21cf5cc929c3574babe82450ffec263f000f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f119fc33187d81eb5a325829867b21cf5cc929c3574babe82450ffec263f000f","first_computed_at":"2026-05-18T03:16:17.835537Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:16:17.835537Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"SOWaqLX2tSf2oNeRQ9Beq+umRhIzP75ksu14P2Sz0HP0qmlaGY6VX6VbpdqXSCoYBP7c2wMmmODQP0MSYl0pCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:16:17.836015Z","signed_message":"canonical_sha256_bytes"},"source_id":"1004.0824","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b7515a59baaa316487d70221b99dcd4a26df8f16f1d53c6bb4968a4ba8629d4e","sha256:e6a6bdca3764d6522208a60d70cc823e1bb3c742cb5ab2d174e6530d0e1177fe"],"state_sha256":"6398485200684113a335b9c18220bdc48a261e4f8ad8960bfc60f345f0ceeeba"}