{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2009:EMDEKZZRBYCJ2FKVQUY2KS2KKB","short_pith_number":"pith:EMDEKZZR","canonical_record":{"source":{"id":"0909.1206","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2009-09-07T10:34:08Z","cross_cats_sorted":[],"title_canon_sha256":"8f0d617456a3baf1f7c5db605cd75b8369ddd6c7f4ec5d877dc59ac8ff973fa0","abstract_canon_sha256":"6440406b0dfce0998669369e961c11a371e0132c53212e31bc637bdb2e094337"},"schema_version":"1.0"},"canonical_sha256":"23064567310e049d15558531a54b4a507abe4476c54d4f345f5bfc23d4864b93","source":{"kind":"arxiv","id":"0909.1206","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0909.1206","created_at":"2026-05-18T04:36:40Z"},{"alias_kind":"arxiv_version","alias_value":"0909.1206v2","created_at":"2026-05-18T04:36:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0909.1206","created_at":"2026-05-18T04:36:40Z"},{"alias_kind":"pith_short_12","alias_value":"EMDEKZZRBYCJ","created_at":"2026-05-18T12:25:59Z"},{"alias_kind":"pith_short_16","alias_value":"EMDEKZZRBYCJ2FKV","created_at":"2026-05-18T12:25:59Z"},{"alias_kind":"pith_short_8","alias_value":"EMDEKZZR","created_at":"2026-05-18T12:25:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2009:EMDEKZZRBYCJ2FKVQUY2KS2KKB","target":"record","payload":{"canonical_record":{"source":{"id":"0909.1206","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2009-09-07T10:34:08Z","cross_cats_sorted":[],"title_canon_sha256":"8f0d617456a3baf1f7c5db605cd75b8369ddd6c7f4ec5d877dc59ac8ff973fa0","abstract_canon_sha256":"6440406b0dfce0998669369e961c11a371e0132c53212e31bc637bdb2e094337"},"schema_version":"1.0"},"canonical_sha256":"23064567310e049d15558531a54b4a507abe4476c54d4f345f5bfc23d4864b93","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:36:40.421679Z","signature_b64":"DQa3UEh3DjMElsSxHoEHbkpBsDiFdDM7YgAJxqPeWI8ejPVaaOV2CfJAKsuJwH5Y0eJYYicHz43TGgTACUL9AA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"23064567310e049d15558531a54b4a507abe4476c54d4f345f5bfc23d4864b93","last_reissued_at":"2026-05-18T04:36:40.421155Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:36:40.421155Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0909.1206","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:36:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2LfcoIXrhB25yBirVHO14sEkmap2lj9cru3qHU1fnhxiHRst96qCpw2ujPuymojI1mdNWUB1VX4AQBroySN6DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T03:31:54.822367Z"},"content_sha256":"e1ab7af51ad814ce1acdaa60af03cd2791a1858f1d8aee03e5c735f29b3abf04","schema_version":"1.0","event_id":"sha256:e1ab7af51ad814ce1acdaa60af03cd2791a1858f1d8aee03e5c735f29b3abf04"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2009:EMDEKZZRBYCJ2FKVQUY2KS2KKB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Outer actions of measured quantum groupoids","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"Michel Enock","submitted_at":"2009-09-07T10:34:08Z","abstract_excerpt":"Mimicking a recent article of Stefaan Vaes, in which was proved that every locally compact quantum group can act outerly, we prove that we get the same result for measured quantum groupoids, with an appropriate definition of outer actions of measured quantum groupoids. This result is used to show that every measured quantum groupoid can be found from some depth 2 inclusion of von Neumann algebras."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0909.1206","kind":"arxiv","version":2},"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":"2026-05-18T04:36:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Vsv3QzuSEz1tQ6vTvglJkgJrHZ7yVLswhZeNsVNh8IJ9FU91SPddVjkGXGbFkNaL7JKbzEtoVU77H3ZgbaaXDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T03:31:54.822723Z"},"content_sha256":"c38d29922562ca98b883a3e48a8eb7f779abe9099610fff450073461fdd30a7e","schema_version":"1.0","event_id":"sha256:c38d29922562ca98b883a3e48a8eb7f779abe9099610fff450073461fdd30a7e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/EMDEKZZRBYCJ2FKVQUY2KS2KKB/bundle.json","state_url":"https://pith.science/pith/EMDEKZZRBYCJ2FKVQUY2KS2KKB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/EMDEKZZRBYCJ2FKVQUY2KS2KKB/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":"2026-06-25T03:31:54Z","links":{"resolver":"https://pith.science/pith/EMDEKZZRBYCJ2FKVQUY2KS2KKB","bundle":"https://pith.science/pith/EMDEKZZRBYCJ2FKVQUY2KS2KKB/bundle.json","state":"https://pith.science/pith/EMDEKZZRBYCJ2FKVQUY2KS2KKB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/EMDEKZZRBYCJ2FKVQUY2KS2KKB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:EMDEKZZRBYCJ2FKVQUY2KS2KKB","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":"6440406b0dfce0998669369e961c11a371e0132c53212e31bc637bdb2e094337","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2009-09-07T10:34:08Z","title_canon_sha256":"8f0d617456a3baf1f7c5db605cd75b8369ddd6c7f4ec5d877dc59ac8ff973fa0"},"schema_version":"1.0","source":{"id":"0909.1206","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0909.1206","created_at":"2026-05-18T04:36:40Z"},{"alias_kind":"arxiv_version","alias_value":"0909.1206v2","created_at":"2026-05-18T04:36:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0909.1206","created_at":"2026-05-18T04:36:40Z"},{"alias_kind":"pith_short_12","alias_value":"EMDEKZZRBYCJ","created_at":"2026-05-18T12:25:59Z"},{"alias_kind":"pith_short_16","alias_value":"EMDEKZZRBYCJ2FKV","created_at":"2026-05-18T12:25:59Z"},{"alias_kind":"pith_short_8","alias_value":"EMDEKZZR","created_at":"2026-05-18T12:25:59Z"}],"graph_snapshots":[{"event_id":"sha256:c38d29922562ca98b883a3e48a8eb7f779abe9099610fff450073461fdd30a7e","target":"graph","created_at":"2026-05-18T04:36:40Z","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":"Mimicking a recent article of Stefaan Vaes, in which was proved that every locally compact quantum group can act outerly, we prove that we get the same result for measured quantum groupoids, with an appropriate definition of outer actions of measured quantum groupoids. This result is used to show that every measured quantum groupoid can be found from some depth 2 inclusion of von Neumann algebras.","authors_text":"Michel Enock","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2009-09-07T10:34:08Z","title":"Outer actions of measured quantum groupoids"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0909.1206","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:e1ab7af51ad814ce1acdaa60af03cd2791a1858f1d8aee03e5c735f29b3abf04","target":"record","created_at":"2026-05-18T04:36:40Z","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":"6440406b0dfce0998669369e961c11a371e0132c53212e31bc637bdb2e094337","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2009-09-07T10:34:08Z","title_canon_sha256":"8f0d617456a3baf1f7c5db605cd75b8369ddd6c7f4ec5d877dc59ac8ff973fa0"},"schema_version":"1.0","source":{"id":"0909.1206","kind":"arxiv","version":2}},"canonical_sha256":"23064567310e049d15558531a54b4a507abe4476c54d4f345f5bfc23d4864b93","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"23064567310e049d15558531a54b4a507abe4476c54d4f345f5bfc23d4864b93","first_computed_at":"2026-05-18T04:36:40.421155Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:36:40.421155Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"DQa3UEh3DjMElsSxHoEHbkpBsDiFdDM7YgAJxqPeWI8ejPVaaOV2CfJAKsuJwH5Y0eJYYicHz43TGgTACUL9AA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:36:40.421679Z","signed_message":"canonical_sha256_bytes"},"source_id":"0909.1206","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e1ab7af51ad814ce1acdaa60af03cd2791a1858f1d8aee03e5c735f29b3abf04","sha256:c38d29922562ca98b883a3e48a8eb7f779abe9099610fff450073461fdd30a7e"],"state_sha256":"1b4431fbfd6868703b61001adc2f0ad2bde986a4022fadfdb4eb6f404a0b2732"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DS64DXuESMRJ+64dqCnAp7bOFxJ+vFvpj1RCI5V3p0tA90uqhEn+K0jaBZvdOmdtjpTD93tqi6ncq0bLbya1Cg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-25T03:31:54.824637Z","bundle_sha256":"4938a9037f72cb6e955b3ad752079f2edaaabb31a221ad074f80faef7e5b654d"}}