{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2000:G2PLAEWU6AYKJ4GY3ZZR52PH6R","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":"eec0eb8472cda0a626aef48844228f97faf0f77b3515036aef456349981deb00","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2000-07-17T17:49:35Z","title_canon_sha256":"236c92b25b2d5b61b3146b135be0827314aefccc9bd473b920de1045b5b4b516"},"schema_version":"1.0","source":{"id":"math/0007109","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0007109","created_at":"2026-05-18T00:20:07Z"},{"alias_kind":"arxiv_version","alias_value":"math/0007109v2","created_at":"2026-05-18T00:20:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0007109","created_at":"2026-05-18T00:20:07Z"},{"alias_kind":"pith_short_12","alias_value":"G2PLAEWU6AYK","created_at":"2026-05-18T12:25:49Z"},{"alias_kind":"pith_short_16","alias_value":"G2PLAEWU6AYKJ4GY","created_at":"2026-05-18T12:25:49Z"},{"alias_kind":"pith_short_8","alias_value":"G2PLAEWU","created_at":"2026-05-18T12:25:49Z"}],"graph_snapshots":[{"event_id":"sha256:5271752251c7f5bb1e8b6acb332d2f4ba3f6077ac99ec9d98768fdb054d6bbf2","target":"graph","created_at":"2026-05-18T00:20:07Z","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 show that any continuous partial action on a topological space has a unique enveloping action, i.e. it is the restriction of a global action. In the case of C^*-algebras we prove that any partial action has an enveloping action up to Morita equivalence. The study of enveloping actions up to Morita equivalence reveals the form that Takai duality takes for partial actions.","authors_text":"Fernando Abadie","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2000-07-17T17:49:35Z","title":"Enveloping actions and Takai duality for partial actions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0007109","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":"sha256:58c0f61fc59bec0c9f5a2249213a0affd4a20b52e2cc76088013a1c2390f3a0f","target":"record","created_at":"2026-05-18T00:20:07Z","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":"eec0eb8472cda0a626aef48844228f97faf0f77b3515036aef456349981deb00","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2000-07-17T17:49:35Z","title_canon_sha256":"236c92b25b2d5b61b3146b135be0827314aefccc9bd473b920de1045b5b4b516"},"schema_version":"1.0","source":{"id":"math/0007109","kind":"arxiv","version":2}},"canonical_sha256":"369eb012d4f030a4f0d8de731ee9e7f4643ac721fef4b8fa9f6b6bb31d878fa1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"369eb012d4f030a4f0d8de731ee9e7f4643ac721fef4b8fa9f6b6bb31d878fa1","first_computed_at":"2026-05-18T00:20:07.964330Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:20:07.964330Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"U7D8lBMR0CzJcAwhtbvSrRr7KrSRQgw2nGJSqf5HX9aqUnQ04vdmj5m9xJocbczO2HWu5rIYvQbz4LQiTZvxDw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:20:07.964971Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0007109","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:58c0f61fc59bec0c9f5a2249213a0affd4a20b52e2cc76088013a1c2390f3a0f","sha256:5271752251c7f5bb1e8b6acb332d2f4ba3f6077ac99ec9d98768fdb054d6bbf2"],"state_sha256":"2460c53642218fe2487efc9b3d10e04e1117d787d2df99d835c1d427513c17f4"}