{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:DLUMUU67N3IFTXULUNYWXPUWR7","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":"5763dcc3af263c6919d9e8a41ebf0a6da537a9a91140a4b1582d6202085d938d","cross_cats_sorted":["math.OA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2013-09-25T06:02:32Z","title_canon_sha256":"13b5cce4014902039fe728f643e295d63c4b267b57e366069b0861429601fb5e"},"schema_version":"1.0","source":{"id":"1309.6406","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1309.6406","created_at":"2026-05-18T03:12:21Z"},{"alias_kind":"arxiv_version","alias_value":"1309.6406v1","created_at":"2026-05-18T03:12:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.6406","created_at":"2026-05-18T03:12:21Z"},{"alias_kind":"pith_short_12","alias_value":"DLUMUU67N3IF","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_16","alias_value":"DLUMUU67N3IFTXUL","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_8","alias_value":"DLUMUU67","created_at":"2026-05-18T12:27:43Z"}],"graph_snapshots":[{"event_id":"sha256:ecc76ea0d52032241b0906d51d43b4b08ad9cf70f3c02a8006b6cbe42150e2f2","target":"graph","created_at":"2026-05-18T03:12:21Z","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":"For $p \\in [1, \\infty),$ we define and study full and reduced crossed products of algebras of operators on $\\sigma$-finite $L^p$ spaces by isometric actions of second countable locally compact groups. We give universal properties for both crossed products. When the group is abelian, we prove the existence of a dual action on the full and reduced $L^p$ operator crossed products. When the group is discrete, we construct a conditional expectation to the original algebra which is faithful in a suitable sense. For a free action of a discrete group on a compact metric space $X,$ we identify all trac","authors_text":"N. Christopher Phillips","cross_cats":["math.OA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2013-09-25T06:02:32Z","title":"Crossed products of $L^p$ operator algebras and the K-theory of Cuntz algebras on $L^p$ spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.6406","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":"sha256:7cb4ba3c52e9ac2ea5c05f2a00e00a45c23d1e9b5266ac56f48ca72bd9dfeeb5","target":"record","created_at":"2026-05-18T03:12:21Z","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":"5763dcc3af263c6919d9e8a41ebf0a6da537a9a91140a4b1582d6202085d938d","cross_cats_sorted":["math.OA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2013-09-25T06:02:32Z","title_canon_sha256":"13b5cce4014902039fe728f643e295d63c4b267b57e366069b0861429601fb5e"},"schema_version":"1.0","source":{"id":"1309.6406","kind":"arxiv","version":1}},"canonical_sha256":"1ae8ca53df6ed059de8ba3716bbe968fef5e2bb7e07027e52dcfccefdcbf34f7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1ae8ca53df6ed059de8ba3716bbe968fef5e2bb7e07027e52dcfccefdcbf34f7","first_computed_at":"2026-05-18T03:12:21.257511Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:12:21.257511Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ZGgbsfFSCHOtVxmy7/zTi9mf3AHH+i6gBALwG+3+/ROtbLv5bFJ8F9RfekAcLPBTVXoxF2w8ddud1PM350V+Cw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:12:21.258301Z","signed_message":"canonical_sha256_bytes"},"source_id":"1309.6406","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7cb4ba3c52e9ac2ea5c05f2a00e00a45c23d1e9b5266ac56f48ca72bd9dfeeb5","sha256:ecc76ea0d52032241b0906d51d43b4b08ad9cf70f3c02a8006b6cbe42150e2f2"],"state_sha256":"3135eb95f3900edc0f3f4a551f82e5c4ac3f02c013a734220f70e040968862dc"}