{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:7E7COHMILXCZICRBVMEGUWGQ5X","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":"ef52d162c72a831708a655271e95906fc24f3c7588424a3395937a450b66be11","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2013-09-10T02:47:50Z","title_canon_sha256":"f574863dc3e2bf0fce3c05c72f84c8a5c15d50d5e6eecb8cc0cb6dc7e3752b83"},"schema_version":"1.0","source":{"id":"1309.2363","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1309.2363","created_at":"2026-05-17T23:53:15Z"},{"alias_kind":"arxiv_version","alias_value":"1309.2363v1","created_at":"2026-05-17T23:53:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.2363","created_at":"2026-05-17T23:53:15Z"},{"alias_kind":"pith_short_12","alias_value":"7E7COHMILXCZ","created_at":"2026-05-18T12:27:36Z"},{"alias_kind":"pith_short_16","alias_value":"7E7COHMILXCZICRB","created_at":"2026-05-18T12:27:36Z"},{"alias_kind":"pith_short_8","alias_value":"7E7COHMI","created_at":"2026-05-18T12:27:36Z"}],"graph_snapshots":[{"event_id":"sha256:8694591802b5a6c5af6f6acdb9479a5b636d7a7a520902a7b292def87149efb2","target":"graph","created_at":"2026-05-17T23:53:15Z","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":"Suppose $\\Gamma^{+}$ is the positive cone of a totally ordered abelian group $\\Gamma$, and $(A,\\Gamma^{+},\\alpha)$ is a system consisting of a $C^*$-algebra $A$, an action $\\alpha$ of $\\Gamma^{+}$ by extendible endomorphisms of $A$. We prove that the partial-isometric crossed product $A\\times_{\\alpha}^{\\piso}\\Gamma^{+}$ is a full corner in the subalgebra of $\\L(\\ell^{2}(\\Gamma^{+},A))$, and that if $\\alpha$ is an action by automorphisms of $A$, then it is the isometric-crossed product $(B_{\\Gamma^{+}}\\otimes A)\\times^{\\iso}\\Gamma^{+}$, which is therefore a full corner in the usual crossed prod","authors_text":"Saeid Zahmatkesh, Sriwulan Adji","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2013-09-10T02:47:50Z","title":"The Partial-Isometric Crossed Products by Semigroups of Endomorphisms as Full Corners"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.2363","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:e3f0870fd2f94b05309ea6eb78014bcfc6b005aeb5ce17ed1446a5526c4db888","target":"record","created_at":"2026-05-17T23:53:15Z","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":"ef52d162c72a831708a655271e95906fc24f3c7588424a3395937a450b66be11","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2013-09-10T02:47:50Z","title_canon_sha256":"f574863dc3e2bf0fce3c05c72f84c8a5c15d50d5e6eecb8cc0cb6dc7e3752b83"},"schema_version":"1.0","source":{"id":"1309.2363","kind":"arxiv","version":1}},"canonical_sha256":"f93e271d885dc5940a21ab086a58d0eddad041a03bf441fb82134d775db5c96a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f93e271d885dc5940a21ab086a58d0eddad041a03bf441fb82134d775db5c96a","first_computed_at":"2026-05-17T23:53:15.127046Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:53:15.127046Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"UDcmC6+Hv8/g1DB/8HLjUQOwCQJxfFkiO+6P5kP8BiYB7rPuWXvth6xDawn7VglTaU4MVyQcKlAuTsWvFKhjAQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:53:15.127839Z","signed_message":"canonical_sha256_bytes"},"source_id":"1309.2363","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e3f0870fd2f94b05309ea6eb78014bcfc6b005aeb5ce17ed1446a5526c4db888","sha256:8694591802b5a6c5af6f6acdb9479a5b636d7a7a520902a7b292def87149efb2"],"state_sha256":"fbc7e178da8cfbaa1dbff04cbb5e24d29da48bde3f24d6e271957dfdd33d0c8e"}