{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:UQTCLY6FNAFMFSSKBKKCKLHU7D","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":"2ab12ee4a268586f542bf9f0101dcca565a80322f4b57ceec776d8ba86fc753e","cross_cats_sorted":["math.KT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2012-03-02T07:10:12Z","title_canon_sha256":"aad0c322351390e02564813ec052cec0f4f21e33562fc0887ab3906aadebdbe2"},"schema_version":"1.0","source":{"id":"1203.0383","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1203.0383","created_at":"2026-05-18T04:01:00Z"},{"alias_kind":"arxiv_version","alias_value":"1203.0383v1","created_at":"2026-05-18T04:01:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1203.0383","created_at":"2026-05-18T04:01:00Z"},{"alias_kind":"pith_short_12","alias_value":"UQTCLY6FNAFM","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_16","alias_value":"UQTCLY6FNAFMFSSK","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_8","alias_value":"UQTCLY6F","created_at":"2026-05-18T12:27:23Z"}],"graph_snapshots":[{"event_id":"sha256:00c6de246803a7895d1bd4b562656d4faf8c45936e6a19688148326b3b755fcd","target":"graph","created_at":"2026-05-18T04:01:00Z","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":"Let $A \\in M_{n}(\\mathbb{R})$ be an invertible matrix. Consider the semi-direct product $\\mathbb{R}^{n} \\rtimes \\mathbb{Z}$ where $\\mathbb{Z}$ acts on $\\mathbb{R}^{n}$ by matrix multiplication. Consider a strongly continuous action $(\\alpha,\\tau)$ of $\\mathbb{R}^{n} \\rtimes \\mathbb{Z}$ on a $C^{*}$-algebra $B$ where $\\alpha$ is a strongly continuous action of $\\mathbb{R}^{n}$ and $\\tau$ is an automorphism. The map $\\tau$ induces a map $\\widetilde{\\tau}$ on $B \\rtimes_{\\alpha} \\mathbb{R}^{n}$. We show that, at the $K$-theory level, $\\tau$ commutes with the Connes-Thom map if $\\det(A)>0$ and ant","authors_text":"S.Sundar","cross_cats":["math.KT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2012-03-02T07:10:12Z","title":"A computation with the Connes-Thom isomorphism"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.0383","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":"sha256:1e4de11c1e078a51b3b07c42709a656b41956af6d2a2ddb8ae54ab6301ab5a8a","target":"record","created_at":"2026-05-18T04:01:00Z","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":"2ab12ee4a268586f542bf9f0101dcca565a80322f4b57ceec776d8ba86fc753e","cross_cats_sorted":["math.KT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2012-03-02T07:10:12Z","title_canon_sha256":"aad0c322351390e02564813ec052cec0f4f21e33562fc0887ab3906aadebdbe2"},"schema_version":"1.0","source":{"id":"1203.0383","kind":"arxiv","version":1}},"canonical_sha256":"a42625e3c5680ac2ca4a0a94252cf4f8fa200f7b1dea83364c92455861913018","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a42625e3c5680ac2ca4a0a94252cf4f8fa200f7b1dea83364c92455861913018","first_computed_at":"2026-05-18T04:01:00.975292Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:01:00.975292Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"jKZqPoI5tfAZJ68xpzujGrcuCOgcXPXlCLsjxykVf9bv+gNhEZ1xeZPzuHJjP0XMhD+LMUtGIwCzd89TqrimBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:01:00.976093Z","signed_message":"canonical_sha256_bytes"},"source_id":"1203.0383","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1e4de11c1e078a51b3b07c42709a656b41956af6d2a2ddb8ae54ab6301ab5a8a","sha256:00c6de246803a7895d1bd4b562656d4faf8c45936e6a19688148326b3b755fcd"],"state_sha256":"9116635617fbd39836246ed14e9a1fe745952cdf990567ccb1f489654e612bc3"}