{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:CYOJ5UERKD34WFRDG3WXUXZAF5","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":"be3455375a3cabc931b92119b1ee5cb9ba4c61719b87936061bd4ab2f70ece62","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2008-06-28T02:31:57Z","title_canon_sha256":"ddae30e3e3f66cd5900a289063bdf83075ad409f739c0bb74d7aab0f4b4742b1"},"schema_version":"1.0","source":{"id":"0806.4643","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0806.4643","created_at":"2026-05-18T04:03:54Z"},{"alias_kind":"arxiv_version","alias_value":"0806.4643v2","created_at":"2026-05-18T04:03:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0806.4643","created_at":"2026-05-18T04:03:54Z"},{"alias_kind":"pith_short_12","alias_value":"CYOJ5UERKD34","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_16","alias_value":"CYOJ5UERKD34WFRD","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_8","alias_value":"CYOJ5UER","created_at":"2026-05-18T12:25:57Z"}],"graph_snapshots":[{"event_id":"sha256:60d326a0446ef16a67b6932fba97b19e530e6dd2c5ff153b23aa3e29ea207925","target":"graph","created_at":"2026-05-18T04:03:54Z","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 a locally compact group $G$, let $A(G)$ be its Fourier algebra, let $M_{cb}A(G)$ denote the completely bounded multipliers of $A(G)$, and let $A_{Mcb}(G)$ stand for the closure of $A(G)$ in $M_{cb}A(G)$. We characterize the norm one idempotents in $M_{cb}A(G)$: the indicator function of a set $E \\subset G$ is a norm one idempotent in $M_{cb}A(G)$ if and only if $E$ is a coset of an open subgroup of $G$. As applications, we describe the closed ideals of $A_{Mcb}(G)$ with an approximate identity bounded by 1, and we characterize those $G$ for which $A_{Mcb}(G)$ is 1-amenable in the sense of ","authors_text":"Brian E. Forrest, Volker Runde","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2008-06-28T02:31:57Z","title":"Norm one idempotent cb-multipliers with applications to the Fourier algebra in the cb-multiplier norm"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0806.4643","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":"sha256:815e42cd302499478bcec917c3866c2dcd761dc17fef89a0f0971eff3a676787","target":"record","created_at":"2026-05-18T04:03:54Z","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":"be3455375a3cabc931b92119b1ee5cb9ba4c61719b87936061bd4ab2f70ece62","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2008-06-28T02:31:57Z","title_canon_sha256":"ddae30e3e3f66cd5900a289063bdf83075ad409f739c0bb74d7aab0f4b4742b1"},"schema_version":"1.0","source":{"id":"0806.4643","kind":"arxiv","version":2}},"canonical_sha256":"161c9ed09150f7cb162336ed7a5f202f43b6302e2e2783616eba13f4308bf7f9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"161c9ed09150f7cb162336ed7a5f202f43b6302e2e2783616eba13f4308bf7f9","first_computed_at":"2026-05-18T04:03:54.823432Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:03:54.823432Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"LhFB7Lt3b3GYwFbMecYSEJInmjmWmpSoHfvNZMD0kSBM/LKkhWEPK96ob/yh39XMXxtB3uCSx3z1Xn3LPDzIAA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:03:54.824161Z","signed_message":"canonical_sha256_bytes"},"source_id":"0806.4643","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:815e42cd302499478bcec917c3866c2dcd761dc17fef89a0f0971eff3a676787","sha256:60d326a0446ef16a67b6932fba97b19e530e6dd2c5ff153b23aa3e29ea207925"],"state_sha256":"b4cbe58ecc37defa2a7bc88d41f847a30f24e125952bd41ed78a4591ae954836"}