{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2009:2UZUEM3F777TSROEHBOA52ZNSC","short_pith_number":"pith:2UZUEM3F","canonical_record":{"source":{"id":"0906.5128","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2009-06-28T10:39:50Z","cross_cats_sorted":["math.OA"],"title_canon_sha256":"eefe5eaf4c8b8e1b07e5bc8288ee9d4348d8c97935c30ae3979b358c0e6ea740","abstract_canon_sha256":"5dc1da567b2bf4021e330994328ebefb75186243343a67c4c510aefc8e42424b"},"schema_version":"1.0"},"canonical_sha256":"d533423365ffff3945c4385c0eeb2d909b5411d05f9a1b899e6fd41a8410efa5","source":{"kind":"arxiv","id":"0906.5128","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0906.5128","created_at":"2026-05-18T04:16:53Z"},{"alias_kind":"arxiv_version","alias_value":"0906.5128v2","created_at":"2026-05-18T04:16:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0906.5128","created_at":"2026-05-18T04:16:53Z"},{"alias_kind":"pith_short_12","alias_value":"2UZUEM3F777T","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"2UZUEM3F777TSROE","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"2UZUEM3F","created_at":"2026-05-18T12:25:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2009:2UZUEM3F777TSROEHBOA52ZNSC","target":"record","payload":{"canonical_record":{"source":{"id":"0906.5128","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2009-06-28T10:39:50Z","cross_cats_sorted":["math.OA"],"title_canon_sha256":"eefe5eaf4c8b8e1b07e5bc8288ee9d4348d8c97935c30ae3979b358c0e6ea740","abstract_canon_sha256":"5dc1da567b2bf4021e330994328ebefb75186243343a67c4c510aefc8e42424b"},"schema_version":"1.0"},"canonical_sha256":"d533423365ffff3945c4385c0eeb2d909b5411d05f9a1b899e6fd41a8410efa5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:16:53.743711Z","signature_b64":"3CF2h/YCCxBgApA7W4Znq/pJO6yVDD1JzxwGabGPNrhXxUePLva5htn3yuY+01llqdYe5qhKSpijCxpqWmPsAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d533423365ffff3945c4385c0eeb2d909b5411d05f9a1b899e6fd41a8410efa5","last_reissued_at":"2026-05-18T04:16:53.743209Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:16:53.743209Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0906.5128","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:16:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"k0u5im/yxwtKBd0ExFuZQkdF6m+pQFVaUWwNaVQ+Z9KPI2bxNLhV7riBNvVnHDUdPKQDXiYoMHE7Z2byIXksBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T12:44:32.397602Z"},"content_sha256":"4d6dbbd445fd44beaf5b8ff3f5ad6112d8eb54d255882c4aebc5827652683257","schema_version":"1.0","event_id":"sha256:4d6dbbd445fd44beaf5b8ff3f5ad6112d8eb54d255882c4aebc5827652683257"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2009:2UZUEM3F777TSROEHBOA52ZNSC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Representing multipliers of the Fourier algebra on non-commutative $L^p$ spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OA"],"primary_cat":"math.FA","authors_text":"Matthew Daws","submitted_at":"2009-06-28T10:39:50Z","abstract_excerpt":"We show that the multiplier algebra of the Fourier algebra on a locally compact group $G$ can be isometrically represented on a direct sum on non-commutative $L^p$ spaces associated to the right von Neumann algebra of $G$. If these spaces are given their canonical Operator space structure, then we get a completely isometric representation of the completely bounded multiplier algebra. We make a careful study of the non-commutative $L^p$ spaces we construct, and show that they are completely isometric to those considered recently by Forrest, Lee and Samei; we improve a result about module homomo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0906.5128","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:16:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QkxUkmRXE3E1RJByQnbJnFQ2sn2r7mKh2p9cLZIfN6oOerL3GedZjZ2GuBWwgXMjBr6kOtCdHINppCeHE8lIAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T12:44:32.397947Z"},"content_sha256":"a4c4173c8f0d0ee023325ac26c45f7f50b7e6755ba313e6fb613012157a2f713","schema_version":"1.0","event_id":"sha256:a4c4173c8f0d0ee023325ac26c45f7f50b7e6755ba313e6fb613012157a2f713"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/2UZUEM3F777TSROEHBOA52ZNSC/bundle.json","state_url":"https://pith.science/pith/2UZUEM3F777TSROEHBOA52ZNSC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/2UZUEM3F777TSROEHBOA52ZNSC/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-22T12:44:32Z","links":{"resolver":"https://pith.science/pith/2UZUEM3F777TSROEHBOA52ZNSC","bundle":"https://pith.science/pith/2UZUEM3F777TSROEHBOA52ZNSC/bundle.json","state":"https://pith.science/pith/2UZUEM3F777TSROEHBOA52ZNSC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/2UZUEM3F777TSROEHBOA52ZNSC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:2UZUEM3F777TSROEHBOA52ZNSC","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":"5dc1da567b2bf4021e330994328ebefb75186243343a67c4c510aefc8e42424b","cross_cats_sorted":["math.OA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2009-06-28T10:39:50Z","title_canon_sha256":"eefe5eaf4c8b8e1b07e5bc8288ee9d4348d8c97935c30ae3979b358c0e6ea740"},"schema_version":"1.0","source":{"id":"0906.5128","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0906.5128","created_at":"2026-05-18T04:16:53Z"},{"alias_kind":"arxiv_version","alias_value":"0906.5128v2","created_at":"2026-05-18T04:16:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0906.5128","created_at":"2026-05-18T04:16:53Z"},{"alias_kind":"pith_short_12","alias_value":"2UZUEM3F777T","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"2UZUEM3F777TSROE","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"2UZUEM3F","created_at":"2026-05-18T12:25:58Z"}],"graph_snapshots":[{"event_id":"sha256:a4c4173c8f0d0ee023325ac26c45f7f50b7e6755ba313e6fb613012157a2f713","target":"graph","created_at":"2026-05-18T04:16:53Z","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 the multiplier algebra of the Fourier algebra on a locally compact group $G$ can be isometrically represented on a direct sum on non-commutative $L^p$ spaces associated to the right von Neumann algebra of $G$. If these spaces are given their canonical Operator space structure, then we get a completely isometric representation of the completely bounded multiplier algebra. We make a careful study of the non-commutative $L^p$ spaces we construct, and show that they are completely isometric to those considered recently by Forrest, Lee and Samei; we improve a result about module homomo","authors_text":"Matthew Daws","cross_cats":["math.OA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2009-06-28T10:39:50Z","title":"Representing multipliers of the Fourier algebra on non-commutative $L^p$ spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0906.5128","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":"sha256:4d6dbbd445fd44beaf5b8ff3f5ad6112d8eb54d255882c4aebc5827652683257","target":"record","created_at":"2026-05-18T04:16:53Z","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":"5dc1da567b2bf4021e330994328ebefb75186243343a67c4c510aefc8e42424b","cross_cats_sorted":["math.OA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2009-06-28T10:39:50Z","title_canon_sha256":"eefe5eaf4c8b8e1b07e5bc8288ee9d4348d8c97935c30ae3979b358c0e6ea740"},"schema_version":"1.0","source":{"id":"0906.5128","kind":"arxiv","version":2}},"canonical_sha256":"d533423365ffff3945c4385c0eeb2d909b5411d05f9a1b899e6fd41a8410efa5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d533423365ffff3945c4385c0eeb2d909b5411d05f9a1b899e6fd41a8410efa5","first_computed_at":"2026-05-18T04:16:53.743209Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:16:53.743209Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3CF2h/YCCxBgApA7W4Znq/pJO6yVDD1JzxwGabGPNrhXxUePLva5htn3yuY+01llqdYe5qhKSpijCxpqWmPsAg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:16:53.743711Z","signed_message":"canonical_sha256_bytes"},"source_id":"0906.5128","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4d6dbbd445fd44beaf5b8ff3f5ad6112d8eb54d255882c4aebc5827652683257","sha256:a4c4173c8f0d0ee023325ac26c45f7f50b7e6755ba313e6fb613012157a2f713"],"state_sha256":"5c7598b27544416cd2609ef30e9e328941894da7c0161d83be7145f4f8f7b87c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oKS4BlPwXnxoE45O6OpkgB6uCYL3Y7ispW6NdiGprfkupkFdCUZvN3Q3u5QqmzWs+Z5uD9xjHKVm+F5TbTriCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-22T12:44:32.399863Z","bundle_sha256":"94f233a6265d9d2bc27a4189da01cc4fcfde27d3240eb55f6271c911b19ed561"}}