{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:B7VFIEF3A6UCIEFGJLCQJYCN37","short_pith_number":"pith:B7VFIEF3","canonical_record":{"source":{"id":"1310.7880","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2013-10-29T17:06:59Z","cross_cats_sorted":["math.GR"],"title_canon_sha256":"bbcd8b26cb2fe3b569d4162c0057123c1530b74dae688fce913ca54bc0dc6014","abstract_canon_sha256":"3497af10ee9a1937a71b298c36cc0b7a3394908b083536b817510d546480f5b1"},"schema_version":"1.0"},"canonical_sha256":"0fea5410bb07a82410a64ac504e04ddfe8c486c23d658c492efe0617ef8d241a","source":{"kind":"arxiv","id":"1310.7880","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1310.7880","created_at":"2026-05-18T03:08:27Z"},{"alias_kind":"arxiv_version","alias_value":"1310.7880v1","created_at":"2026-05-18T03:08:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.7880","created_at":"2026-05-18T03:08:27Z"},{"alias_kind":"pith_short_12","alias_value":"B7VFIEF3A6UC","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_16","alias_value":"B7VFIEF3A6UCIEFG","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_8","alias_value":"B7VFIEF3","created_at":"2026-05-18T12:27:38Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:B7VFIEF3A6UCIEFGJLCQJYCN37","target":"record","payload":{"canonical_record":{"source":{"id":"1310.7880","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2013-10-29T17:06:59Z","cross_cats_sorted":["math.GR"],"title_canon_sha256":"bbcd8b26cb2fe3b569d4162c0057123c1530b74dae688fce913ca54bc0dc6014","abstract_canon_sha256":"3497af10ee9a1937a71b298c36cc0b7a3394908b083536b817510d546480f5b1"},"schema_version":"1.0"},"canonical_sha256":"0fea5410bb07a82410a64ac504e04ddfe8c486c23d658c492efe0617ef8d241a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:08:27.742198Z","signature_b64":"s4y9HHYJjxugbxTRk6qZBAbvAY88y+34pb7HDl31cv+f01390wPmol7elwtSBRL88tgKuL83qhiLehyMr4ObDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0fea5410bb07a82410a64ac504e04ddfe8c486c23d658c492efe0617ef8d241a","last_reissued_at":"2026-05-18T03:08:27.741513Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:08:27.741513Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1310.7880","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:08:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"q5NnzoNhyNqEpHvD86I4KBYbUhxHHMkOtQhTHWeR1ZA8qnhHkYYMX847GG4rsoAuPHiWr++Q1julBvAJJDosAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T02:29:41.919564Z"},"content_sha256":"572229732b1285d656e647f78eb501556cd8080b26c40abca0e65a3b89428d2a","schema_version":"1.0","event_id":"sha256:572229732b1285d656e647f78eb501556cd8080b26c40abca0e65a3b89428d2a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:B7VFIEF3A6UCIEFGJLCQJYCN37","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Radial multipliers on arbitrary amalgamated free products of finite von Neumann algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.OA","authors_text":"Steven Deprez","submitted_at":"2013-10-29T17:06:59Z","abstract_excerpt":"Let $(M_i)_{i}$ be a (finite or infinite) family of finite von Neumann algebras with a common subalgebra $P$. When $\\varphi:\\IN\\rightarrow\\IC$ is a function, we define the radial multiplier $M_\\varphi$ on the amalgamated free product $M=M_1\\free_P M_2\\free_P\\ldots$ setting $M_{\\varphi}(x)=\\varphi(n)x$ for every reduced expression $x$ of length $n$. In this paper we give a sufficient condition on $\\varphi$ to ensure that the corresponding radial multiplier $M_\\varphi$ is a completely bounded map, and moreover we give an upper bound on its completely bounded norm. Our condition on $\\varphi$ does"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.7880","kind":"arxiv","version":1},"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":"2026-05-18T03:08:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0UOU4FHH6ns2wX1rvo93SZoI0XNkQ+6IlFMWBAe5jzZq5Oi/EoGnXnxNyGIdWXCFlnYkZ7QbiIINX/Ts7iO6Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T02:29:41.919911Z"},"content_sha256":"4d55f99417573435c66509d78439096e55fa428e13bf21746a377dea49c83f2b","schema_version":"1.0","event_id":"sha256:4d55f99417573435c66509d78439096e55fa428e13bf21746a377dea49c83f2b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/B7VFIEF3A6UCIEFGJLCQJYCN37/bundle.json","state_url":"https://pith.science/pith/B7VFIEF3A6UCIEFGJLCQJYCN37/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/B7VFIEF3A6UCIEFGJLCQJYCN37/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":"2026-06-05T02:29:41Z","links":{"resolver":"https://pith.science/pith/B7VFIEF3A6UCIEFGJLCQJYCN37","bundle":"https://pith.science/pith/B7VFIEF3A6UCIEFGJLCQJYCN37/bundle.json","state":"https://pith.science/pith/B7VFIEF3A6UCIEFGJLCQJYCN37/state.json","well_known_bundle":"https://pith.science/.well-known/pith/B7VFIEF3A6UCIEFGJLCQJYCN37/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:B7VFIEF3A6UCIEFGJLCQJYCN37","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":"3497af10ee9a1937a71b298c36cc0b7a3394908b083536b817510d546480f5b1","cross_cats_sorted":["math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2013-10-29T17:06:59Z","title_canon_sha256":"bbcd8b26cb2fe3b569d4162c0057123c1530b74dae688fce913ca54bc0dc6014"},"schema_version":"1.0","source":{"id":"1310.7880","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1310.7880","created_at":"2026-05-18T03:08:27Z"},{"alias_kind":"arxiv_version","alias_value":"1310.7880v1","created_at":"2026-05-18T03:08:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.7880","created_at":"2026-05-18T03:08:27Z"},{"alias_kind":"pith_short_12","alias_value":"B7VFIEF3A6UC","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_16","alias_value":"B7VFIEF3A6UCIEFG","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_8","alias_value":"B7VFIEF3","created_at":"2026-05-18T12:27:38Z"}],"graph_snapshots":[{"event_id":"sha256:4d55f99417573435c66509d78439096e55fa428e13bf21746a377dea49c83f2b","target":"graph","created_at":"2026-05-18T03:08:27Z","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 $(M_i)_{i}$ be a (finite or infinite) family of finite von Neumann algebras with a common subalgebra $P$. When $\\varphi:\\IN\\rightarrow\\IC$ is a function, we define the radial multiplier $M_\\varphi$ on the amalgamated free product $M=M_1\\free_P M_2\\free_P\\ldots$ setting $M_{\\varphi}(x)=\\varphi(n)x$ for every reduced expression $x$ of length $n$. In this paper we give a sufficient condition on $\\varphi$ to ensure that the corresponding radial multiplier $M_\\varphi$ is a completely bounded map, and moreover we give an upper bound on its completely bounded norm. Our condition on $\\varphi$ does","authors_text":"Steven Deprez","cross_cats":["math.GR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2013-10-29T17:06:59Z","title":"Radial multipliers on arbitrary amalgamated free products of finite von Neumann algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.7880","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":"sha256:572229732b1285d656e647f78eb501556cd8080b26c40abca0e65a3b89428d2a","target":"record","created_at":"2026-05-18T03:08:27Z","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":"3497af10ee9a1937a71b298c36cc0b7a3394908b083536b817510d546480f5b1","cross_cats_sorted":["math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2013-10-29T17:06:59Z","title_canon_sha256":"bbcd8b26cb2fe3b569d4162c0057123c1530b74dae688fce913ca54bc0dc6014"},"schema_version":"1.0","source":{"id":"1310.7880","kind":"arxiv","version":1}},"canonical_sha256":"0fea5410bb07a82410a64ac504e04ddfe8c486c23d658c492efe0617ef8d241a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0fea5410bb07a82410a64ac504e04ddfe8c486c23d658c492efe0617ef8d241a","first_computed_at":"2026-05-18T03:08:27.741513Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:08:27.741513Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"s4y9HHYJjxugbxTRk6qZBAbvAY88y+34pb7HDl31cv+f01390wPmol7elwtSBRL88tgKuL83qhiLehyMr4ObDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:08:27.742198Z","signed_message":"canonical_sha256_bytes"},"source_id":"1310.7880","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:572229732b1285d656e647f78eb501556cd8080b26c40abca0e65a3b89428d2a","sha256:4d55f99417573435c66509d78439096e55fa428e13bf21746a377dea49c83f2b"],"state_sha256":"3b8be02b7cc59214b9ebcd32e01524acc5ac2c857b12cfeb6684a22dfe6d30f0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gjLxMWrsnb21YGeobvdI77UX8bPYJo6lcHx0xlwM15CnR3PX5jvXij+neaMvd63HNKOc3rmMpB/wGaocwVTvDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T02:29:41.921964Z","bundle_sha256":"17ab1cd5eaed5ff3d5d8aa37704a6130171d65ca9e3ab92d620dcaf198f1a5a7"}}