{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:F2AJXU3K2QAVBDDHAP5LFEF7K7","short_pith_number":"pith:F2AJXU3K","canonical_record":{"source":{"id":"1712.07499","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2017-12-20T14:43:49Z","cross_cats_sorted":[],"title_canon_sha256":"ad1b78d74db86237a6714192d9801a7304fec60adadddc1fbc0b2e7250f55743","abstract_canon_sha256":"1fb238c071f691e034ebc786ae0288eb85a83d42fe39c1cd220d19cd4455beb2"},"schema_version":"1.0"},"canonical_sha256":"2e809bd36ad401508c6703fab290bf57de90fba8810548f7f9636a647c8da37e","source":{"kind":"arxiv","id":"1712.07499","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1712.07499","created_at":"2026-05-18T00:27:24Z"},{"alias_kind":"arxiv_version","alias_value":"1712.07499v2","created_at":"2026-05-18T00:27:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1712.07499","created_at":"2026-05-18T00:27:24Z"},{"alias_kind":"pith_short_12","alias_value":"F2AJXU3K2QAV","created_at":"2026-05-18T12:31:12Z"},{"alias_kind":"pith_short_16","alias_value":"F2AJXU3K2QAVBDDH","created_at":"2026-05-18T12:31:12Z"},{"alias_kind":"pith_short_8","alias_value":"F2AJXU3K","created_at":"2026-05-18T12:31:12Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:F2AJXU3K2QAVBDDHAP5LFEF7K7","target":"record","payload":{"canonical_record":{"source":{"id":"1712.07499","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2017-12-20T14:43:49Z","cross_cats_sorted":[],"title_canon_sha256":"ad1b78d74db86237a6714192d9801a7304fec60adadddc1fbc0b2e7250f55743","abstract_canon_sha256":"1fb238c071f691e034ebc786ae0288eb85a83d42fe39c1cd220d19cd4455beb2"},"schema_version":"1.0"},"canonical_sha256":"2e809bd36ad401508c6703fab290bf57de90fba8810548f7f9636a647c8da37e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:27:24.314711Z","signature_b64":"qeZBGgs1ROr/sk2+kkP4Gs+Zh72eeRstOGNzY4rW7IVCJEMWU4bUWW76iH6dEOpIww1bCdSesxdpY747rCl6CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2e809bd36ad401508c6703fab290bf57de90fba8810548f7f9636a647c8da37e","last_reissued_at":"2026-05-18T00:27:24.314140Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:27:24.314140Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1712.07499","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":"2026-05-18T00:27:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Larr16v+Oze5C5T3qFK1P5QAKo5LSlVh06XK7vi7dR9p7N5XIUhRZ4XumiO8A9NlQ3c6HvXjtO0yzmfrBgDvBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T09:19:21.715893Z"},"content_sha256":"e6a36e355a21c07d0b6f3a75cf9b8d70c4e9ab25215638e9f9a0b8337c839b00","schema_version":"1.0","event_id":"sha256:e6a36e355a21c07d0b6f3a75cf9b8d70c4e9ab25215638e9f9a0b8337c839b00"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:F2AJXU3K2QAVBDDHAP5LFEF7K7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Preservers of $\\lambda$-Aluthge transforms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"Ahlem Ben Ali Essaleh, Antonio M. Peralta","submitted_at":"2017-12-20T14:43:49Z","abstract_excerpt":"Let $M$ and $N$ be arbitrary von Neumann algebras. For any $a$ in $M$ or in $N$, let $\\Delta_{\\lambda}(a)$ denote the $\\lambda$-Aluthge transform of $a$. Suppose that $M$ has no abelian direct summand. We prove that every bijective map $\\Phi:M\\to N$ satisfying $$\\Phi(\\Delta_{\\lambda}(a\\circ b^*))=\\Delta_{\\lambda}(\\Phi(a) \\circ \\Phi(b)^*), \\hbox{ for all } a,\\;b\\in M,$$ (for a fixed $\\lambda\\in [0,1]$), maps the hermitian part of $M$ onto the hermitian part of $N$ (i.e. $\\Phi (M_{sa}) = N_{sa}$) and its restriction $\\Phi|_{M_{sa}} : M_{sa}\\to N_{sa}$ is a Jordan isomorphism. If we also assume t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.07499","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":"2026-05-18T00:27:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xc+Om0Uwhmp8DpRAvHTZVY8f27K8hR16GdUz4J4zK9v8ML5i1poVlfWUyHmQI9c7pAVD/i90s9TMVF2QiSetCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T09:19:21.716232Z"},"content_sha256":"e8a724853228ddf4b96bc03c9b507d6e6c101ddb1bf0a52f9c7354d204a279e2","schema_version":"1.0","event_id":"sha256:e8a724853228ddf4b96bc03c9b507d6e6c101ddb1bf0a52f9c7354d204a279e2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/F2AJXU3K2QAVBDDHAP5LFEF7K7/bundle.json","state_url":"https://pith.science/pith/F2AJXU3K2QAVBDDHAP5LFEF7K7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/F2AJXU3K2QAVBDDHAP5LFEF7K7/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":"2026-06-27T09:19:21Z","links":{"resolver":"https://pith.science/pith/F2AJXU3K2QAVBDDHAP5LFEF7K7","bundle":"https://pith.science/pith/F2AJXU3K2QAVBDDHAP5LFEF7K7/bundle.json","state":"https://pith.science/pith/F2AJXU3K2QAVBDDHAP5LFEF7K7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/F2AJXU3K2QAVBDDHAP5LFEF7K7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:F2AJXU3K2QAVBDDHAP5LFEF7K7","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":"1fb238c071f691e034ebc786ae0288eb85a83d42fe39c1cd220d19cd4455beb2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2017-12-20T14:43:49Z","title_canon_sha256":"ad1b78d74db86237a6714192d9801a7304fec60adadddc1fbc0b2e7250f55743"},"schema_version":"1.0","source":{"id":"1712.07499","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1712.07499","created_at":"2026-05-18T00:27:24Z"},{"alias_kind":"arxiv_version","alias_value":"1712.07499v2","created_at":"2026-05-18T00:27:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1712.07499","created_at":"2026-05-18T00:27:24Z"},{"alias_kind":"pith_short_12","alias_value":"F2AJXU3K2QAV","created_at":"2026-05-18T12:31:12Z"},{"alias_kind":"pith_short_16","alias_value":"F2AJXU3K2QAVBDDH","created_at":"2026-05-18T12:31:12Z"},{"alias_kind":"pith_short_8","alias_value":"F2AJXU3K","created_at":"2026-05-18T12:31:12Z"}],"graph_snapshots":[{"event_id":"sha256:e8a724853228ddf4b96bc03c9b507d6e6c101ddb1bf0a52f9c7354d204a279e2","target":"graph","created_at":"2026-05-18T00:27:24Z","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 $M$ and $N$ be arbitrary von Neumann algebras. For any $a$ in $M$ or in $N$, let $\\Delta_{\\lambda}(a)$ denote the $\\lambda$-Aluthge transform of $a$. Suppose that $M$ has no abelian direct summand. We prove that every bijective map $\\Phi:M\\to N$ satisfying $$\\Phi(\\Delta_{\\lambda}(a\\circ b^*))=\\Delta_{\\lambda}(\\Phi(a) \\circ \\Phi(b)^*), \\hbox{ for all } a,\\;b\\in M,$$ (for a fixed $\\lambda\\in [0,1]$), maps the hermitian part of $M$ onto the hermitian part of $N$ (i.e. $\\Phi (M_{sa}) = N_{sa}$) and its restriction $\\Phi|_{M_{sa}} : M_{sa}\\to N_{sa}$ is a Jordan isomorphism. If we also assume t","authors_text":"Ahlem Ben Ali Essaleh, Antonio M. Peralta","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2017-12-20T14:43:49Z","title":"Preservers of $\\lambda$-Aluthge transforms"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.07499","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:e6a36e355a21c07d0b6f3a75cf9b8d70c4e9ab25215638e9f9a0b8337c839b00","target":"record","created_at":"2026-05-18T00:27:24Z","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":"1fb238c071f691e034ebc786ae0288eb85a83d42fe39c1cd220d19cd4455beb2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2017-12-20T14:43:49Z","title_canon_sha256":"ad1b78d74db86237a6714192d9801a7304fec60adadddc1fbc0b2e7250f55743"},"schema_version":"1.0","source":{"id":"1712.07499","kind":"arxiv","version":2}},"canonical_sha256":"2e809bd36ad401508c6703fab290bf57de90fba8810548f7f9636a647c8da37e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2e809bd36ad401508c6703fab290bf57de90fba8810548f7f9636a647c8da37e","first_computed_at":"2026-05-18T00:27:24.314140Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:27:24.314140Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"qeZBGgs1ROr/sk2+kkP4Gs+Zh72eeRstOGNzY4rW7IVCJEMWU4bUWW76iH6dEOpIww1bCdSesxdpY747rCl6CA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:27:24.314711Z","signed_message":"canonical_sha256_bytes"},"source_id":"1712.07499","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e6a36e355a21c07d0b6f3a75cf9b8d70c4e9ab25215638e9f9a0b8337c839b00","sha256:e8a724853228ddf4b96bc03c9b507d6e6c101ddb1bf0a52f9c7354d204a279e2"],"state_sha256":"7365ab11594d52ac8ffd0dd69ed00dc3d6b6534804a77af7aaace9d8c93f275d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8v268fBfHVVAihl/imhrBjh/AJv/ViKimCSExq5YfmNpkw6mAppEQB703+jxdnuXZzWEbjpYTy1FwQdhfNIMBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-27T09:19:21.718097Z","bundle_sha256":"540683b04a2910fe1fd8af9fd70e33b9066f68201cec9fd20b4d2cba55a54f03"}}