{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:A6KSLOAMRLL7WGZQQJF6EQAGYY","short_pith_number":"pith:A6KSLOAM","canonical_record":{"source":{"id":"1309.2748","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2013-09-11T07:32:27Z","cross_cats_sorted":[],"title_canon_sha256":"dddcde0ede8a5a9a42c7b80b168a77afd8a2988db28b0020530b6dbe8e33ffce","abstract_canon_sha256":"fa50aa4898fe2b482681a139dbc2c0b265aa73cede5386daccc3671ad734cd6b"},"schema_version":"1.0"},"canonical_sha256":"079525b80c8ad7fb1b30824be24006c625789702e33e22703c20ca5c10fe182d","source":{"kind":"arxiv","id":"1309.2748","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1309.2748","created_at":"2026-05-18T01:27:24Z"},{"alias_kind":"arxiv_version","alias_value":"1309.2748v4","created_at":"2026-05-18T01:27:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.2748","created_at":"2026-05-18T01:27:24Z"},{"alias_kind":"pith_short_12","alias_value":"A6KSLOAMRLL7","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_16","alias_value":"A6KSLOAMRLL7WGZQ","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_8","alias_value":"A6KSLOAM","created_at":"2026-05-18T12:27:38Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:A6KSLOAMRLL7WGZQQJF6EQAGYY","target":"record","payload":{"canonical_record":{"source":{"id":"1309.2748","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2013-09-11T07:32:27Z","cross_cats_sorted":[],"title_canon_sha256":"dddcde0ede8a5a9a42c7b80b168a77afd8a2988db28b0020530b6dbe8e33ffce","abstract_canon_sha256":"fa50aa4898fe2b482681a139dbc2c0b265aa73cede5386daccc3671ad734cd6b"},"schema_version":"1.0"},"canonical_sha256":"079525b80c8ad7fb1b30824be24006c625789702e33e22703c20ca5c10fe182d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:27:24.564967Z","signature_b64":"ysAaeGafoFVld4m5j31XblPqpRioOAw+mlpUOfG6OFYM+M5ko49Bg3EKy6N6Qf1VP6VvJsHXoJAeG1TrwxMiCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"079525b80c8ad7fb1b30824be24006c625789702e33e22703c20ca5c10fe182d","last_reissued_at":"2026-05-18T01:27:24.564446Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:27:24.564446Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1309.2748","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:27:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KcI4VGU2y+pIlUWZoRs7mFVPk88MgliIxEiZBfC2QZJEGha4gVXPeY4RuSmBzTH+NaTqVsA3Qkd5YbhYSatmBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T16:35:01.476800Z"},"content_sha256":"24813a623d5104261b2fba158029c70a3a6364024de32454517c79595ed853bf","schema_version":"1.0","event_id":"sha256:24813a623d5104261b2fba158029c70a3a6364024de32454517c79595ed853bf"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:A6KSLOAMRLL7WGZQQJF6EQAGYY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On a functional equation for symmetric linear operators on $C^{*}$ algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"Ali Taghavi","submitted_at":"2013-09-11T07:32:27Z","abstract_excerpt":"Let $A$ be a $C^{*}$ algebra and $T: A\\rightarrow A$ be a linear map which satisfies the functional equation $\\begin{cases}T(x)T(y)=T^{2}(xy)\\\\T(x^{*})=T(x)^{*} \\end{cases}$ We prove that under each of the following conditions, $T$ must be the trivial map $T(x)=\\lambda x$ for some $\\lambda \\in \\mathbb{R}:$\\\\ \\begin{enumerate} \\item $A$ is a simple $C^{*}$-algebra.\n  \\item $A$ is unital with trivial center and has a faithful trace such that each zero-trace element lies in the closure of the span of commutator elements.\n  \\item $A=B(H)$ where H is a separable Hilbert space. \\end{enumerate}\n  For"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.2748","kind":"arxiv","version":4},"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":"2026-05-18T01:27:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+pCxaK68Ky0/0dRDInwGBXX1YRLzGhnb+kJlgMddNZsQ84cT/WTCJTotDORx8gxcaUTvSJ2i5qsnixxZnwUYBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T16:35:01.477270Z"},"content_sha256":"80cba6bde7d806b57e67105fb525fedf8526b52ac0c868d22145ea9adfedf3cc","schema_version":"1.0","event_id":"sha256:80cba6bde7d806b57e67105fb525fedf8526b52ac0c868d22145ea9adfedf3cc"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/A6KSLOAMRLL7WGZQQJF6EQAGYY/bundle.json","state_url":"https://pith.science/pith/A6KSLOAMRLL7WGZQQJF6EQAGYY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/A6KSLOAMRLL7WGZQQJF6EQAGYY/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":"2026-06-23T16:35:01Z","links":{"resolver":"https://pith.science/pith/A6KSLOAMRLL7WGZQQJF6EQAGYY","bundle":"https://pith.science/pith/A6KSLOAMRLL7WGZQQJF6EQAGYY/bundle.json","state":"https://pith.science/pith/A6KSLOAMRLL7WGZQQJF6EQAGYY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/A6KSLOAMRLL7WGZQQJF6EQAGYY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:A6KSLOAMRLL7WGZQQJF6EQAGYY","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":"fa50aa4898fe2b482681a139dbc2c0b265aa73cede5386daccc3671ad734cd6b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2013-09-11T07:32:27Z","title_canon_sha256":"dddcde0ede8a5a9a42c7b80b168a77afd8a2988db28b0020530b6dbe8e33ffce"},"schema_version":"1.0","source":{"id":"1309.2748","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1309.2748","created_at":"2026-05-18T01:27:24Z"},{"alias_kind":"arxiv_version","alias_value":"1309.2748v4","created_at":"2026-05-18T01:27:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.2748","created_at":"2026-05-18T01:27:24Z"},{"alias_kind":"pith_short_12","alias_value":"A6KSLOAMRLL7","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_16","alias_value":"A6KSLOAMRLL7WGZQ","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_8","alias_value":"A6KSLOAM","created_at":"2026-05-18T12:27:38Z"}],"graph_snapshots":[{"event_id":"sha256:80cba6bde7d806b57e67105fb525fedf8526b52ac0c868d22145ea9adfedf3cc","target":"graph","created_at":"2026-05-18T01:27:24Z","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 $A$ be a $C^{*}$ algebra and $T: A\\rightarrow A$ be a linear map which satisfies the functional equation $\\begin{cases}T(x)T(y)=T^{2}(xy)\\\\T(x^{*})=T(x)^{*} \\end{cases}$ We prove that under each of the following conditions, $T$ must be the trivial map $T(x)=\\lambda x$ for some $\\lambda \\in \\mathbb{R}:$\\\\ \\begin{enumerate} \\item $A$ is a simple $C^{*}$-algebra.\n  \\item $A$ is unital with trivial center and has a faithful trace such that each zero-trace element lies in the closure of the span of commutator elements.\n  \\item $A=B(H)$ where H is a separable Hilbert space. \\end{enumerate}\n  For","authors_text":"Ali Taghavi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2013-09-11T07:32:27Z","title":"On a functional equation for symmetric linear operators on $C^{*}$ algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.2748","kind":"arxiv","version":4},"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":"sha256:24813a623d5104261b2fba158029c70a3a6364024de32454517c79595ed853bf","target":"record","created_at":"2026-05-18T01:27:24Z","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":"fa50aa4898fe2b482681a139dbc2c0b265aa73cede5386daccc3671ad734cd6b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2013-09-11T07:32:27Z","title_canon_sha256":"dddcde0ede8a5a9a42c7b80b168a77afd8a2988db28b0020530b6dbe8e33ffce"},"schema_version":"1.0","source":{"id":"1309.2748","kind":"arxiv","version":4}},"canonical_sha256":"079525b80c8ad7fb1b30824be24006c625789702e33e22703c20ca5c10fe182d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"079525b80c8ad7fb1b30824be24006c625789702e33e22703c20ca5c10fe182d","first_computed_at":"2026-05-18T01:27:24.564446Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:27:24.564446Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ysAaeGafoFVld4m5j31XblPqpRioOAw+mlpUOfG6OFYM+M5ko49Bg3EKy6N6Qf1VP6VvJsHXoJAeG1TrwxMiCA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:27:24.564967Z","signed_message":"canonical_sha256_bytes"},"source_id":"1309.2748","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:24813a623d5104261b2fba158029c70a3a6364024de32454517c79595ed853bf","sha256:80cba6bde7d806b57e67105fb525fedf8526b52ac0c868d22145ea9adfedf3cc"],"state_sha256":"610f3258d846ea12e23dd7a9c46418d3e06b5754e6cec2b67a1c20f504f2a6a0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tDTWc+/oBnMCT03b0DTZ1rt1inHkkbT8rwOb/DYuIkfwAm4ReQNGmlsJsULUB20SLH4NFzD7EpcnFZ3WdGVMAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T16:35:01.479956Z","bundle_sha256":"5d566e25d619db74e043f22adf6c68467f4fd4a7b8f13fdc53cb39734e49b84b"}}