{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:Z2RJGEI5PNCEU3A6WOHVVQFQOC","short_pith_number":"pith:Z2RJGEI5","canonical_record":{"source":{"id":"1301.2043","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2013-01-10T07:57:00Z","cross_cats_sorted":["math.OA","math.RT"],"title_canon_sha256":"5038984d8ead124ca556dd08e4f4ed904920c79f04fe6368184d57dd53194c95","abstract_canon_sha256":"c7f3f610b23d9a402fe7eb49653638a9bf8c671fa51dc0af63bf170a28d5176b"},"schema_version":"1.0"},"canonical_sha256":"cea293111d7b444a6c1eb38f5ac0b0709b334e1f0d6278de421b8a1dfafa670e","source":{"kind":"arxiv","id":"1301.2043","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1301.2043","created_at":"2026-05-18T03:36:47Z"},{"alias_kind":"arxiv_version","alias_value":"1301.2043v1","created_at":"2026-05-18T03:36:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.2043","created_at":"2026-05-18T03:36:47Z"},{"alias_kind":"pith_short_12","alias_value":"Z2RJGEI5PNCE","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_16","alias_value":"Z2RJGEI5PNCEU3A6","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_8","alias_value":"Z2RJGEI5","created_at":"2026-05-18T12:28:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:Z2RJGEI5PNCEU3A6WOHVVQFQOC","target":"record","payload":{"canonical_record":{"source":{"id":"1301.2043","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2013-01-10T07:57:00Z","cross_cats_sorted":["math.OA","math.RT"],"title_canon_sha256":"5038984d8ead124ca556dd08e4f4ed904920c79f04fe6368184d57dd53194c95","abstract_canon_sha256":"c7f3f610b23d9a402fe7eb49653638a9bf8c671fa51dc0af63bf170a28d5176b"},"schema_version":"1.0"},"canonical_sha256":"cea293111d7b444a6c1eb38f5ac0b0709b334e1f0d6278de421b8a1dfafa670e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:36:47.580606Z","signature_b64":"H0e3bTAmdFBeK6wT+0EVf1py4soVUIBFVsNuRDd7/m0hoIwcHJ9O/EKzzvT//LLD8Mj6tu1pivOQyxQHtO4aBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cea293111d7b444a6c1eb38f5ac0b0709b334e1f0d6278de421b8a1dfafa670e","last_reissued_at":"2026-05-18T03:36:47.580166Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:36:47.580166Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1301.2043","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":"2026-05-18T03:36:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WLUYkWZv9jnfRxloy89O3joGq8m4asXxMCW0p/AvKFg1aKB/A2/EzZA1Nve2lwgdYsX3lZM3iXowkFa5kCvMDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T05:11:37.027860Z"},"content_sha256":"c1826d56612c434ef0d197e515f77e0cdfec1fbaea5a4e50ed17003f2985cc2e","schema_version":"1.0","event_id":"sha256:c1826d56612c434ef0d197e515f77e0cdfec1fbaea5a4e50ed17003f2985cc2e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:Z2RJGEI5PNCEU3A6WOHVVQFQOC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Centralizing Traces and Lie Triple Isomorphisms on Triangular Algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OA","math.RT"],"primary_cat":"math.RA","authors_text":"Feng Wei, Xinfeng Liang, Zhankui Xiao","submitted_at":"2013-01-10T07:57:00Z","abstract_excerpt":"Let $\\mathcal{T}$ be a triangular algebra over a commutative ring $\\mathcal{R}$ and $\\mathcal{Z(T)}$ be the center of $\\mathcal{T}$. Suppose that ${\\mathfrak q}\\colon \\mathcal{T}\\times \\mathcal{T}\\longrightarrow \\mathcal{T}$ is an $\\mathcal{R}$-bilinear mapping and that ${\\mathfrak T}_{\\mathfrak q}\\colon: \\mathcal{T}\\longrightarrow \\mathcal{T}$ is a trace of $\\mathfrak{q}$. We describe the form of ${\\mathfrak T}_{\\mathfrak q}$ satisfying the condition $[{\\mathfrak T}_{\\mathfrak q}(T), T]\\in \\mathcal{Z(T)}$ for all $T\\in \\mathcal{T}$. The question of when ${\\mathfrak T}_{\\mathfrak q}$ has the p"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.2043","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":"2026-05-18T03:36:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XIJojQK2aISYrp9Fon8vO5m+3EHkGfBrqg6w0vJbr2BBobIv5LkcnQYVU1SHjFMMzHM7rMZ3Ew/IMwaRqs6nBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T05:11:37.028548Z"},"content_sha256":"be858d3048c16d4df19901d5e11beb1282a4572ab0336c12002221e8e040040c","schema_version":"1.0","event_id":"sha256:be858d3048c16d4df19901d5e11beb1282a4572ab0336c12002221e8e040040c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/Z2RJGEI5PNCEU3A6WOHVVQFQOC/bundle.json","state_url":"https://pith.science/pith/Z2RJGEI5PNCEU3A6WOHVVQFQOC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/Z2RJGEI5PNCEU3A6WOHVVQFQOC/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":"2026-05-31T05:11:37Z","links":{"resolver":"https://pith.science/pith/Z2RJGEI5PNCEU3A6WOHVVQFQOC","bundle":"https://pith.science/pith/Z2RJGEI5PNCEU3A6WOHVVQFQOC/bundle.json","state":"https://pith.science/pith/Z2RJGEI5PNCEU3A6WOHVVQFQOC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/Z2RJGEI5PNCEU3A6WOHVVQFQOC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:Z2RJGEI5PNCEU3A6WOHVVQFQOC","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":"c7f3f610b23d9a402fe7eb49653638a9bf8c671fa51dc0af63bf170a28d5176b","cross_cats_sorted":["math.OA","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2013-01-10T07:57:00Z","title_canon_sha256":"5038984d8ead124ca556dd08e4f4ed904920c79f04fe6368184d57dd53194c95"},"schema_version":"1.0","source":{"id":"1301.2043","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1301.2043","created_at":"2026-05-18T03:36:47Z"},{"alias_kind":"arxiv_version","alias_value":"1301.2043v1","created_at":"2026-05-18T03:36:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.2043","created_at":"2026-05-18T03:36:47Z"},{"alias_kind":"pith_short_12","alias_value":"Z2RJGEI5PNCE","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_16","alias_value":"Z2RJGEI5PNCEU3A6","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_8","alias_value":"Z2RJGEI5","created_at":"2026-05-18T12:28:09Z"}],"graph_snapshots":[{"event_id":"sha256:be858d3048c16d4df19901d5e11beb1282a4572ab0336c12002221e8e040040c","target":"graph","created_at":"2026-05-18T03:36:47Z","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 $\\mathcal{T}$ be a triangular algebra over a commutative ring $\\mathcal{R}$ and $\\mathcal{Z(T)}$ be the center of $\\mathcal{T}$. Suppose that ${\\mathfrak q}\\colon \\mathcal{T}\\times \\mathcal{T}\\longrightarrow \\mathcal{T}$ is an $\\mathcal{R}$-bilinear mapping and that ${\\mathfrak T}_{\\mathfrak q}\\colon: \\mathcal{T}\\longrightarrow \\mathcal{T}$ is a trace of $\\mathfrak{q}$. We describe the form of ${\\mathfrak T}_{\\mathfrak q}$ satisfying the condition $[{\\mathfrak T}_{\\mathfrak q}(T), T]\\in \\mathcal{Z(T)}$ for all $T\\in \\mathcal{T}$. The question of when ${\\mathfrak T}_{\\mathfrak q}$ has the p","authors_text":"Feng Wei, Xinfeng Liang, Zhankui Xiao","cross_cats":["math.OA","math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2013-01-10T07:57:00Z","title":"Centralizing Traces and Lie Triple Isomorphisms on Triangular Algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.2043","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:c1826d56612c434ef0d197e515f77e0cdfec1fbaea5a4e50ed17003f2985cc2e","target":"record","created_at":"2026-05-18T03:36:47Z","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":"c7f3f610b23d9a402fe7eb49653638a9bf8c671fa51dc0af63bf170a28d5176b","cross_cats_sorted":["math.OA","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2013-01-10T07:57:00Z","title_canon_sha256":"5038984d8ead124ca556dd08e4f4ed904920c79f04fe6368184d57dd53194c95"},"schema_version":"1.0","source":{"id":"1301.2043","kind":"arxiv","version":1}},"canonical_sha256":"cea293111d7b444a6c1eb38f5ac0b0709b334e1f0d6278de421b8a1dfafa670e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cea293111d7b444a6c1eb38f5ac0b0709b334e1f0d6278de421b8a1dfafa670e","first_computed_at":"2026-05-18T03:36:47.580166Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:36:47.580166Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"H0e3bTAmdFBeK6wT+0EVf1py4soVUIBFVsNuRDd7/m0hoIwcHJ9O/EKzzvT//LLD8Mj6tu1pivOQyxQHtO4aBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:36:47.580606Z","signed_message":"canonical_sha256_bytes"},"source_id":"1301.2043","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c1826d56612c434ef0d197e515f77e0cdfec1fbaea5a4e50ed17003f2985cc2e","sha256:be858d3048c16d4df19901d5e11beb1282a4572ab0336c12002221e8e040040c"],"state_sha256":"c0477f9508794c097b83f77250c2bcf34004ecf00b689a28b7c6d1a2f15a53db"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"r4qTETukMTITf6aI/N5djzDLtr+U2FcaAyVTRBqpOssm6pqx7lRnJvZ+tZJwDscFOcrqPCbLCuvrfMvy7R9jBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T05:11:37.032030Z","bundle_sha256":"aa50b5eec4412d23c1b7d0dc0035dfe7190c0e63b786fb21ff3673f3f98a8ad9"}}