{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:TMIMDWUETRWH6MMS62UKF35S4L","short_pith_number":"pith:TMIMDWUE","canonical_record":{"source":{"id":"1209.4575","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2012-09-20T16:10:55Z","cross_cats_sorted":[],"title_canon_sha256":"d69ddf18121af43a10e14060de47b6db2dcc7fb4630968f9809557bd55496a4c","abstract_canon_sha256":"9d49c3bd5389d5ea8d61273afb110e69038694c41126672b176ff307f415037a"},"schema_version":"1.0"},"canonical_sha256":"9b10c1da849c6c7f3192f6a8a2efb2e2cc8b2081a0cf11cefd3a85ccf345a953","source":{"kind":"arxiv","id":"1209.4575","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1209.4575","created_at":"2026-05-18T01:54:20Z"},{"alias_kind":"arxiv_version","alias_value":"1209.4575v3","created_at":"2026-05-18T01:54:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1209.4575","created_at":"2026-05-18T01:54:20Z"},{"alias_kind":"pith_short_12","alias_value":"TMIMDWUETRWH","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_16","alias_value":"TMIMDWUETRWH6MMS","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_8","alias_value":"TMIMDWUE","created_at":"2026-05-18T12:27:23Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:TMIMDWUETRWH6MMS62UKF35S4L","target":"record","payload":{"canonical_record":{"source":{"id":"1209.4575","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2012-09-20T16:10:55Z","cross_cats_sorted":[],"title_canon_sha256":"d69ddf18121af43a10e14060de47b6db2dcc7fb4630968f9809557bd55496a4c","abstract_canon_sha256":"9d49c3bd5389d5ea8d61273afb110e69038694c41126672b176ff307f415037a"},"schema_version":"1.0"},"canonical_sha256":"9b10c1da849c6c7f3192f6a8a2efb2e2cc8b2081a0cf11cefd3a85ccf345a953","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:54:20.595444Z","signature_b64":"cZBotuNma+MWlNGNQr/mCGe2gYiiafnscqmLYvdJx6IrCRizPNH0GoQolzHuZ5wzlk3VXRiP+Z4lnytnYu7gBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9b10c1da849c6c7f3192f6a8a2efb2e2cc8b2081a0cf11cefd3a85ccf345a953","last_reissued_at":"2026-05-18T01:54:20.595006Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:54:20.595006Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1209.4575","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:54:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IjtY4heFo9RY63xeg5vOOEChOAOEu+YY5UlWtwrrfTE0F/BVi4a5l4ir8TDSbZWMHp6FL7DbNaWzNPinJ0opDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T19:16:11.810797Z"},"content_sha256":"5204f0f5beeb5c0bbeb1d5c759ae63bf5669abd6ab94414fe0a1bee5076f9d97","schema_version":"1.0","event_id":"sha256:5204f0f5beeb5c0bbeb1d5c759ae63bf5669abd6ab94414fe0a1bee5076f9d97"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:TMIMDWUETRWH6MMS62UKF35S4L","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Inclusions of ternary rings of operators and conditional expectations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"Adam Skalski, Pekka Salmi","submitted_at":"2012-09-20T16:10:55Z","abstract_excerpt":"It is shown that if T is a ternary ring of operators (TRO), X is a nondegenerate sub-TRO of T and there exists a contractive idempotent surjective map P:T-->X, then P has a unique, explicitly described extension to a conditional expectation between the associated linking algebras. A version of the result for W*-TROs is also presented and some applications mentioned."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.4575","kind":"arxiv","version":3},"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":"2026-05-18T01:54:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ecbPw0P4EnpX50gFcj1py3iWzHC7DTV9wB1k8q1Z5qjPlEo/6f5RzHFnGeZYY9x7M7pdu+bTwg9mqGXqE4bMCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T19:16:11.811146Z"},"content_sha256":"12e8135a85a96db9372c2f5f07e75faaf40b4e766005157d56c51cab115ad1db","schema_version":"1.0","event_id":"sha256:12e8135a85a96db9372c2f5f07e75faaf40b4e766005157d56c51cab115ad1db"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TMIMDWUETRWH6MMS62UKF35S4L/bundle.json","state_url":"https://pith.science/pith/TMIMDWUETRWH6MMS62UKF35S4L/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TMIMDWUETRWH6MMS62UKF35S4L/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":"2026-06-21T19:16:11Z","links":{"resolver":"https://pith.science/pith/TMIMDWUETRWH6MMS62UKF35S4L","bundle":"https://pith.science/pith/TMIMDWUETRWH6MMS62UKF35S4L/bundle.json","state":"https://pith.science/pith/TMIMDWUETRWH6MMS62UKF35S4L/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TMIMDWUETRWH6MMS62UKF35S4L/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:TMIMDWUETRWH6MMS62UKF35S4L","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":"9d49c3bd5389d5ea8d61273afb110e69038694c41126672b176ff307f415037a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2012-09-20T16:10:55Z","title_canon_sha256":"d69ddf18121af43a10e14060de47b6db2dcc7fb4630968f9809557bd55496a4c"},"schema_version":"1.0","source":{"id":"1209.4575","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1209.4575","created_at":"2026-05-18T01:54:20Z"},{"alias_kind":"arxiv_version","alias_value":"1209.4575v3","created_at":"2026-05-18T01:54:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1209.4575","created_at":"2026-05-18T01:54:20Z"},{"alias_kind":"pith_short_12","alias_value":"TMIMDWUETRWH","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_16","alias_value":"TMIMDWUETRWH6MMS","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_8","alias_value":"TMIMDWUE","created_at":"2026-05-18T12:27:23Z"}],"graph_snapshots":[{"event_id":"sha256:12e8135a85a96db9372c2f5f07e75faaf40b4e766005157d56c51cab115ad1db","target":"graph","created_at":"2026-05-18T01:54:20Z","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":"It is shown that if T is a ternary ring of operators (TRO), X is a nondegenerate sub-TRO of T and there exists a contractive idempotent surjective map P:T-->X, then P has a unique, explicitly described extension to a conditional expectation between the associated linking algebras. A version of the result for W*-TROs is also presented and some applications mentioned.","authors_text":"Adam Skalski, Pekka Salmi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2012-09-20T16:10:55Z","title":"Inclusions of ternary rings of operators and conditional expectations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.4575","kind":"arxiv","version":3},"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":"sha256:5204f0f5beeb5c0bbeb1d5c759ae63bf5669abd6ab94414fe0a1bee5076f9d97","target":"record","created_at":"2026-05-18T01:54:20Z","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":"9d49c3bd5389d5ea8d61273afb110e69038694c41126672b176ff307f415037a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2012-09-20T16:10:55Z","title_canon_sha256":"d69ddf18121af43a10e14060de47b6db2dcc7fb4630968f9809557bd55496a4c"},"schema_version":"1.0","source":{"id":"1209.4575","kind":"arxiv","version":3}},"canonical_sha256":"9b10c1da849c6c7f3192f6a8a2efb2e2cc8b2081a0cf11cefd3a85ccf345a953","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9b10c1da849c6c7f3192f6a8a2efb2e2cc8b2081a0cf11cefd3a85ccf345a953","first_computed_at":"2026-05-18T01:54:20.595006Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:54:20.595006Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"cZBotuNma+MWlNGNQr/mCGe2gYiiafnscqmLYvdJx6IrCRizPNH0GoQolzHuZ5wzlk3VXRiP+Z4lnytnYu7gBw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:54:20.595444Z","signed_message":"canonical_sha256_bytes"},"source_id":"1209.4575","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5204f0f5beeb5c0bbeb1d5c759ae63bf5669abd6ab94414fe0a1bee5076f9d97","sha256:12e8135a85a96db9372c2f5f07e75faaf40b4e766005157d56c51cab115ad1db"],"state_sha256":"c287c3e154e4c6cbab7f8803d9c93e6e22230d555ba88389422f2d7232da4f06"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kIAxeYHjU7HVKBZuC963eDV4ASDfhToN8EaNvK0KLLDnCNSqzEYs1IdR4LBu8lOSFdpndD+Jv8/tOU5S7q72Ag==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-21T19:16:11.813171Z","bundle_sha256":"d3477fa5fb059029ee2a867d2dfc39639d4fea5697045dadc892a3d99dc1b371"}}