{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:JPXWZFBE2OLJ3B6YSLW4GPUSMC","short_pith_number":"pith:JPXWZFBE","canonical_record":{"source":{"id":"1506.06523","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2015-06-22T09:39:39Z","cross_cats_sorted":[],"title_canon_sha256":"b8077e6f1c38f47a4afe5ba8d8434c578134df17c7e951cd71115ab895afce9d","abstract_canon_sha256":"494e624ef2ea2f56619eb68d0fac4bc26639983e8fa9343535f2d00c5e99bf17"},"schema_version":"1.0"},"canonical_sha256":"4bef6c9424d3969d87d892edc33e9260924d7c566c7096d9bd70b498ba78f095","source":{"kind":"arxiv","id":"1506.06523","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1506.06523","created_at":"2026-05-18T01:41:44Z"},{"alias_kind":"arxiv_version","alias_value":"1506.06523v1","created_at":"2026-05-18T01:41:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.06523","created_at":"2026-05-18T01:41:44Z"},{"alias_kind":"pith_short_12","alias_value":"JPXWZFBE2OLJ","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_16","alias_value":"JPXWZFBE2OLJ3B6Y","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_8","alias_value":"JPXWZFBE","created_at":"2026-05-18T12:29:27Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:JPXWZFBE2OLJ3B6YSLW4GPUSMC","target":"record","payload":{"canonical_record":{"source":{"id":"1506.06523","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2015-06-22T09:39:39Z","cross_cats_sorted":[],"title_canon_sha256":"b8077e6f1c38f47a4afe5ba8d8434c578134df17c7e951cd71115ab895afce9d","abstract_canon_sha256":"494e624ef2ea2f56619eb68d0fac4bc26639983e8fa9343535f2d00c5e99bf17"},"schema_version":"1.0"},"canonical_sha256":"4bef6c9424d3969d87d892edc33e9260924d7c566c7096d9bd70b498ba78f095","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:41:44.962861Z","signature_b64":"1n4ztuuITpmqDtJZticsFYNobtGPX73GsWIRRYFfh3GN81SxcI8XHOJOD2Fl6Uino1Rxrfpwqy95P4gWl4H5Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4bef6c9424d3969d87d892edc33e9260924d7c566c7096d9bd70b498ba78f095","last_reissued_at":"2026-05-18T01:41:44.962294Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:41:44.962294Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1506.06523","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":"2026-05-18T01:41:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DBb0wBVAnUhfbCsDSLhXygZvA/gxrDV/szUUEdx+YpnS9wv4T7SZIb8CKuVJAWI9sJMyE6CKRsGdZF15K0ujBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T05:19:25.864008Z"},"content_sha256":"cf38cf1602912d45251d60995f7767b9fd651cf4e34db5af5ee7a82cbb928dd0","schema_version":"1.0","event_id":"sha256:cf38cf1602912d45251d60995f7767b9fd651cf4e34db5af5ee7a82cbb928dd0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:JPXWZFBE2OLJ3B6YSLW4GPUSMC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Geometric aspects of similarity problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Martin Miglioli, Peter Schlicht","submitted_at":"2015-06-22T09:39:39Z","abstract_excerpt":"This article presents a geometric approach to some similarity problems involving metric arguments in the non-positively curved space of positive invertible operators of an operator algebra and the canonical isometric action by invertible elements on the cone given by $g\\cdot a=gag^*$. Through this approach, we extend and put into a geometric framework results by G. Pisier and partially answer a question by Andruchow, Corach and Stojanoff about minimality properties of canonical unitarizers."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.06523","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":"2026-05-18T01:41:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"g1oQ/Ssb/77xpP5qb9fZpaOLW+6CJI3yx4Mt6E4RjJC8LNYiu8DNMn6Z9awUtGYmvUaz8Ej/gB3wy97NTzihDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T05:19:25.864733Z"},"content_sha256":"7d0d7934b15e068dcd38008d19213422f90abc8f01b8596ea5244cf9cbf270b3","schema_version":"1.0","event_id":"sha256:7d0d7934b15e068dcd38008d19213422f90abc8f01b8596ea5244cf9cbf270b3"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JPXWZFBE2OLJ3B6YSLW4GPUSMC/bundle.json","state_url":"https://pith.science/pith/JPXWZFBE2OLJ3B6YSLW4GPUSMC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JPXWZFBE2OLJ3B6YSLW4GPUSMC/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":"2026-06-12T05:19:25Z","links":{"resolver":"https://pith.science/pith/JPXWZFBE2OLJ3B6YSLW4GPUSMC","bundle":"https://pith.science/pith/JPXWZFBE2OLJ3B6YSLW4GPUSMC/bundle.json","state":"https://pith.science/pith/JPXWZFBE2OLJ3B6YSLW4GPUSMC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JPXWZFBE2OLJ3B6YSLW4GPUSMC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:JPXWZFBE2OLJ3B6YSLW4GPUSMC","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":"494e624ef2ea2f56619eb68d0fac4bc26639983e8fa9343535f2d00c5e99bf17","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2015-06-22T09:39:39Z","title_canon_sha256":"b8077e6f1c38f47a4afe5ba8d8434c578134df17c7e951cd71115ab895afce9d"},"schema_version":"1.0","source":{"id":"1506.06523","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1506.06523","created_at":"2026-05-18T01:41:44Z"},{"alias_kind":"arxiv_version","alias_value":"1506.06523v1","created_at":"2026-05-18T01:41:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.06523","created_at":"2026-05-18T01:41:44Z"},{"alias_kind":"pith_short_12","alias_value":"JPXWZFBE2OLJ","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_16","alias_value":"JPXWZFBE2OLJ3B6Y","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_8","alias_value":"JPXWZFBE","created_at":"2026-05-18T12:29:27Z"}],"graph_snapshots":[{"event_id":"sha256:7d0d7934b15e068dcd38008d19213422f90abc8f01b8596ea5244cf9cbf270b3","target":"graph","created_at":"2026-05-18T01:41:44Z","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":"This article presents a geometric approach to some similarity problems involving metric arguments in the non-positively curved space of positive invertible operators of an operator algebra and the canonical isometric action by invertible elements on the cone given by $g\\cdot a=gag^*$. Through this approach, we extend and put into a geometric framework results by G. Pisier and partially answer a question by Andruchow, Corach and Stojanoff about minimality properties of canonical unitarizers.","authors_text":"Martin Miglioli, Peter Schlicht","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2015-06-22T09:39:39Z","title":"Geometric aspects of similarity problems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.06523","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:cf38cf1602912d45251d60995f7767b9fd651cf4e34db5af5ee7a82cbb928dd0","target":"record","created_at":"2026-05-18T01:41:44Z","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":"494e624ef2ea2f56619eb68d0fac4bc26639983e8fa9343535f2d00c5e99bf17","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2015-06-22T09:39:39Z","title_canon_sha256":"b8077e6f1c38f47a4afe5ba8d8434c578134df17c7e951cd71115ab895afce9d"},"schema_version":"1.0","source":{"id":"1506.06523","kind":"arxiv","version":1}},"canonical_sha256":"4bef6c9424d3969d87d892edc33e9260924d7c566c7096d9bd70b498ba78f095","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4bef6c9424d3969d87d892edc33e9260924d7c566c7096d9bd70b498ba78f095","first_computed_at":"2026-05-18T01:41:44.962294Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:41:44.962294Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1n4ztuuITpmqDtJZticsFYNobtGPX73GsWIRRYFfh3GN81SxcI8XHOJOD2Fl6Uino1Rxrfpwqy95P4gWl4H5Dw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:41:44.962861Z","signed_message":"canonical_sha256_bytes"},"source_id":"1506.06523","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cf38cf1602912d45251d60995f7767b9fd651cf4e34db5af5ee7a82cbb928dd0","sha256:7d0d7934b15e068dcd38008d19213422f90abc8f01b8596ea5244cf9cbf270b3"],"state_sha256":"5dc9331937e6f50ef28c89623399145d9b2b52a7e3f3a6abffb98f9ee7875614"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wBtg7NY6MWgpGngXhwEdnHngUyrSqrPH/JhYq1b8m19Pu3u1R+It+64CWsIvl+ZE3olZ5YGKFnhZbxvs8hcKAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-12T05:19:25.867756Z","bundle_sha256":"dc593bd7e5332a4d728602f4493f537958b87f41ea1cd4f8ff0216ee6e703ee5"}}