{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:E3KNNNHI36KU4KRLGE4XNTOOZF","short_pith_number":"pith:E3KNNNHI","canonical_record":{"source":{"id":"1706.08411","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2017-06-26T14:39:08Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"b22ede262aa0eb847ccac7ffbba6dbcd645c0c03a141019a640b5d40aeb90480","abstract_canon_sha256":"9b263692b2ad885e560dacb5690daa42a58416b93f26a595d3f8099e78e1241b"},"schema_version":"1.0"},"canonical_sha256":"26d4d6b4e8df954e2a2b313976cdcec961d2393f7f4b8fa91d43a404709d5c54","source":{"kind":"arxiv","id":"1706.08411","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1706.08411","created_at":"2026-05-18T00:22:20Z"},{"alias_kind":"arxiv_version","alias_value":"1706.08411v3","created_at":"2026-05-18T00:22:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.08411","created_at":"2026-05-18T00:22:20Z"},{"alias_kind":"pith_short_12","alias_value":"E3KNNNHI36KU","created_at":"2026-05-18T12:31:12Z"},{"alias_kind":"pith_short_16","alias_value":"E3KNNNHI36KU4KRL","created_at":"2026-05-18T12:31:12Z"},{"alias_kind":"pith_short_8","alias_value":"E3KNNNHI","created_at":"2026-05-18T12:31:12Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:E3KNNNHI36KU4KRLGE4XNTOOZF","target":"record","payload":{"canonical_record":{"source":{"id":"1706.08411","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2017-06-26T14:39:08Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"b22ede262aa0eb847ccac7ffbba6dbcd645c0c03a141019a640b5d40aeb90480","abstract_canon_sha256":"9b263692b2ad885e560dacb5690daa42a58416b93f26a595d3f8099e78e1241b"},"schema_version":"1.0"},"canonical_sha256":"26d4d6b4e8df954e2a2b313976cdcec961d2393f7f4b8fa91d43a404709d5c54","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:22:20.923607Z","signature_b64":"kA813Fs3t1KT6ZMidCJySJkvuLcWn7QVAR7AKY7Aal+YTcQTmZMUF+/c7yQHQVsqeWYpiCLEpOw8aRTBqzVnBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"26d4d6b4e8df954e2a2b313976cdcec961d2393f7f4b8fa91d43a404709d5c54","last_reissued_at":"2026-05-18T00:22:20.922994Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:22:20.922994Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1706.08411","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":"2026-05-18T00:22:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"m5st83nTggpnBxgUoxOXhnVkCaauinKkGS+30QR4unpS7QhufZRz5BZUaMW81eGER6yW31xZFuYrS2cDuJ1PBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T21:37:51.889389Z"},"content_sha256":"36f0b5c904b5a36be439d4cc7b02f281dcc7eeb09003360eed2a7044e9b3ec82","schema_version":"1.0","event_id":"sha256:36f0b5c904b5a36be439d4cc7b02f281dcc7eeb09003360eed2a7044e9b3ec82"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:E3KNNNHI36KU4KRLGE4XNTOOZF","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Unperforated pairs of operator spaces and hyperrigidity of operator systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.OA","authors_text":"Rapha\\\"el Clou\\^atre","submitted_at":"2017-06-26T14:39:08Z","abstract_excerpt":"We study restriction and extension properties for states on C$^*$-algebras with an eye towards hyperrigidity of operator systems. We use these ideas to provide supporting evidence for Arveson's hyperrigidity conjecture. Prompted by various characterizations of hyperrigidity in terms of states, we examine unperforated pairs of self-adjoint subspaces in a C$^*$-algebra. The configuration of the subspaces forming an unperforated pair is in some sense compatible with the order structure of the ambient C$^*$-algebra. We prove that commuting pairs are unperforated, and obtain consequences for hyperr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.08411","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":"2026-05-18T00:22:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sBbRPrXsbthkd1GSwe7KZa2Nx2/hv6zkSNyzFHZT+aQg5YinHVsX0qS02UDt1reoo7Q1xZRk6lvmDOzobWXCAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T21:37:51.889868Z"},"content_sha256":"bb50d66ed17fcc1c0015a1884d63aeaf5fa3c3552a47869110fd8ba0569f4dac","schema_version":"1.0","event_id":"sha256:bb50d66ed17fcc1c0015a1884d63aeaf5fa3c3552a47869110fd8ba0569f4dac"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/E3KNNNHI36KU4KRLGE4XNTOOZF/bundle.json","state_url":"https://pith.science/pith/E3KNNNHI36KU4KRLGE4XNTOOZF/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/E3KNNNHI36KU4KRLGE4XNTOOZF/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":"2026-06-25T21:37:51Z","links":{"resolver":"https://pith.science/pith/E3KNNNHI36KU4KRLGE4XNTOOZF","bundle":"https://pith.science/pith/E3KNNNHI36KU4KRLGE4XNTOOZF/bundle.json","state":"https://pith.science/pith/E3KNNNHI36KU4KRLGE4XNTOOZF/state.json","well_known_bundle":"https://pith.science/.well-known/pith/E3KNNNHI36KU4KRLGE4XNTOOZF/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:E3KNNNHI36KU4KRLGE4XNTOOZF","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":"9b263692b2ad885e560dacb5690daa42a58416b93f26a595d3f8099e78e1241b","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2017-06-26T14:39:08Z","title_canon_sha256":"b22ede262aa0eb847ccac7ffbba6dbcd645c0c03a141019a640b5d40aeb90480"},"schema_version":"1.0","source":{"id":"1706.08411","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1706.08411","created_at":"2026-05-18T00:22:20Z"},{"alias_kind":"arxiv_version","alias_value":"1706.08411v3","created_at":"2026-05-18T00:22:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.08411","created_at":"2026-05-18T00:22:20Z"},{"alias_kind":"pith_short_12","alias_value":"E3KNNNHI36KU","created_at":"2026-05-18T12:31:12Z"},{"alias_kind":"pith_short_16","alias_value":"E3KNNNHI36KU4KRL","created_at":"2026-05-18T12:31:12Z"},{"alias_kind":"pith_short_8","alias_value":"E3KNNNHI","created_at":"2026-05-18T12:31:12Z"}],"graph_snapshots":[{"event_id":"sha256:bb50d66ed17fcc1c0015a1884d63aeaf5fa3c3552a47869110fd8ba0569f4dac","target":"graph","created_at":"2026-05-18T00:22:20Z","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":"We study restriction and extension properties for states on C$^*$-algebras with an eye towards hyperrigidity of operator systems. We use these ideas to provide supporting evidence for Arveson's hyperrigidity conjecture. Prompted by various characterizations of hyperrigidity in terms of states, we examine unperforated pairs of self-adjoint subspaces in a C$^*$-algebra. The configuration of the subspaces forming an unperforated pair is in some sense compatible with the order structure of the ambient C$^*$-algebra. We prove that commuting pairs are unperforated, and obtain consequences for hyperr","authors_text":"Rapha\\\"el Clou\\^atre","cross_cats":["math.FA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2017-06-26T14:39:08Z","title":"Unperforated pairs of operator spaces and hyperrigidity of operator systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.08411","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":"sha256:36f0b5c904b5a36be439d4cc7b02f281dcc7eeb09003360eed2a7044e9b3ec82","target":"record","created_at":"2026-05-18T00:22:20Z","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":"9b263692b2ad885e560dacb5690daa42a58416b93f26a595d3f8099e78e1241b","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2017-06-26T14:39:08Z","title_canon_sha256":"b22ede262aa0eb847ccac7ffbba6dbcd645c0c03a141019a640b5d40aeb90480"},"schema_version":"1.0","source":{"id":"1706.08411","kind":"arxiv","version":3}},"canonical_sha256":"26d4d6b4e8df954e2a2b313976cdcec961d2393f7f4b8fa91d43a404709d5c54","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"26d4d6b4e8df954e2a2b313976cdcec961d2393f7f4b8fa91d43a404709d5c54","first_computed_at":"2026-05-18T00:22:20.922994Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:22:20.922994Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"kA813Fs3t1KT6ZMidCJySJkvuLcWn7QVAR7AKY7Aal+YTcQTmZMUF+/c7yQHQVsqeWYpiCLEpOw8aRTBqzVnBw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:22:20.923607Z","signed_message":"canonical_sha256_bytes"},"source_id":"1706.08411","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:36f0b5c904b5a36be439d4cc7b02f281dcc7eeb09003360eed2a7044e9b3ec82","sha256:bb50d66ed17fcc1c0015a1884d63aeaf5fa3c3552a47869110fd8ba0569f4dac"],"state_sha256":"4cce5fcc97195c89fdcf4f9d83ba4b5f9179f354354244caa5465b1ebfb118bc"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MXih8jVScjnhJpV1xafrbeV0yuc50gKCPuRhE6lmq30zpdW2jB62Mrq37pHeWqOwh3FE5vtTPvrk+gIdj2oIDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-25T21:37:51.892434Z","bundle_sha256":"f8da79d9a368b3030de619157e23600ca2181592d22250928e27d6fdf5dccb4c"}}