{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:7IXJRPB3JALVAEC363AJQINZZC","short_pith_number":"pith:7IXJRPB3","canonical_record":{"source":{"id":"1009.2249","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2010-09-12T17:03:35Z","cross_cats_sorted":["math.CV"],"title_canon_sha256":"6f03ed89138562e7294bca6fadcb37ab6f53eeae8269c72e2ee8fa5333136673","abstract_canon_sha256":"2fb3c99943a7fbde305165dcd0cc42d9361fabed6bfcf4a501da431bbb6d7da0"},"schema_version":"1.0"},"canonical_sha256":"fa2e98bc3b481750105bf6c09821b9c893e2564f7325ac80ed6778c0f8b8492b","source":{"kind":"arxiv","id":"1009.2249","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1009.2249","created_at":"2026-05-18T04:34:18Z"},{"alias_kind":"arxiv_version","alias_value":"1009.2249v2","created_at":"2026-05-18T04:34:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1009.2249","created_at":"2026-05-18T04:34:18Z"},{"alias_kind":"pith_short_12","alias_value":"7IXJRPB3JALV","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_16","alias_value":"7IXJRPB3JALVAEC3","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_8","alias_value":"7IXJRPB3","created_at":"2026-05-18T12:26:04Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:7IXJRPB3JALVAEC363AJQINZZC","target":"record","payload":{"canonical_record":{"source":{"id":"1009.2249","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2010-09-12T17:03:35Z","cross_cats_sorted":["math.CV"],"title_canon_sha256":"6f03ed89138562e7294bca6fadcb37ab6f53eeae8269c72e2ee8fa5333136673","abstract_canon_sha256":"2fb3c99943a7fbde305165dcd0cc42d9361fabed6bfcf4a501da431bbb6d7da0"},"schema_version":"1.0"},"canonical_sha256":"fa2e98bc3b481750105bf6c09821b9c893e2564f7325ac80ed6778c0f8b8492b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:34:18.109311Z","signature_b64":"z5BQLai0Qrx5PsZf55WXVPD9vX69T+vLEjYjcIGOJYF9nW81Wz4rL2DkTnL7d26CwEW0m/y7mdG8FhrdvZhzDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fa2e98bc3b481750105bf6c09821b9c893e2564f7325ac80ed6778c0f8b8492b","last_reissued_at":"2026-05-18T04:34:18.108740Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:34:18.108740Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1009.2249","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:34:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"twTA2pYAWf+efzb7K9pzpsRI3bl3uqDYu40r7uunZE1UNIj5by5htf2CBcrCFGC4S8+vUwRf38h/i2Wt3o90CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T17:33:10.163063Z"},"content_sha256":"89472d5e542ce47b99ad8cf5359422458a28ffbf145b5e895ad7f8b7c0281430","schema_version":"1.0","event_id":"sha256:89472d5e542ce47b99ad8cf5359422458a28ffbf145b5e895ad7f8b7c0281430"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:7IXJRPB3JALVAEC363AJQINZZC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Numerical ranges of $C_0(N)$ contractions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.FA","authors_text":"Chafiq Benhida, Dan Timotin, Pamela Gorkin","submitted_at":"2010-09-12T17:03:35Z","abstract_excerpt":"A conjecture of Halmos proved by Choi and Li states that the closure of the numerical range of a contraction on a Hilbert space is the intersection of the closure of the numerical ranges of all its unitary dilations. We show that for $C_0(N)$ contractions one can restrict the intersection to a smaller family of dilations. This generalizes a finite dimensional result of Gau and Wu."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.2249","kind":"arxiv","version":2},"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":"2026-05-18T04:34:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SxZ6j9YyBUjzIxvOWbBLt5MgWuCKF85fa/RbyJSRz9OSa8E3aefWso7RlY3D1uTiZfPqvmgRbPX4tAsIyNbICA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T17:33:10.163433Z"},"content_sha256":"95f0a5ebfa845ed6ad91e2df8d3b11c63ebb13f22e6e49f6fa48dc22ffe6a40a","schema_version":"1.0","event_id":"sha256:95f0a5ebfa845ed6ad91e2df8d3b11c63ebb13f22e6e49f6fa48dc22ffe6a40a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7IXJRPB3JALVAEC363AJQINZZC/bundle.json","state_url":"https://pith.science/pith/7IXJRPB3JALVAEC363AJQINZZC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7IXJRPB3JALVAEC363AJQINZZC/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":"2026-06-01T17:33:10Z","links":{"resolver":"https://pith.science/pith/7IXJRPB3JALVAEC363AJQINZZC","bundle":"https://pith.science/pith/7IXJRPB3JALVAEC363AJQINZZC/bundle.json","state":"https://pith.science/pith/7IXJRPB3JALVAEC363AJQINZZC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7IXJRPB3JALVAEC363AJQINZZC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:7IXJRPB3JALVAEC363AJQINZZC","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":"2fb3c99943a7fbde305165dcd0cc42d9361fabed6bfcf4a501da431bbb6d7da0","cross_cats_sorted":["math.CV"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2010-09-12T17:03:35Z","title_canon_sha256":"6f03ed89138562e7294bca6fadcb37ab6f53eeae8269c72e2ee8fa5333136673"},"schema_version":"1.0","source":{"id":"1009.2249","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1009.2249","created_at":"2026-05-18T04:34:18Z"},{"alias_kind":"arxiv_version","alias_value":"1009.2249v2","created_at":"2026-05-18T04:34:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1009.2249","created_at":"2026-05-18T04:34:18Z"},{"alias_kind":"pith_short_12","alias_value":"7IXJRPB3JALV","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_16","alias_value":"7IXJRPB3JALVAEC3","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_8","alias_value":"7IXJRPB3","created_at":"2026-05-18T12:26:04Z"}],"graph_snapshots":[{"event_id":"sha256:95f0a5ebfa845ed6ad91e2df8d3b11c63ebb13f22e6e49f6fa48dc22ffe6a40a","target":"graph","created_at":"2026-05-18T04:34:18Z","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":"A conjecture of Halmos proved by Choi and Li states that the closure of the numerical range of a contraction on a Hilbert space is the intersection of the closure of the numerical ranges of all its unitary dilations. We show that for $C_0(N)$ contractions one can restrict the intersection to a smaller family of dilations. This generalizes a finite dimensional result of Gau and Wu.","authors_text":"Chafiq Benhida, Dan Timotin, Pamela Gorkin","cross_cats":["math.CV"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2010-09-12T17:03:35Z","title":"Numerical ranges of $C_0(N)$ contractions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.2249","kind":"arxiv","version":2},"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":"sha256:89472d5e542ce47b99ad8cf5359422458a28ffbf145b5e895ad7f8b7c0281430","target":"record","created_at":"2026-05-18T04:34:18Z","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":"2fb3c99943a7fbde305165dcd0cc42d9361fabed6bfcf4a501da431bbb6d7da0","cross_cats_sorted":["math.CV"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2010-09-12T17:03:35Z","title_canon_sha256":"6f03ed89138562e7294bca6fadcb37ab6f53eeae8269c72e2ee8fa5333136673"},"schema_version":"1.0","source":{"id":"1009.2249","kind":"arxiv","version":2}},"canonical_sha256":"fa2e98bc3b481750105bf6c09821b9c893e2564f7325ac80ed6778c0f8b8492b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fa2e98bc3b481750105bf6c09821b9c893e2564f7325ac80ed6778c0f8b8492b","first_computed_at":"2026-05-18T04:34:18.108740Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:34:18.108740Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"z5BQLai0Qrx5PsZf55WXVPD9vX69T+vLEjYjcIGOJYF9nW81Wz4rL2DkTnL7d26CwEW0m/y7mdG8FhrdvZhzDA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:34:18.109311Z","signed_message":"canonical_sha256_bytes"},"source_id":"1009.2249","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:89472d5e542ce47b99ad8cf5359422458a28ffbf145b5e895ad7f8b7c0281430","sha256:95f0a5ebfa845ed6ad91e2df8d3b11c63ebb13f22e6e49f6fa48dc22ffe6a40a"],"state_sha256":"412252f31910dfb7e416a7fa4e47e30c20c69013cbdf1684496a7ba2d42612d9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ovOPtDlA7Hp/g+OLTrgXxdkDc37WlkK44+LhcOsKaxbBvf4+NCIdI2FbxHWtR7ZtMPPLOSj0tFbFapCStv8ABg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T17:33:10.165564Z","bundle_sha256":"836a45135ac93990dddf23cd16460c829eb3a5ef3a6ee57e4a5231ccea77f4d0"}}