{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:HZZUXNC2YDU3XR3VL7UY5F67ZY","short_pith_number":"pith:HZZUXNC2","canonical_record":{"source":{"id":"1101.3098","kind":"arxiv","version":6},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-01-16T22:33:50Z","cross_cats_sorted":["cs.IT","math.IT","math.MP","quant-ph"],"title_canon_sha256":"c4bb10a8ca1dad71b91ad870e2cbb901d99f69a8ccb53404ab405ded522e709e","abstract_canon_sha256":"992ca2af7679ad5d66715fcbcc23a56aea43b595669475e502ea52ff87f03b15"},"schema_version":"1.0"},"canonical_sha256":"3e734bb45ac0e9bbc7755fe98e97dfce19d507b2a1bf7a4dd15d0a55d3f4092f","source":{"kind":"arxiv","id":"1101.3098","version":6},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1101.3098","created_at":"2026-05-18T01:14:53Z"},{"alias_kind":"arxiv_version","alias_value":"1101.3098v6","created_at":"2026-05-18T01:14:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1101.3098","created_at":"2026-05-18T01:14:53Z"},{"alias_kind":"pith_short_12","alias_value":"HZZUXNC2YDU3","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_16","alias_value":"HZZUXNC2YDU3XR3V","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_8","alias_value":"HZZUXNC2","created_at":"2026-05-18T12:26:30Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:HZZUXNC2YDU3XR3VL7UY5F67ZY","target":"record","payload":{"canonical_record":{"source":{"id":"1101.3098","kind":"arxiv","version":6},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-01-16T22:33:50Z","cross_cats_sorted":["cs.IT","math.IT","math.MP","quant-ph"],"title_canon_sha256":"c4bb10a8ca1dad71b91ad870e2cbb901d99f69a8ccb53404ab405ded522e709e","abstract_canon_sha256":"992ca2af7679ad5d66715fcbcc23a56aea43b595669475e502ea52ff87f03b15"},"schema_version":"1.0"},"canonical_sha256":"3e734bb45ac0e9bbc7755fe98e97dfce19d507b2a1bf7a4dd15d0a55d3f4092f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:14:53.704346Z","signature_b64":"Qw8TtxCJ5nnfLCaCqhdIjmUkVWIR+SGFl1isO2Ly+Rh+zsR/T2qWeIUHMQCo/Wcx7azBVwngT7hj2Alxpc2oBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3e734bb45ac0e9bbc7755fe98e97dfce19d507b2a1bf7a4dd15d0a55d3f4092f","last_reissued_at":"2026-05-18T01:14:53.703743Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:14:53.703743Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1101.3098","source_version":6,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:14:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AUQNb13XSLyiR9EfM3u1uF9T6ZNl6Fh0z/fBze4MM8x7wC7WNMnNA8Ho/lTdJ2QTYyT+D81u/+sdZnzpUW3UCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T00:11:04.446386Z"},"content_sha256":"3db62a20161086be278c4d9a6904ba02222a4fd1cd2c29a66c37192e6bed26a4","schema_version":"1.0","event_id":"sha256:3db62a20161086be278c4d9a6904ba02222a4fd1cd2c29a66c37192e6bed26a4"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:HZZUXNC2YDU3XR3VL7UY5F67ZY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Quantum Convex Support","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.IT","math.IT","math.MP","quant-ph"],"primary_cat":"math-ph","authors_text":"Stephan Weis","submitted_at":"2011-01-16T22:33:50Z","abstract_excerpt":"Convex support, the mean values of a set of random variables, is central in information theory and statistics. Equally central in quantum information theory are mean values of a set of observables in a finite-dimensional C*-algebra A, which we call (quantum) convex support. The convex support can be viewed as a projection of the state space of A and it is a projection of a spectrahedron.\n  Spectrahedra are increasingly investigated at least since the 1990's boom in semidefinite programming. We recall the geometry of the positive semi-definite cone and of the state space. We write a convex dual"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1101.3098","kind":"arxiv","version":6},"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":"2026-05-18T01:14:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"eCfEM/eo5JsmHNKdUgnzaOD1seDAZ+gLHrIq06lknIx9avn9dOnym0GBaiu+/VL0BAq1R70Xs/0metAJk1g4CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T00:11:04.446742Z"},"content_sha256":"6870ad0e0cf8b567d52912ca764e304fa270d6e50dc906583019de1151e983c0","schema_version":"1.0","event_id":"sha256:6870ad0e0cf8b567d52912ca764e304fa270d6e50dc906583019de1151e983c0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HZZUXNC2YDU3XR3VL7UY5F67ZY/bundle.json","state_url":"https://pith.science/pith/HZZUXNC2YDU3XR3VL7UY5F67ZY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HZZUXNC2YDU3XR3VL7UY5F67ZY/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":"2026-06-03T00:11:04Z","links":{"resolver":"https://pith.science/pith/HZZUXNC2YDU3XR3VL7UY5F67ZY","bundle":"https://pith.science/pith/HZZUXNC2YDU3XR3VL7UY5F67ZY/bundle.json","state":"https://pith.science/pith/HZZUXNC2YDU3XR3VL7UY5F67ZY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HZZUXNC2YDU3XR3VL7UY5F67ZY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:HZZUXNC2YDU3XR3VL7UY5F67ZY","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":"992ca2af7679ad5d66715fcbcc23a56aea43b595669475e502ea52ff87f03b15","cross_cats_sorted":["cs.IT","math.IT","math.MP","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-01-16T22:33:50Z","title_canon_sha256":"c4bb10a8ca1dad71b91ad870e2cbb901d99f69a8ccb53404ab405ded522e709e"},"schema_version":"1.0","source":{"id":"1101.3098","kind":"arxiv","version":6}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1101.3098","created_at":"2026-05-18T01:14:53Z"},{"alias_kind":"arxiv_version","alias_value":"1101.3098v6","created_at":"2026-05-18T01:14:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1101.3098","created_at":"2026-05-18T01:14:53Z"},{"alias_kind":"pith_short_12","alias_value":"HZZUXNC2YDU3","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_16","alias_value":"HZZUXNC2YDU3XR3V","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_8","alias_value":"HZZUXNC2","created_at":"2026-05-18T12:26:30Z"}],"graph_snapshots":[{"event_id":"sha256:6870ad0e0cf8b567d52912ca764e304fa270d6e50dc906583019de1151e983c0","target":"graph","created_at":"2026-05-18T01:14:53Z","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":"Convex support, the mean values of a set of random variables, is central in information theory and statistics. Equally central in quantum information theory are mean values of a set of observables in a finite-dimensional C*-algebra A, which we call (quantum) convex support. The convex support can be viewed as a projection of the state space of A and it is a projection of a spectrahedron.\n  Spectrahedra are increasingly investigated at least since the 1990's boom in semidefinite programming. We recall the geometry of the positive semi-definite cone and of the state space. We write a convex dual","authors_text":"Stephan Weis","cross_cats":["cs.IT","math.IT","math.MP","quant-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-01-16T22:33:50Z","title":"Quantum Convex Support"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1101.3098","kind":"arxiv","version":6},"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":"sha256:3db62a20161086be278c4d9a6904ba02222a4fd1cd2c29a66c37192e6bed26a4","target":"record","created_at":"2026-05-18T01:14:53Z","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":"992ca2af7679ad5d66715fcbcc23a56aea43b595669475e502ea52ff87f03b15","cross_cats_sorted":["cs.IT","math.IT","math.MP","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-01-16T22:33:50Z","title_canon_sha256":"c4bb10a8ca1dad71b91ad870e2cbb901d99f69a8ccb53404ab405ded522e709e"},"schema_version":"1.0","source":{"id":"1101.3098","kind":"arxiv","version":6}},"canonical_sha256":"3e734bb45ac0e9bbc7755fe98e97dfce19d507b2a1bf7a4dd15d0a55d3f4092f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3e734bb45ac0e9bbc7755fe98e97dfce19d507b2a1bf7a4dd15d0a55d3f4092f","first_computed_at":"2026-05-18T01:14:53.703743Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:14:53.703743Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Qw8TtxCJ5nnfLCaCqhdIjmUkVWIR+SGFl1isO2Ly+Rh+zsR/T2qWeIUHMQCo/Wcx7azBVwngT7hj2Alxpc2oBg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:14:53.704346Z","signed_message":"canonical_sha256_bytes"},"source_id":"1101.3098","source_kind":"arxiv","source_version":6}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3db62a20161086be278c4d9a6904ba02222a4fd1cd2c29a66c37192e6bed26a4","sha256:6870ad0e0cf8b567d52912ca764e304fa270d6e50dc906583019de1151e983c0"],"state_sha256":"2c9b36ec8fb863405a15963c66f61e7ccdaf50421980b52defc2603c62371624"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"102fl0NrUa9vqnCwb/UTEqbAa8E8/jRacxYDo1EWKA+vhR0A2J87lunELNY1gEOI+Vz+YAwbxr12SODSmkqrBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T00:11:04.448703Z","bundle_sha256":"5edd768f1ebe82b384509a9b7954589dd04332a0b6c0c0896d6ee9a8731b5be1"}}