{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:IBWLIGTFVM6KTYWHAIEPFESQFX","short_pith_number":"pith:IBWLIGTF","canonical_record":{"source":{"id":"1012.2111","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2010-12-09T20:58:45Z","cross_cats_sorted":[],"title_canon_sha256":"c4035e540c3cb81bc48438ca0d79ad72253eb9b83b36eaac6610d8fc35f51a80","abstract_canon_sha256":"a6ce2ba8fd5fb3d23c9c5ae83b2993ed633e768d49da3fa2a88e8d9cc01a3e05"},"schema_version":"1.0"},"canonical_sha256":"406cb41a65ab3ca9e2c70208f292502df3dd54c1576fe8b82971060b5b13738c","source":{"kind":"arxiv","id":"1012.2111","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1012.2111","created_at":"2026-05-18T04:16:22Z"},{"alias_kind":"arxiv_version","alias_value":"1012.2111v2","created_at":"2026-05-18T04:16:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1012.2111","created_at":"2026-05-18T04:16:22Z"},{"alias_kind":"pith_short_12","alias_value":"IBWLIGTFVM6K","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_16","alias_value":"IBWLIGTFVM6KTYWH","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_8","alias_value":"IBWLIGTF","created_at":"2026-05-18T12:26:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:IBWLIGTFVM6KTYWHAIEPFESQFX","target":"record","payload":{"canonical_record":{"source":{"id":"1012.2111","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2010-12-09T20:58:45Z","cross_cats_sorted":[],"title_canon_sha256":"c4035e540c3cb81bc48438ca0d79ad72253eb9b83b36eaac6610d8fc35f51a80","abstract_canon_sha256":"a6ce2ba8fd5fb3d23c9c5ae83b2993ed633e768d49da3fa2a88e8d9cc01a3e05"},"schema_version":"1.0"},"canonical_sha256":"406cb41a65ab3ca9e2c70208f292502df3dd54c1576fe8b82971060b5b13738c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:16:22.707732Z","signature_b64":"KsobZwi0dSit2iFNHlV4y9ZfmXJVFc4pA0RtivC9fFgOE1plXHRTfpFntVBiqmDi3aApzVM+mp0akuknagHXDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"406cb41a65ab3ca9e2c70208f292502df3dd54c1576fe8b82971060b5b13738c","last_reissued_at":"2026-05-18T04:16:22.707183Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:16:22.707183Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1012.2111","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":"2026-05-18T04:16:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oselozLSJ8swGGIj56bVHunFVOp0XFapcxzmvoe8SwI1n7YpBZreBQGuBpSuqYTJwOs8lv3cEdy4rA1LsNLtCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T19:14:35.879649Z"},"content_sha256":"7c6f50c31f1913379c5f6382e33eea990e5547490d0d30db846f766d273ad487","schema_version":"1.0","event_id":"sha256:7c6f50c31f1913379c5f6382e33eea990e5547490d0d30db846f766d273ad487"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:IBWLIGTFVM6KTYWHAIEPFESQFX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Three commuting, unital, completely positive maps that have no minimal dilation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"Michael Skeide, Orr Shalit","submitted_at":"2010-12-09T20:58:45Z","abstract_excerpt":"In this note we prove that there exist at least two examples of three commuting, unital, completely positive maps that have no dilation on a type I factor, and no minimal dilation on any von Neumann algebra."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1012.2111","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":"2026-05-18T04:16:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"R6N4wNfF5kO4yDcccTpGHFIzUhVzb+AAOL5SPiMPnyq8RUYSjRsGQ4D5BPW+4Gwt/MkblB3Em0xPoCo0uai3AA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T19:14:35.880331Z"},"content_sha256":"93328e5ea2d12f9fb413917f5d4eed9910aa9befb1a9e7f1b56e6b4e0293bf81","schema_version":"1.0","event_id":"sha256:93328e5ea2d12f9fb413917f5d4eed9910aa9befb1a9e7f1b56e6b4e0293bf81"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/IBWLIGTFVM6KTYWHAIEPFESQFX/bundle.json","state_url":"https://pith.science/pith/IBWLIGTFVM6KTYWHAIEPFESQFX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/IBWLIGTFVM6KTYWHAIEPFESQFX/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":"2026-05-27T19:14:35Z","links":{"resolver":"https://pith.science/pith/IBWLIGTFVM6KTYWHAIEPFESQFX","bundle":"https://pith.science/pith/IBWLIGTFVM6KTYWHAIEPFESQFX/bundle.json","state":"https://pith.science/pith/IBWLIGTFVM6KTYWHAIEPFESQFX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/IBWLIGTFVM6KTYWHAIEPFESQFX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:IBWLIGTFVM6KTYWHAIEPFESQFX","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":"a6ce2ba8fd5fb3d23c9c5ae83b2993ed633e768d49da3fa2a88e8d9cc01a3e05","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2010-12-09T20:58:45Z","title_canon_sha256":"c4035e540c3cb81bc48438ca0d79ad72253eb9b83b36eaac6610d8fc35f51a80"},"schema_version":"1.0","source":{"id":"1012.2111","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1012.2111","created_at":"2026-05-18T04:16:22Z"},{"alias_kind":"arxiv_version","alias_value":"1012.2111v2","created_at":"2026-05-18T04:16:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1012.2111","created_at":"2026-05-18T04:16:22Z"},{"alias_kind":"pith_short_12","alias_value":"IBWLIGTFVM6K","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_16","alias_value":"IBWLIGTFVM6KTYWH","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_8","alias_value":"IBWLIGTF","created_at":"2026-05-18T12:26:09Z"}],"graph_snapshots":[{"event_id":"sha256:93328e5ea2d12f9fb413917f5d4eed9910aa9befb1a9e7f1b56e6b4e0293bf81","target":"graph","created_at":"2026-05-18T04:16:22Z","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":"In this note we prove that there exist at least two examples of three commuting, unital, completely positive maps that have no dilation on a type I factor, and no minimal dilation on any von Neumann algebra.","authors_text":"Michael Skeide, Orr Shalit","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2010-12-09T20:58:45Z","title":"Three commuting, unital, completely positive maps that have no minimal dilation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1012.2111","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":"sha256:7c6f50c31f1913379c5f6382e33eea990e5547490d0d30db846f766d273ad487","target":"record","created_at":"2026-05-18T04:16:22Z","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":"a6ce2ba8fd5fb3d23c9c5ae83b2993ed633e768d49da3fa2a88e8d9cc01a3e05","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2010-12-09T20:58:45Z","title_canon_sha256":"c4035e540c3cb81bc48438ca0d79ad72253eb9b83b36eaac6610d8fc35f51a80"},"schema_version":"1.0","source":{"id":"1012.2111","kind":"arxiv","version":2}},"canonical_sha256":"406cb41a65ab3ca9e2c70208f292502df3dd54c1576fe8b82971060b5b13738c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"406cb41a65ab3ca9e2c70208f292502df3dd54c1576fe8b82971060b5b13738c","first_computed_at":"2026-05-18T04:16:22.707183Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:16:22.707183Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"KsobZwi0dSit2iFNHlV4y9ZfmXJVFc4pA0RtivC9fFgOE1plXHRTfpFntVBiqmDi3aApzVM+mp0akuknagHXDg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:16:22.707732Z","signed_message":"canonical_sha256_bytes"},"source_id":"1012.2111","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7c6f50c31f1913379c5f6382e33eea990e5547490d0d30db846f766d273ad487","sha256:93328e5ea2d12f9fb413917f5d4eed9910aa9befb1a9e7f1b56e6b4e0293bf81"],"state_sha256":"9019bb4749f4a6225d1bf426036ad0bdf98f48b63e70d97652dc664412438ee5"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5D1btrCMmohvY+CYBmsudn5pe37EaR47fYXnmwlzb6Veuhmt3l0E88csTmrtHdGn+6f0g54xmploJc5zX2QwBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T19:14:35.883650Z","bundle_sha256":"c4983bf19f85f5dd90bfb26c622ae67ab31740f588475309ab8f2c98fba0d820"}}