{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:M6L3EVH3PEU4GE5WZ4X3GZ4BWT","short_pith_number":"pith:M6L3EVH3","canonical_record":{"source":{"id":"1606.02278","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2016-06-07T19:49:50Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"1aa225697adef840233b970ee95699429e891bce7f8678b62bae805bdb13aac1","abstract_canon_sha256":"59d9c48e06f84d7aba55b01312a68a9a2164979451be549cf88eca73f3be3fb0"},"schema_version":"1.0"},"canonical_sha256":"6797b254fb7929c313b6cf2fb36781b4e844e11a00addc5c7072ae99ab8410e7","source":{"kind":"arxiv","id":"1606.02278","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1606.02278","created_at":"2026-05-18T00:51:48Z"},{"alias_kind":"arxiv_version","alias_value":"1606.02278v1","created_at":"2026-05-18T00:51:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.02278","created_at":"2026-05-18T00:51:48Z"},{"alias_kind":"pith_short_12","alias_value":"M6L3EVH3PEU4","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_16","alias_value":"M6L3EVH3PEU4GE5W","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_8","alias_value":"M6L3EVH3","created_at":"2026-05-18T12:30:29Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:M6L3EVH3PEU4GE5WZ4X3GZ4BWT","target":"record","payload":{"canonical_record":{"source":{"id":"1606.02278","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2016-06-07T19:49:50Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"1aa225697adef840233b970ee95699429e891bce7f8678b62bae805bdb13aac1","abstract_canon_sha256":"59d9c48e06f84d7aba55b01312a68a9a2164979451be549cf88eca73f3be3fb0"},"schema_version":"1.0"},"canonical_sha256":"6797b254fb7929c313b6cf2fb36781b4e844e11a00addc5c7072ae99ab8410e7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:51:48.690620Z","signature_b64":"D9G129VisNS9jZa8b2Fp1Z/lus3dshY0Pdj0w2vQHHl51GEHtP6x6I/4Lgk9hW0Er4/geWFClj41ZQIDvuRCDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6797b254fb7929c313b6cf2fb36781b4e844e11a00addc5c7072ae99ab8410e7","last_reissued_at":"2026-05-18T00:51:48.690001Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:51:48.690001Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1606.02278","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":"2026-05-18T00:51:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"niL0JGfp7n/TrRTaID7J0kMM3hkuFh7XbMMRy4QsWAkX9ClCIxeDkwTgidCZZwZCzkc2z9atudrkgpJ3E50hBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T09:59:10.512426Z"},"content_sha256":"2ce78783a35c216abf3ac4c04b7b23b73541397ca0e16a8fb568a3d8136f2798","schema_version":"1.0","event_id":"sha256:2ce78783a35c216abf3ac4c04b7b23b73541397ca0e16a8fb568a3d8136f2798"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:M6L3EVH3PEU4GE5WZ4X3GZ4BWT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Perfect Commuting-Operator Strategies for Linear System Games","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"quant-ph","authors_text":"Li Liu, Richard Cleve, William Slofstra","submitted_at":"2016-06-07T19:49:50Z","abstract_excerpt":"Linear system games are a generalization of Mermin's magic square game introduced by Cleve and Mittal. They show that perfect strategies for linear system games in the tensor-product model of entanglement correspond to finite-dimensional operator solutions of a certain set of non-commutative equations. We investigate linear system games in the commuting-operator model of entanglement, where Alice and Bob's measurement operators act on a joint Hilbert space, and Alice's operators must commute with Bob's operators. We show that perfect strategies in this model correspond to possibly-infinite-dim"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.02278","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":"2026-05-18T00:51:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tYVMn0pc4OT7NIw0nu4z2kd9Vbp+RXgte26wZ1YcTjEWq4Y3lkmbk5m9OWuUU7KoDCl/RhovjvOFwyQHVqfZAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T09:59:10.512774Z"},"content_sha256":"1eae2295065c627ca98be82acacfbd3e7b6c80cf6f8587757a6294c01f9c4e47","schema_version":"1.0","event_id":"sha256:1eae2295065c627ca98be82acacfbd3e7b6c80cf6f8587757a6294c01f9c4e47"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/M6L3EVH3PEU4GE5WZ4X3GZ4BWT/bundle.json","state_url":"https://pith.science/pith/M6L3EVH3PEU4GE5WZ4X3GZ4BWT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/M6L3EVH3PEU4GE5WZ4X3GZ4BWT/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":"2026-06-03T09:59:10Z","links":{"resolver":"https://pith.science/pith/M6L3EVH3PEU4GE5WZ4X3GZ4BWT","bundle":"https://pith.science/pith/M6L3EVH3PEU4GE5WZ4X3GZ4BWT/bundle.json","state":"https://pith.science/pith/M6L3EVH3PEU4GE5WZ4X3GZ4BWT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/M6L3EVH3PEU4GE5WZ4X3GZ4BWT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:M6L3EVH3PEU4GE5WZ4X3GZ4BWT","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":"59d9c48e06f84d7aba55b01312a68a9a2164979451be549cf88eca73f3be3fb0","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2016-06-07T19:49:50Z","title_canon_sha256":"1aa225697adef840233b970ee95699429e891bce7f8678b62bae805bdb13aac1"},"schema_version":"1.0","source":{"id":"1606.02278","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1606.02278","created_at":"2026-05-18T00:51:48Z"},{"alias_kind":"arxiv_version","alias_value":"1606.02278v1","created_at":"2026-05-18T00:51:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.02278","created_at":"2026-05-18T00:51:48Z"},{"alias_kind":"pith_short_12","alias_value":"M6L3EVH3PEU4","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_16","alias_value":"M6L3EVH3PEU4GE5W","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_8","alias_value":"M6L3EVH3","created_at":"2026-05-18T12:30:29Z"}],"graph_snapshots":[{"event_id":"sha256:1eae2295065c627ca98be82acacfbd3e7b6c80cf6f8587757a6294c01f9c4e47","target":"graph","created_at":"2026-05-18T00:51:48Z","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":"Linear system games are a generalization of Mermin's magic square game introduced by Cleve and Mittal. They show that perfect strategies for linear system games in the tensor-product model of entanglement correspond to finite-dimensional operator solutions of a certain set of non-commutative equations. We investigate linear system games in the commuting-operator model of entanglement, where Alice and Bob's measurement operators act on a joint Hilbert space, and Alice's operators must commute with Bob's operators. We show that perfect strategies in this model correspond to possibly-infinite-dim","authors_text":"Li Liu, Richard Cleve, William Slofstra","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2016-06-07T19:49:50Z","title":"Perfect Commuting-Operator Strategies for Linear System Games"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.02278","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":"sha256:2ce78783a35c216abf3ac4c04b7b23b73541397ca0e16a8fb568a3d8136f2798","target":"record","created_at":"2026-05-18T00:51:48Z","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":"59d9c48e06f84d7aba55b01312a68a9a2164979451be549cf88eca73f3be3fb0","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2016-06-07T19:49:50Z","title_canon_sha256":"1aa225697adef840233b970ee95699429e891bce7f8678b62bae805bdb13aac1"},"schema_version":"1.0","source":{"id":"1606.02278","kind":"arxiv","version":1}},"canonical_sha256":"6797b254fb7929c313b6cf2fb36781b4e844e11a00addc5c7072ae99ab8410e7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6797b254fb7929c313b6cf2fb36781b4e844e11a00addc5c7072ae99ab8410e7","first_computed_at":"2026-05-18T00:51:48.690001Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:51:48.690001Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"D9G129VisNS9jZa8b2Fp1Z/lus3dshY0Pdj0w2vQHHl51GEHtP6x6I/4Lgk9hW0Er4/geWFClj41ZQIDvuRCDw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:51:48.690620Z","signed_message":"canonical_sha256_bytes"},"source_id":"1606.02278","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2ce78783a35c216abf3ac4c04b7b23b73541397ca0e16a8fb568a3d8136f2798","sha256:1eae2295065c627ca98be82acacfbd3e7b6c80cf6f8587757a6294c01f9c4e47"],"state_sha256":"53ac042a8566e56eadf8551bf246e82de9548c3c8ae956df6cc339825b13b4b0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"inWrlxHr+7BLRf4lfeXduOAL8kIpujeClvFGnm9+Q0mXYyZG27n6MBBnsjJchqgnWdDswOCzCr7CwbBRrKJoBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T09:59:10.514800Z","bundle_sha256":"668246707e182cea0d3731b1f393a6e1e2fc4831674d7a88b2de6958ac0c7867"}}