{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:RHY76HQQ6I3ZDQSM7SFYLPVH3M","short_pith_number":"pith:RHY76HQQ","canonical_record":{"source":{"id":"1106.5367","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2011-06-27T11:52:50Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"a8c5b728bd22593d735e4d476ca79bd353f5c36e9339959bb151cc35857b68e1","abstract_canon_sha256":"8500f56e5b28182d99145aee823fd03345a9e0a4f22ecfe938c0f2595a3b4f24"},"schema_version":"1.0"},"canonical_sha256":"89f1ff1e10f23791c24cfc8b85bea7db3ca9b0bddea155c7d02b8c3e5f3c5148","source":{"kind":"arxiv","id":"1106.5367","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1106.5367","created_at":"2026-05-18T02:01:30Z"},{"alias_kind":"arxiv_version","alias_value":"1106.5367v1","created_at":"2026-05-18T02:01:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1106.5367","created_at":"2026-05-18T02:01:30Z"},{"alias_kind":"pith_short_12","alias_value":"RHY76HQQ6I3Z","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_16","alias_value":"RHY76HQQ6I3ZDQSM","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_8","alias_value":"RHY76HQQ","created_at":"2026-05-18T12:26:41Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:RHY76HQQ6I3ZDQSM7SFYLPVH3M","target":"record","payload":{"canonical_record":{"source":{"id":"1106.5367","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2011-06-27T11:52:50Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"a8c5b728bd22593d735e4d476ca79bd353f5c36e9339959bb151cc35857b68e1","abstract_canon_sha256":"8500f56e5b28182d99145aee823fd03345a9e0a4f22ecfe938c0f2595a3b4f24"},"schema_version":"1.0"},"canonical_sha256":"89f1ff1e10f23791c24cfc8b85bea7db3ca9b0bddea155c7d02b8c3e5f3c5148","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:01:30.421396Z","signature_b64":"lMfYuy7sxa//vIVdcdPMRkIdzGOWWsfGWtvDXxeALZlRUji4oel141I+VCD429Uz/zrDU5Y0Jv7mIS/4nvwIAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"89f1ff1e10f23791c24cfc8b85bea7db3ca9b0bddea155c7d02b8c3e5f3c5148","last_reissued_at":"2026-05-18T02:01:30.421018Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:01:30.421018Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1106.5367","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":"2026-05-18T02:01:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lESHxYnPmXmBgFwYtkctir5sVqCNxeq+YHUUsUbSe3yUSejvwRHFyMeLdigV/poN2fbMKCho0ROe3PZ8YAAEDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T05:28:18.687970Z"},"content_sha256":"0e448182dfbb7a0a28a923fa2cf6afe4be03d703f0c692a1932c2728165c1af1","schema_version":"1.0","event_id":"sha256:0e448182dfbb7a0a28a923fa2cf6afe4be03d703f0c692a1932c2728165c1af1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:RHY76HQQ6I3ZDQSM7SFYLPVH3M","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Partial Interference Alignment for K-user MIMO Interference Channels","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Huang Huang, Vincent K. N. Lau","submitted_at":"2011-06-27T11:52:50Z","abstract_excerpt":"In this paper, we consider a Partial Interference Alignment and Interference Detection (PIAID) design for $K$-user quasi-static MIMO interference channels with discrete constellation inputs. Each transmitter has M antennas and transmits L independent data streams to the desired receiver with N receive antennas. We focus on the case where not all K-1 interfering transmitters can be aligned at every receiver. As a result, there will be residual interference at each receiver that cannot be aligned. Each receiver detects and cancels the residual interference based on the constellation map. However"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.5367","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":"2026-05-18T02:01:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/0uJKdzoMjErlU0pS5Ux7N1edHXMzCiH2yOvN2fwlWik2hx2uDVcRbHYDi53Eb4eTaBCT9sw9qYzzBG7NHAVDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T05:28:18.688347Z"},"content_sha256":"b72bad386e9c965b279c52a6ae62498e8178aa4438224dcb066cc7604a863b5f","schema_version":"1.0","event_id":"sha256:b72bad386e9c965b279c52a6ae62498e8178aa4438224dcb066cc7604a863b5f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/RHY76HQQ6I3ZDQSM7SFYLPVH3M/bundle.json","state_url":"https://pith.science/pith/RHY76HQQ6I3ZDQSM7SFYLPVH3M/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/RHY76HQQ6I3ZDQSM7SFYLPVH3M/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":"2026-06-04T05:28:18Z","links":{"resolver":"https://pith.science/pith/RHY76HQQ6I3ZDQSM7SFYLPVH3M","bundle":"https://pith.science/pith/RHY76HQQ6I3ZDQSM7SFYLPVH3M/bundle.json","state":"https://pith.science/pith/RHY76HQQ6I3ZDQSM7SFYLPVH3M/state.json","well_known_bundle":"https://pith.science/.well-known/pith/RHY76HQQ6I3ZDQSM7SFYLPVH3M/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:RHY76HQQ6I3ZDQSM7SFYLPVH3M","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":"8500f56e5b28182d99145aee823fd03345a9e0a4f22ecfe938c0f2595a3b4f24","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2011-06-27T11:52:50Z","title_canon_sha256":"a8c5b728bd22593d735e4d476ca79bd353f5c36e9339959bb151cc35857b68e1"},"schema_version":"1.0","source":{"id":"1106.5367","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1106.5367","created_at":"2026-05-18T02:01:30Z"},{"alias_kind":"arxiv_version","alias_value":"1106.5367v1","created_at":"2026-05-18T02:01:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1106.5367","created_at":"2026-05-18T02:01:30Z"},{"alias_kind":"pith_short_12","alias_value":"RHY76HQQ6I3Z","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_16","alias_value":"RHY76HQQ6I3ZDQSM","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_8","alias_value":"RHY76HQQ","created_at":"2026-05-18T12:26:41Z"}],"graph_snapshots":[{"event_id":"sha256:b72bad386e9c965b279c52a6ae62498e8178aa4438224dcb066cc7604a863b5f","target":"graph","created_at":"2026-05-18T02:01:30Z","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 paper, we consider a Partial Interference Alignment and Interference Detection (PIAID) design for $K$-user quasi-static MIMO interference channels with discrete constellation inputs. Each transmitter has M antennas and transmits L independent data streams to the desired receiver with N receive antennas. We focus on the case where not all K-1 interfering transmitters can be aligned at every receiver. As a result, there will be residual interference at each receiver that cannot be aligned. Each receiver detects and cancels the residual interference based on the constellation map. However","authors_text":"Huang Huang, Vincent K. N. Lau","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2011-06-27T11:52:50Z","title":"Partial Interference Alignment for K-user MIMO Interference Channels"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.5367","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":"sha256:0e448182dfbb7a0a28a923fa2cf6afe4be03d703f0c692a1932c2728165c1af1","target":"record","created_at":"2026-05-18T02:01:30Z","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":"8500f56e5b28182d99145aee823fd03345a9e0a4f22ecfe938c0f2595a3b4f24","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2011-06-27T11:52:50Z","title_canon_sha256":"a8c5b728bd22593d735e4d476ca79bd353f5c36e9339959bb151cc35857b68e1"},"schema_version":"1.0","source":{"id":"1106.5367","kind":"arxiv","version":1}},"canonical_sha256":"89f1ff1e10f23791c24cfc8b85bea7db3ca9b0bddea155c7d02b8c3e5f3c5148","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"89f1ff1e10f23791c24cfc8b85bea7db3ca9b0bddea155c7d02b8c3e5f3c5148","first_computed_at":"2026-05-18T02:01:30.421018Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:01:30.421018Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"lMfYuy7sxa//vIVdcdPMRkIdzGOWWsfGWtvDXxeALZlRUji4oel141I+VCD429Uz/zrDU5Y0Jv7mIS/4nvwIAA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:01:30.421396Z","signed_message":"canonical_sha256_bytes"},"source_id":"1106.5367","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0e448182dfbb7a0a28a923fa2cf6afe4be03d703f0c692a1932c2728165c1af1","sha256:b72bad386e9c965b279c52a6ae62498e8178aa4438224dcb066cc7604a863b5f"],"state_sha256":"76dda8df3fa8759c18133cc03f4a1decb86fb887604fabc2088507979ab5b52a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8ClIibeHIItTVi8ZDkoGT0OYDFgJafKgoSmU/zNhScdq+/ENQ4zn/c4AuzekNoi3oHudKGW5tBCgoFrGX/3kBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T05:28:18.691077Z","bundle_sha256":"e23182a3ef549d7e7ac61dd41090f0399f90d4c758494fe77f45404a175fb068"}}