{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:5XE6XBLIQXXLGSIM2C5H4OYLMH","short_pith_number":"pith:5XE6XBLI","canonical_record":{"source":{"id":"1103.4525","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2011-03-23T14:18:37Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"5d1bfaddbec64f5ad9c5a245b5e6a54e88b1a8adbe17446a65754de2d54d0e13","abstract_canon_sha256":"a06a861196911f51b621750ba2ee7e2a81ee023876512252bd138364945aa446"},"schema_version":"1.0"},"canonical_sha256":"edc9eb856885eeb3490cd0ba7e3b0b61e7116d0f78a434b1f732f96f4f9ccf70","source":{"kind":"arxiv","id":"1103.4525","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1103.4525","created_at":"2026-05-18T02:02:47Z"},{"alias_kind":"arxiv_version","alias_value":"1103.4525v1","created_at":"2026-05-18T02:02:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1103.4525","created_at":"2026-05-18T02:02:47Z"},{"alias_kind":"pith_short_12","alias_value":"5XE6XBLIQXXL","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_16","alias_value":"5XE6XBLIQXXLGSIM","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_8","alias_value":"5XE6XBLI","created_at":"2026-05-18T12:26:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:5XE6XBLIQXXLGSIM2C5H4OYLMH","target":"record","payload":{"canonical_record":{"source":{"id":"1103.4525","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2011-03-23T14:18:37Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"5d1bfaddbec64f5ad9c5a245b5e6a54e88b1a8adbe17446a65754de2d54d0e13","abstract_canon_sha256":"a06a861196911f51b621750ba2ee7e2a81ee023876512252bd138364945aa446"},"schema_version":"1.0"},"canonical_sha256":"edc9eb856885eeb3490cd0ba7e3b0b61e7116d0f78a434b1f732f96f4f9ccf70","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:02:47.807261Z","signature_b64":"IhhHjrq0hv/vVtbtuF9IQ3L2Q6PHCxhq1cCIDnbg8sgJPPW+fLttlf4/X+uWCVVnuVtHGTgLdMrc6vnDHsdbCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"edc9eb856885eeb3490cd0ba7e3b0b61e7116d0f78a434b1f732f96f4f9ccf70","last_reissued_at":"2026-05-18T02:02:47.806551Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:02:47.806551Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1103.4525","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":"2026-05-18T02:02:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VKFh2k6zehdV0dSQEcjpWTWs8RpQzyOtXwcjXj6qeNyX+RV3Lb8C0/s6M6wN+VKClm/t3JMK2lFQPLIbX0qqBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T04:26:39.564345Z"},"content_sha256":"812ee7fab556e65e5190883c2d28d6b9cf080e5f262bbdedb95e3d5a3d54ab73","schema_version":"1.0","event_id":"sha256:812ee7fab556e65e5190883c2d28d6b9cf080e5f262bbdedb95e3d5a3d54ab73"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:5XE6XBLIQXXLGSIM2C5H4OYLMH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Robust Lattice Alignment for K-user MIMO Interference Channels with Imperfect Channel Knowledge","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Huang Huang, Sheng Liu, Vincent K. N. Lau, Yinggang Du","submitted_at":"2011-03-23T14:18:37Z","abstract_excerpt":"In this paper, we consider a robust lattice alignment design for K-user quasi-static MIMO interference channels with imperfect channel knowledge. With random Gaussian inputs, the conventional interference alignment (IA) method has the feasibility problem when the channel is quasi-static. On the other hand, structured lattices can create structured interference as opposed to the random interference caused by random Gaussian symbols. The structured interference space can be exploited to transmit the desired signals over the gaps. However, the existing alignment methods on the lattice codes for q"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.4525","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":"2026-05-18T02:02:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oJHnlY7FcNixiddAcpKAW/NuGfeM+eaTZZXmwrfEDfweEC5t73zuO1S8ONMPv+zN9YvgjgWsaHxGiAxtrmv+Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T04:26:39.564709Z"},"content_sha256":"0959c7b131fb0c6107c06bf176a9a17dd45a8f83dba02cced53178dde9446fc3","schema_version":"1.0","event_id":"sha256:0959c7b131fb0c6107c06bf176a9a17dd45a8f83dba02cced53178dde9446fc3"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5XE6XBLIQXXLGSIM2C5H4OYLMH/bundle.json","state_url":"https://pith.science/pith/5XE6XBLIQXXLGSIM2C5H4OYLMH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5XE6XBLIQXXLGSIM2C5H4OYLMH/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":"2026-05-27T04:26:39Z","links":{"resolver":"https://pith.science/pith/5XE6XBLIQXXLGSIM2C5H4OYLMH","bundle":"https://pith.science/pith/5XE6XBLIQXXLGSIM2C5H4OYLMH/bundle.json","state":"https://pith.science/pith/5XE6XBLIQXXLGSIM2C5H4OYLMH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5XE6XBLIQXXLGSIM2C5H4OYLMH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:5XE6XBLIQXXLGSIM2C5H4OYLMH","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":"a06a861196911f51b621750ba2ee7e2a81ee023876512252bd138364945aa446","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2011-03-23T14:18:37Z","title_canon_sha256":"5d1bfaddbec64f5ad9c5a245b5e6a54e88b1a8adbe17446a65754de2d54d0e13"},"schema_version":"1.0","source":{"id":"1103.4525","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1103.4525","created_at":"2026-05-18T02:02:47Z"},{"alias_kind":"arxiv_version","alias_value":"1103.4525v1","created_at":"2026-05-18T02:02:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1103.4525","created_at":"2026-05-18T02:02:47Z"},{"alias_kind":"pith_short_12","alias_value":"5XE6XBLIQXXL","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_16","alias_value":"5XE6XBLIQXXLGSIM","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_8","alias_value":"5XE6XBLI","created_at":"2026-05-18T12:26:22Z"}],"graph_snapshots":[{"event_id":"sha256:0959c7b131fb0c6107c06bf176a9a17dd45a8f83dba02cced53178dde9446fc3","target":"graph","created_at":"2026-05-18T02:02:47Z","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 robust lattice alignment design for K-user quasi-static MIMO interference channels with imperfect channel knowledge. With random Gaussian inputs, the conventional interference alignment (IA) method has the feasibility problem when the channel is quasi-static. On the other hand, structured lattices can create structured interference as opposed to the random interference caused by random Gaussian symbols. The structured interference space can be exploited to transmit the desired signals over the gaps. However, the existing alignment methods on the lattice codes for q","authors_text":"Huang Huang, Sheng Liu, Vincent K. N. Lau, Yinggang Du","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2011-03-23T14:18:37Z","title":"Robust Lattice Alignment for K-user MIMO Interference Channels with Imperfect Channel Knowledge"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.4525","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":"sha256:812ee7fab556e65e5190883c2d28d6b9cf080e5f262bbdedb95e3d5a3d54ab73","target":"record","created_at":"2026-05-18T02:02:47Z","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":"a06a861196911f51b621750ba2ee7e2a81ee023876512252bd138364945aa446","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2011-03-23T14:18:37Z","title_canon_sha256":"5d1bfaddbec64f5ad9c5a245b5e6a54e88b1a8adbe17446a65754de2d54d0e13"},"schema_version":"1.0","source":{"id":"1103.4525","kind":"arxiv","version":1}},"canonical_sha256":"edc9eb856885eeb3490cd0ba7e3b0b61e7116d0f78a434b1f732f96f4f9ccf70","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"edc9eb856885eeb3490cd0ba7e3b0b61e7116d0f78a434b1f732f96f4f9ccf70","first_computed_at":"2026-05-18T02:02:47.806551Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:02:47.806551Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"IhhHjrq0hv/vVtbtuF9IQ3L2Q6PHCxhq1cCIDnbg8sgJPPW+fLttlf4/X+uWCVVnuVtHGTgLdMrc6vnDHsdbCA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:02:47.807261Z","signed_message":"canonical_sha256_bytes"},"source_id":"1103.4525","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:812ee7fab556e65e5190883c2d28d6b9cf080e5f262bbdedb95e3d5a3d54ab73","sha256:0959c7b131fb0c6107c06bf176a9a17dd45a8f83dba02cced53178dde9446fc3"],"state_sha256":"c2a3e1ac327f165c19eda7acb3f7efc4baf85327e141ebf2f7bf2df448a48ef2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KGCxyudYZKv6SHAbfIS4Zqvu6HU2+jRi6nFmuu8G9/CiWav3PymL2RIpn7rXL71vIZCL5cXjlKtGQTcMDppECw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T04:26:39.567241Z","bundle_sha256":"106d36b56a342f9c2acec6a6d75c4c892b382bb546165e5f27c558ac2ea7733e"}}