{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:KGJXM55SOUWJKYRWEYMVOA4A75","short_pith_number":"pith:KGJXM55S","canonical_record":{"source":{"id":"1002.0424","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2010-02-02T08:54:23Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"25de1fbad3beff1548f7264ce3c3af12fd40f70760ef065f950095309ab00f7b","abstract_canon_sha256":"eb365b9047544c7c2fb590c818d5ea374d4a2872dfb911a63cf6fd21fa673f79"},"schema_version":"1.0"},"canonical_sha256":"51937677b2752c9562362619570380ff500633afefedfae6d815ee557b56e922","source":{"kind":"arxiv","id":"1002.0424","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1002.0424","created_at":"2026-05-18T04:39:59Z"},{"alias_kind":"arxiv_version","alias_value":"1002.0424v2","created_at":"2026-05-18T04:39:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1002.0424","created_at":"2026-05-18T04:39:59Z"},{"alias_kind":"pith_short_12","alias_value":"KGJXM55SOUWJ","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_16","alias_value":"KGJXM55SOUWJKYRW","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_8","alias_value":"KGJXM55S","created_at":"2026-05-18T12:26:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:KGJXM55SOUWJKYRWEYMVOA4A75","target":"record","payload":{"canonical_record":{"source":{"id":"1002.0424","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2010-02-02T08:54:23Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"25de1fbad3beff1548f7264ce3c3af12fd40f70760ef065f950095309ab00f7b","abstract_canon_sha256":"eb365b9047544c7c2fb590c818d5ea374d4a2872dfb911a63cf6fd21fa673f79"},"schema_version":"1.0"},"canonical_sha256":"51937677b2752c9562362619570380ff500633afefedfae6d815ee557b56e922","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:39:59.365753Z","signature_b64":"GZFW5thm8GBNA7DU2E9ILy9Y02kxqf+zTy2iA9ux3Q80XwpEu9t6zXWWe0YV/Fse/J6aBjAKyx7EdcN77U03Cg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"51937677b2752c9562362619570380ff500633afefedfae6d815ee557b56e922","last_reissued_at":"2026-05-18T04:39:59.365296Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:39:59.365296Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1002.0424","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":"2026-05-18T04:39:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uvQRPHqMOBnV1AfWnigLauHwOm8xdDDMDWfGP3IXSP7lGpJPF0zGVCnqtIguWF/BZR4zwCT5vhti4jM6bITNAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T19:33:16.577385Z"},"content_sha256":"c51a0b4d0ff1fd79393eaed82bcc8c4acfa8b38d4dd2419973890992abda4c92","schema_version":"1.0","event_id":"sha256:c51a0b4d0ff1fd79393eaed82bcc8c4acfa8b38d4dd2419973890992abda4c92"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:KGJXM55SOUWJKYRWEYMVOA4A75","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Cooperative Algorithms for MIMO Interference Channels","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Robert W. Heath Jr, Steven W. Peters","submitted_at":"2010-02-02T08:54:23Z","abstract_excerpt":"Interference alignment is a transmission technique for exploiting all available degrees of freedom in the interference channel with an arbitrary number of users. Most prior work on interference alignment, however, neglects interference from other nodes in the network not participating in the alignment operation. This paper proposes three generalizations of interference alignment for the multiple-antenna interference channel with multiple users that account for colored noise, which models uncoordinated interference. First, a minimum interference-plus-noise leakage algorithm is presented, and sh"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1002.0424","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":"2026-05-18T04:39:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jNbA4deuypg//ics4X7xUXLCcsJq2qS5DGWftCRAwWdZXFlnX/IA99f1ulr1jd4UQEVV9Dr4u1+vJuxRLu92Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T19:33:16.577738Z"},"content_sha256":"7ca71b489afab89633a1cf29fb461915b1b30c5cb9cbf11579f73de7436f98e8","schema_version":"1.0","event_id":"sha256:7ca71b489afab89633a1cf29fb461915b1b30c5cb9cbf11579f73de7436f98e8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KGJXM55SOUWJKYRWEYMVOA4A75/bundle.json","state_url":"https://pith.science/pith/KGJXM55SOUWJKYRWEYMVOA4A75/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KGJXM55SOUWJKYRWEYMVOA4A75/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":"2026-06-04T19:33:16Z","links":{"resolver":"https://pith.science/pith/KGJXM55SOUWJKYRWEYMVOA4A75","bundle":"https://pith.science/pith/KGJXM55SOUWJKYRWEYMVOA4A75/bundle.json","state":"https://pith.science/pith/KGJXM55SOUWJKYRWEYMVOA4A75/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KGJXM55SOUWJKYRWEYMVOA4A75/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:KGJXM55SOUWJKYRWEYMVOA4A75","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":"eb365b9047544c7c2fb590c818d5ea374d4a2872dfb911a63cf6fd21fa673f79","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2010-02-02T08:54:23Z","title_canon_sha256":"25de1fbad3beff1548f7264ce3c3af12fd40f70760ef065f950095309ab00f7b"},"schema_version":"1.0","source":{"id":"1002.0424","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1002.0424","created_at":"2026-05-18T04:39:59Z"},{"alias_kind":"arxiv_version","alias_value":"1002.0424v2","created_at":"2026-05-18T04:39:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1002.0424","created_at":"2026-05-18T04:39:59Z"},{"alias_kind":"pith_short_12","alias_value":"KGJXM55SOUWJ","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_16","alias_value":"KGJXM55SOUWJKYRW","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_8","alias_value":"KGJXM55S","created_at":"2026-05-18T12:26:09Z"}],"graph_snapshots":[{"event_id":"sha256:7ca71b489afab89633a1cf29fb461915b1b30c5cb9cbf11579f73de7436f98e8","target":"graph","created_at":"2026-05-18T04:39:59Z","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":"Interference alignment is a transmission technique for exploiting all available degrees of freedom in the interference channel with an arbitrary number of users. Most prior work on interference alignment, however, neglects interference from other nodes in the network not participating in the alignment operation. This paper proposes three generalizations of interference alignment for the multiple-antenna interference channel with multiple users that account for colored noise, which models uncoordinated interference. First, a minimum interference-plus-noise leakage algorithm is presented, and sh","authors_text":"Robert W. Heath Jr, Steven W. Peters","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2010-02-02T08:54:23Z","title":"Cooperative Algorithms for MIMO Interference Channels"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1002.0424","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:c51a0b4d0ff1fd79393eaed82bcc8c4acfa8b38d4dd2419973890992abda4c92","target":"record","created_at":"2026-05-18T04:39:59Z","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":"eb365b9047544c7c2fb590c818d5ea374d4a2872dfb911a63cf6fd21fa673f79","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2010-02-02T08:54:23Z","title_canon_sha256":"25de1fbad3beff1548f7264ce3c3af12fd40f70760ef065f950095309ab00f7b"},"schema_version":"1.0","source":{"id":"1002.0424","kind":"arxiv","version":2}},"canonical_sha256":"51937677b2752c9562362619570380ff500633afefedfae6d815ee557b56e922","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"51937677b2752c9562362619570380ff500633afefedfae6d815ee557b56e922","first_computed_at":"2026-05-18T04:39:59.365296Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:39:59.365296Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"GZFW5thm8GBNA7DU2E9ILy9Y02kxqf+zTy2iA9ux3Q80XwpEu9t6zXWWe0YV/Fse/J6aBjAKyx7EdcN77U03Cg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:39:59.365753Z","signed_message":"canonical_sha256_bytes"},"source_id":"1002.0424","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c51a0b4d0ff1fd79393eaed82bcc8c4acfa8b38d4dd2419973890992abda4c92","sha256:7ca71b489afab89633a1cf29fb461915b1b30c5cb9cbf11579f73de7436f98e8"],"state_sha256":"a39cfd83083e6199ea36e022e6c8cdbc0874cea4e19e33d9e843e7a8d151331c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1D7hKsgKbhZC0Owv1QzUWw8YSIGu6IUoarcjNAy4HzD1PtBP2Xq7sKWXqTC6Fzii4ZYKl5D1BMW2sxYM6hFMDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T19:33:16.579798Z","bundle_sha256":"81facfc658b11bf8c8f769cc712fade263656f3bdf37a4932fc0b99dcee92a63"}}