{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:BDZ6NL522YTNP7SGLHPTB7TYRW","short_pith_number":"pith:BDZ6NL52","canonical_record":{"source":{"id":"1307.2105","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2013-07-08T14:19:21Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"0cf106b353e5e83cd76888c3ff1de999f19931a7c72c08b8b3171f84045a566a","abstract_canon_sha256":"6082886216af2995b15deb40b09a72c9545c914466685e0326f1d26836d23db1"},"schema_version":"1.0"},"canonical_sha256":"08f3e6afbad626d7fe4659df30fe788da7f0a1f724bddc69e4b9670748d96d48","source":{"kind":"arxiv","id":"1307.2105","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1307.2105","created_at":"2026-05-18T03:19:02Z"},{"alias_kind":"arxiv_version","alias_value":"1307.2105v1","created_at":"2026-05-18T03:19:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.2105","created_at":"2026-05-18T03:19:02Z"},{"alias_kind":"pith_short_12","alias_value":"BDZ6NL522YTN","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_16","alias_value":"BDZ6NL522YTNP7SG","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_8","alias_value":"BDZ6NL52","created_at":"2026-05-18T12:27:38Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:BDZ6NL522YTNP7SGLHPTB7TYRW","target":"record","payload":{"canonical_record":{"source":{"id":"1307.2105","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2013-07-08T14:19:21Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"0cf106b353e5e83cd76888c3ff1de999f19931a7c72c08b8b3171f84045a566a","abstract_canon_sha256":"6082886216af2995b15deb40b09a72c9545c914466685e0326f1d26836d23db1"},"schema_version":"1.0"},"canonical_sha256":"08f3e6afbad626d7fe4659df30fe788da7f0a1f724bddc69e4b9670748d96d48","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:19:02.400503Z","signature_b64":"H6OUW35jKeb/9YIDpcka7JiWlZSHiFYSdW/97u8eBfmMzdvsEGm/+vvhrtP9LxTBi0vijB8/fUg7cCJbHk3fCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"08f3e6afbad626d7fe4659df30fe788da7f0a1f724bddc69e4b9670748d96d48","last_reissued_at":"2026-05-18T03:19:02.399778Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:19:02.399778Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1307.2105","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":"2026-05-18T03:19:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VCbdgzfBj+khZ+s5Zf59qWLUwafj5r4VDdGjfR6JXUYKjPUYxTivU3pCDQOiqLvYlQTl14iurd8MFC974671Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T08:17:37.783729Z"},"content_sha256":"4c0616dc63dc66fb54deea6dbfd485abbb651094170aec68ea848ee0c94c8cd7","schema_version":"1.0","event_id":"sha256:4c0616dc63dc66fb54deea6dbfd485abbb651094170aec68ea848ee0c94c8cd7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:BDZ6NL522YTNP7SGLHPTB7TYRW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Successive Integer-Forcing and its Sum-Rate Optimality","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Bobak Nazer, Or Ordentlich, Uri Erez","submitted_at":"2013-07-08T14:19:21Z","abstract_excerpt":"Integer-forcing receivers generalize traditional linear receivers for the multiple-input multiple-output channel by decoding integer-linear combinations of the transmitted streams, rather then the streams themselves. Previous works have shown that the additional degree of freedom in choosing the integer coefficients enables this receiver to approach the performance of maximum-likelihood decoding in various scenarios. Nonetheless, even for the optimal choice of integer coefficients, the additive noise at the equalizer's output is still correlated. In this work we study a variant of integer-forc"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.2105","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":"2026-05-18T03:19:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uywasYperHIPZOX02vJcJ90DRuJHA/rY+KvPt5hV8jB0w9azb5Oba12PGOU9Zqccw6Ysy4RSOMwU+Jd8x8LLAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T08:17:37.784074Z"},"content_sha256":"c15434897e26b2ae36c403b65161ab51a959bbd0e26db9db99ee9e253ebbd75b","schema_version":"1.0","event_id":"sha256:c15434897e26b2ae36c403b65161ab51a959bbd0e26db9db99ee9e253ebbd75b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BDZ6NL522YTNP7SGLHPTB7TYRW/bundle.json","state_url":"https://pith.science/pith/BDZ6NL522YTNP7SGLHPTB7TYRW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BDZ6NL522YTNP7SGLHPTB7TYRW/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":"2026-05-31T08:17:37Z","links":{"resolver":"https://pith.science/pith/BDZ6NL522YTNP7SGLHPTB7TYRW","bundle":"https://pith.science/pith/BDZ6NL522YTNP7SGLHPTB7TYRW/bundle.json","state":"https://pith.science/pith/BDZ6NL522YTNP7SGLHPTB7TYRW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BDZ6NL522YTNP7SGLHPTB7TYRW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:BDZ6NL522YTNP7SGLHPTB7TYRW","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":"6082886216af2995b15deb40b09a72c9545c914466685e0326f1d26836d23db1","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2013-07-08T14:19:21Z","title_canon_sha256":"0cf106b353e5e83cd76888c3ff1de999f19931a7c72c08b8b3171f84045a566a"},"schema_version":"1.0","source":{"id":"1307.2105","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1307.2105","created_at":"2026-05-18T03:19:02Z"},{"alias_kind":"arxiv_version","alias_value":"1307.2105v1","created_at":"2026-05-18T03:19:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.2105","created_at":"2026-05-18T03:19:02Z"},{"alias_kind":"pith_short_12","alias_value":"BDZ6NL522YTN","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_16","alias_value":"BDZ6NL522YTNP7SG","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_8","alias_value":"BDZ6NL52","created_at":"2026-05-18T12:27:38Z"}],"graph_snapshots":[{"event_id":"sha256:c15434897e26b2ae36c403b65161ab51a959bbd0e26db9db99ee9e253ebbd75b","target":"graph","created_at":"2026-05-18T03:19:02Z","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":"Integer-forcing receivers generalize traditional linear receivers for the multiple-input multiple-output channel by decoding integer-linear combinations of the transmitted streams, rather then the streams themselves. Previous works have shown that the additional degree of freedom in choosing the integer coefficients enables this receiver to approach the performance of maximum-likelihood decoding in various scenarios. Nonetheless, even for the optimal choice of integer coefficients, the additive noise at the equalizer's output is still correlated. In this work we study a variant of integer-forc","authors_text":"Bobak Nazer, Or Ordentlich, Uri Erez","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2013-07-08T14:19:21Z","title":"Successive Integer-Forcing and its Sum-Rate Optimality"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.2105","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":"sha256:4c0616dc63dc66fb54deea6dbfd485abbb651094170aec68ea848ee0c94c8cd7","target":"record","created_at":"2026-05-18T03:19:02Z","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":"6082886216af2995b15deb40b09a72c9545c914466685e0326f1d26836d23db1","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2013-07-08T14:19:21Z","title_canon_sha256":"0cf106b353e5e83cd76888c3ff1de999f19931a7c72c08b8b3171f84045a566a"},"schema_version":"1.0","source":{"id":"1307.2105","kind":"arxiv","version":1}},"canonical_sha256":"08f3e6afbad626d7fe4659df30fe788da7f0a1f724bddc69e4b9670748d96d48","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"08f3e6afbad626d7fe4659df30fe788da7f0a1f724bddc69e4b9670748d96d48","first_computed_at":"2026-05-18T03:19:02.399778Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:19:02.399778Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"H6OUW35jKeb/9YIDpcka7JiWlZSHiFYSdW/97u8eBfmMzdvsEGm/+vvhrtP9LxTBi0vijB8/fUg7cCJbHk3fCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:19:02.400503Z","signed_message":"canonical_sha256_bytes"},"source_id":"1307.2105","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4c0616dc63dc66fb54deea6dbfd485abbb651094170aec68ea848ee0c94c8cd7","sha256:c15434897e26b2ae36c403b65161ab51a959bbd0e26db9db99ee9e253ebbd75b"],"state_sha256":"91d77eed6ac324d5efbcfed5aa7be3becc63715d7330e43cb63d0521f73aefd8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nqwI6sMucs59JjEj8EZrv3sPjIDyZd75D9Y26ZzrCKi6VM+JLt/m7a4/YupOpQXiRGMh6HbVrjmN81qISa7FBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T08:17:37.786369Z","bundle_sha256":"d9382034f88c1f2d20c1da9d13d5c1509800701e739ede712ccb3dc0f74f4368"}}