{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:N73QKJ2E6CCD5ULBIR5T3GIWHX","short_pith_number":"pith:N73QKJ2E","canonical_record":{"source":{"id":"1501.02012","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-01-09T01:23:03Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"7e116b9c70ff4d75623c45214bd17740f4c10b9b15e487a909da4c847bb5e6b6","abstract_canon_sha256":"e05b31e7bcf590fb6a99113253e9f74600031ae02e7f6f5ae861721080162428"},"schema_version":"1.0"},"canonical_sha256":"6ff7052744f0843ed161447b3d99163de81d92902e11cdfa8470c0291b8be8fb","source":{"kind":"arxiv","id":"1501.02012","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1501.02012","created_at":"2026-05-18T02:19:50Z"},{"alias_kind":"arxiv_version","alias_value":"1501.02012v2","created_at":"2026-05-18T02:19:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.02012","created_at":"2026-05-18T02:19:50Z"},{"alias_kind":"pith_short_12","alias_value":"N73QKJ2E6CCD","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_16","alias_value":"N73QKJ2E6CCD5ULB","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_8","alias_value":"N73QKJ2E","created_at":"2026-05-18T12:29:32Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:N73QKJ2E6CCD5ULBIR5T3GIWHX","target":"record","payload":{"canonical_record":{"source":{"id":"1501.02012","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-01-09T01:23:03Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"7e116b9c70ff4d75623c45214bd17740f4c10b9b15e487a909da4c847bb5e6b6","abstract_canon_sha256":"e05b31e7bcf590fb6a99113253e9f74600031ae02e7f6f5ae861721080162428"},"schema_version":"1.0"},"canonical_sha256":"6ff7052744f0843ed161447b3d99163de81d92902e11cdfa8470c0291b8be8fb","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:19:50.195613Z","signature_b64":"BuwrkXpp1wf3cMT7bHpv1XJVmRxQjZ7JZNA5FB+m/PjuS37A0pqwPDblk5/Eo30S9aFMJUsEqxE19yM1osn5Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6ff7052744f0843ed161447b3d99163de81d92902e11cdfa8470c0291b8be8fb","last_reissued_at":"2026-05-18T02:19:50.195134Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:19:50.195134Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1501.02012","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":"2026-05-18T02:19:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KHu4kXQQ+4pd97VvSh6zKp8NjwmhFa7V8ozZJwTbLqe9z2ICGuBZplNXj8MrR3YUBtJjWqb49ebIqUBrGfu6DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-01T07:22:27.254652Z"},"content_sha256":"0d3ad34d7d9f517fdff262615169a967af273a4a6aa31205c35fc1543748478a","schema_version":"1.0","event_id":"sha256:0d3ad34d7d9f517fdff262615169a967af273a4a6aa31205c35fc1543748478a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:N73QKJ2E6CCD5ULBIR5T3GIWHX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Full Diversity Unitary Precoded Integer-Forcing","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Amin Sakzad, Emanuele Viterbo","submitted_at":"2015-01-09T01:23:03Z","abstract_excerpt":"We consider a point-to-point flat-fading MIMO channel with channel state information known both at transmitter and receiver. At the transmitter side, a lattice coding scheme is employed at each antenna to map information symbols to independent lattice codewords drawn from the same codebook. Each lattice codeword is then multiplied by a unitary precoding matrix ${\\bf P}$ and sent through the channel. At the receiver side, an integer-forcing (IF) linear receiver is employed. We denote this scheme as unitary precoded integer-forcing (UPIF). We show that UPIF can achieve full-diversity under a con"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.02012","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":"2026-05-18T02:19:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1Rs8sMbfiIVtqcK5Ppx3OCdMsaEce+aUxCbfM4ZX982fTwEMpI8QggWYg49kUErTtCQNiIrCut/6Heqa8dexDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-01T07:22:27.255005Z"},"content_sha256":"6803a65f556c9731d5314072ac6c1a79390e4924f36bf986252ef94319297674","schema_version":"1.0","event_id":"sha256:6803a65f556c9731d5314072ac6c1a79390e4924f36bf986252ef94319297674"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/N73QKJ2E6CCD5ULBIR5T3GIWHX/bundle.json","state_url":"https://pith.science/pith/N73QKJ2E6CCD5ULBIR5T3GIWHX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/N73QKJ2E6CCD5ULBIR5T3GIWHX/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":"2026-07-01T07:22:27Z","links":{"resolver":"https://pith.science/pith/N73QKJ2E6CCD5ULBIR5T3GIWHX","bundle":"https://pith.science/pith/N73QKJ2E6CCD5ULBIR5T3GIWHX/bundle.json","state":"https://pith.science/pith/N73QKJ2E6CCD5ULBIR5T3GIWHX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/N73QKJ2E6CCD5ULBIR5T3GIWHX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:N73QKJ2E6CCD5ULBIR5T3GIWHX","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":"e05b31e7bcf590fb6a99113253e9f74600031ae02e7f6f5ae861721080162428","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-01-09T01:23:03Z","title_canon_sha256":"7e116b9c70ff4d75623c45214bd17740f4c10b9b15e487a909da4c847bb5e6b6"},"schema_version":"1.0","source":{"id":"1501.02012","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1501.02012","created_at":"2026-05-18T02:19:50Z"},{"alias_kind":"arxiv_version","alias_value":"1501.02012v2","created_at":"2026-05-18T02:19:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.02012","created_at":"2026-05-18T02:19:50Z"},{"alias_kind":"pith_short_12","alias_value":"N73QKJ2E6CCD","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_16","alias_value":"N73QKJ2E6CCD5ULB","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_8","alias_value":"N73QKJ2E","created_at":"2026-05-18T12:29:32Z"}],"graph_snapshots":[{"event_id":"sha256:6803a65f556c9731d5314072ac6c1a79390e4924f36bf986252ef94319297674","target":"graph","created_at":"2026-05-18T02:19:50Z","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":"We consider a point-to-point flat-fading MIMO channel with channel state information known both at transmitter and receiver. At the transmitter side, a lattice coding scheme is employed at each antenna to map information symbols to independent lattice codewords drawn from the same codebook. Each lattice codeword is then multiplied by a unitary precoding matrix ${\\bf P}$ and sent through the channel. At the receiver side, an integer-forcing (IF) linear receiver is employed. We denote this scheme as unitary precoded integer-forcing (UPIF). We show that UPIF can achieve full-diversity under a con","authors_text":"Amin Sakzad, Emanuele Viterbo","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-01-09T01:23:03Z","title":"Full Diversity Unitary Precoded Integer-Forcing"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.02012","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":"sha256:0d3ad34d7d9f517fdff262615169a967af273a4a6aa31205c35fc1543748478a","target":"record","created_at":"2026-05-18T02:19:50Z","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":"e05b31e7bcf590fb6a99113253e9f74600031ae02e7f6f5ae861721080162428","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-01-09T01:23:03Z","title_canon_sha256":"7e116b9c70ff4d75623c45214bd17740f4c10b9b15e487a909da4c847bb5e6b6"},"schema_version":"1.0","source":{"id":"1501.02012","kind":"arxiv","version":2}},"canonical_sha256":"6ff7052744f0843ed161447b3d99163de81d92902e11cdfa8470c0291b8be8fb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6ff7052744f0843ed161447b3d99163de81d92902e11cdfa8470c0291b8be8fb","first_computed_at":"2026-05-18T02:19:50.195134Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:19:50.195134Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"BuwrkXpp1wf3cMT7bHpv1XJVmRxQjZ7JZNA5FB+m/PjuS37A0pqwPDblk5/Eo30S9aFMJUsEqxE19yM1osn5Dw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:19:50.195613Z","signed_message":"canonical_sha256_bytes"},"source_id":"1501.02012","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0d3ad34d7d9f517fdff262615169a967af273a4a6aa31205c35fc1543748478a","sha256:6803a65f556c9731d5314072ac6c1a79390e4924f36bf986252ef94319297674"],"state_sha256":"028da81f6f638d72d4fbdc6ca4c8d8fef6a676412524a08ba746ed24d4829f70"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0gRfGdzI6Y/eOtO9A+sUPEa/vqvOk6fp0D1vPsJiCcQE4oI0iKkwzAXtTtL3ok/d1Hi/3scqHnjto+JB432SBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-01T07:22:27.257535Z","bundle_sha256":"937993e60d5971d6a0ad7d269ce5b638baa688dae504937628d7321b03075f12"}}