{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:TPQQKEXO5JA6H2KN2I7HJFKXUK","short_pith_number":"pith:TPQQKEXO","canonical_record":{"source":{"id":"1501.04775","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-01-20T12:18:21Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"dbe4f92fce7adb654b1603f396ae0e729c03725923ac8c11499aa026dd756886","abstract_canon_sha256":"8fff41600399406f3cc02ca6a7efdd7193eeed88bb22b9d40ba0116360b48230"},"schema_version":"1.0"},"canonical_sha256":"9be10512eeea41e3e94dd23e749557a28f4e1958ab9ff825532cc4fe0c6162dd","source":{"kind":"arxiv","id":"1501.04775","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1501.04775","created_at":"2026-05-18T02:28:30Z"},{"alias_kind":"arxiv_version","alias_value":"1501.04775v2","created_at":"2026-05-18T02:28:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.04775","created_at":"2026-05-18T02:28:30Z"},{"alias_kind":"pith_short_12","alias_value":"TPQQKEXO5JA6","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_16","alias_value":"TPQQKEXO5JA6H2KN","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_8","alias_value":"TPQQKEXO","created_at":"2026-05-18T12:29:42Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:TPQQKEXO5JA6H2KN2I7HJFKXUK","target":"record","payload":{"canonical_record":{"source":{"id":"1501.04775","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-01-20T12:18:21Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"dbe4f92fce7adb654b1603f396ae0e729c03725923ac8c11499aa026dd756886","abstract_canon_sha256":"8fff41600399406f3cc02ca6a7efdd7193eeed88bb22b9d40ba0116360b48230"},"schema_version":"1.0"},"canonical_sha256":"9be10512eeea41e3e94dd23e749557a28f4e1958ab9ff825532cc4fe0c6162dd","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:28:30.998622Z","signature_b64":"VItE0SIUmOkgzjsxh7cAz59BuMc3KS9OMfPGysgYA+c7Lfd6EpoOWtmoMlJNJPAMnO0tBh9/f5WvxiVoeohmDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9be10512eeea41e3e94dd23e749557a28f4e1958ab9ff825532cc4fe0c6162dd","last_reissued_at":"2026-05-18T02:28:30.997806Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:28:30.997806Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1501.04775","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":"2026-05-18T02:28:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"daRoDvzrZUXybgWtrIKFf7ObiYKuqLCGcGDT4/bQ8sp+vuZhuq8Md3Hrtg7TrnHU6/f7ftOhB1omugSJ1cBWAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T12:18:26.269525Z"},"content_sha256":"a0d3df60170a9d4072ff4a46f8fb62f9c7c19595fe355e6400f740c62dd1a73f","schema_version":"1.0","event_id":"sha256:a0d3df60170a9d4072ff4a46f8fb62f9c7c19595fe355e6400f740c62dd1a73f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:TPQQKEXO5JA6H2KN2I7HJFKXUK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Interference Aligned Space-Time Transmission with Diversity for the $2 \\times 2$ X-Network","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Abhinav Ganesan, K. Pavan Srinath","submitted_at":"2015-01-20T12:18:21Z","abstract_excerpt":"The sum degrees of freedom (DoF) of the two-transmitter, two-receiver multiple-input multiple-output (MIMO) X-Network ($2 \\times 2$ MIMO X-Network) with $M$ antennas at each node is known to be $\\frac{4M}{3}$. Transmission schemes which couple local channel-state-information-at-the-transmitter (CSIT) based precoding with space-time block coding to achieve the sum-DoF of this network are known specifically for $M=2,4$. These schemes have been proven to guarantee a diversity gain of $M$ when a finite-sized input constellation is employed. In this paper, an explicit transmission scheme that achie"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.04775","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":"2026-05-18T02:28:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pTJWvxVqHOqLtls1WxZvxZBVFmgAP3fEJIx37aArYgKQnHWjrfNlLr0f463SbYL4VWhY66GGM2yaR4hlL7bIBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T12:18:26.269899Z"},"content_sha256":"547464f219623e552f65983306c0d6100497c74c6118fc3394363f8179c2cb4b","schema_version":"1.0","event_id":"sha256:547464f219623e552f65983306c0d6100497c74c6118fc3394363f8179c2cb4b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TPQQKEXO5JA6H2KN2I7HJFKXUK/bundle.json","state_url":"https://pith.science/pith/TPQQKEXO5JA6H2KN2I7HJFKXUK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TPQQKEXO5JA6H2KN2I7HJFKXUK/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":"2026-05-28T12:18:26Z","links":{"resolver":"https://pith.science/pith/TPQQKEXO5JA6H2KN2I7HJFKXUK","bundle":"https://pith.science/pith/TPQQKEXO5JA6H2KN2I7HJFKXUK/bundle.json","state":"https://pith.science/pith/TPQQKEXO5JA6H2KN2I7HJFKXUK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TPQQKEXO5JA6H2KN2I7HJFKXUK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:TPQQKEXO5JA6H2KN2I7HJFKXUK","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":"8fff41600399406f3cc02ca6a7efdd7193eeed88bb22b9d40ba0116360b48230","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-01-20T12:18:21Z","title_canon_sha256":"dbe4f92fce7adb654b1603f396ae0e729c03725923ac8c11499aa026dd756886"},"schema_version":"1.0","source":{"id":"1501.04775","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1501.04775","created_at":"2026-05-18T02:28:30Z"},{"alias_kind":"arxiv_version","alias_value":"1501.04775v2","created_at":"2026-05-18T02:28:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.04775","created_at":"2026-05-18T02:28:30Z"},{"alias_kind":"pith_short_12","alias_value":"TPQQKEXO5JA6","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_16","alias_value":"TPQQKEXO5JA6H2KN","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_8","alias_value":"TPQQKEXO","created_at":"2026-05-18T12:29:42Z"}],"graph_snapshots":[{"event_id":"sha256:547464f219623e552f65983306c0d6100497c74c6118fc3394363f8179c2cb4b","target":"graph","created_at":"2026-05-18T02:28:30Z","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":"The sum degrees of freedom (DoF) of the two-transmitter, two-receiver multiple-input multiple-output (MIMO) X-Network ($2 \\times 2$ MIMO X-Network) with $M$ antennas at each node is known to be $\\frac{4M}{3}$. Transmission schemes which couple local channel-state-information-at-the-transmitter (CSIT) based precoding with space-time block coding to achieve the sum-DoF of this network are known specifically for $M=2,4$. These schemes have been proven to guarantee a diversity gain of $M$ when a finite-sized input constellation is employed. In this paper, an explicit transmission scheme that achie","authors_text":"Abhinav Ganesan, K. Pavan Srinath","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-01-20T12:18:21Z","title":"Interference Aligned Space-Time Transmission with Diversity for the $2 \\times 2$ X-Network"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.04775","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:a0d3df60170a9d4072ff4a46f8fb62f9c7c19595fe355e6400f740c62dd1a73f","target":"record","created_at":"2026-05-18T02:28:30Z","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":"8fff41600399406f3cc02ca6a7efdd7193eeed88bb22b9d40ba0116360b48230","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-01-20T12:18:21Z","title_canon_sha256":"dbe4f92fce7adb654b1603f396ae0e729c03725923ac8c11499aa026dd756886"},"schema_version":"1.0","source":{"id":"1501.04775","kind":"arxiv","version":2}},"canonical_sha256":"9be10512eeea41e3e94dd23e749557a28f4e1958ab9ff825532cc4fe0c6162dd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9be10512eeea41e3e94dd23e749557a28f4e1958ab9ff825532cc4fe0c6162dd","first_computed_at":"2026-05-18T02:28:30.997806Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:28:30.997806Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"VItE0SIUmOkgzjsxh7cAz59BuMc3KS9OMfPGysgYA+c7Lfd6EpoOWtmoMlJNJPAMnO0tBh9/f5WvxiVoeohmDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:28:30.998622Z","signed_message":"canonical_sha256_bytes"},"source_id":"1501.04775","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a0d3df60170a9d4072ff4a46f8fb62f9c7c19595fe355e6400f740c62dd1a73f","sha256:547464f219623e552f65983306c0d6100497c74c6118fc3394363f8179c2cb4b"],"state_sha256":"8e3db7ac5f99ed0cc9704fb8013ad7466944b58e8e776604f522341bd6e1455b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yCUGwo38w9UQ+lIQQbGL0ZVcAhe+SIl9yYOYZCNn4FNM5RhDGsaAG5cT22W7AnAnG+vV6ImyQSRwGBdWKsWYCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T12:18:26.272269Z","bundle_sha256":"57ad8c2043e78cfe51d3381655e13259d7679db03596ff7d4e1f232638183350"}}