{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:B5GKGUBTKEZKKTYY5NRPDJ6VXY","short_pith_number":"pith:B5GKGUBT","canonical_record":{"source":{"id":"1405.0724","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2014-05-04T17:53:42Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"ad755da886c6667947b35f6b2424d1f127824bc9781cf81156ae2df4128d5fc8","abstract_canon_sha256":"f37e777832b474ab9ad442da66d4c31a42f93555ada060d433f5504fd8d8ba52"},"schema_version":"1.0"},"canonical_sha256":"0f4ca350335132a54f18eb62f1a7d5be0a527cd1142e9c7f8388b663d480a2ed","source":{"kind":"arxiv","id":"1405.0724","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1405.0724","created_at":"2026-05-18T02:51:00Z"},{"alias_kind":"arxiv_version","alias_value":"1405.0724v2","created_at":"2026-05-18T02:51:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1405.0724","created_at":"2026-05-18T02:51:00Z"},{"alias_kind":"pith_short_12","alias_value":"B5GKGUBTKEZK","created_at":"2026-05-18T12:28:22Z"},{"alias_kind":"pith_short_16","alias_value":"B5GKGUBTKEZKKTYY","created_at":"2026-05-18T12:28:22Z"},{"alias_kind":"pith_short_8","alias_value":"B5GKGUBT","created_at":"2026-05-18T12:28:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:B5GKGUBTKEZKKTYY5NRPDJ6VXY","target":"record","payload":{"canonical_record":{"source":{"id":"1405.0724","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2014-05-04T17:53:42Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"ad755da886c6667947b35f6b2424d1f127824bc9781cf81156ae2df4128d5fc8","abstract_canon_sha256":"f37e777832b474ab9ad442da66d4c31a42f93555ada060d433f5504fd8d8ba52"},"schema_version":"1.0"},"canonical_sha256":"0f4ca350335132a54f18eb62f1a7d5be0a527cd1142e9c7f8388b663d480a2ed","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:51:00.567012Z","signature_b64":"oFmEY/UyL7I2zJFP4HlCOXNDIByff44WKFsunevmEeX+r45LdT35wyhl0GljGgfwYSnUlXyLpivdNT3QMaXMBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0f4ca350335132a54f18eb62f1a7d5be0a527cd1142e9c7f8388b663d480a2ed","last_reissued_at":"2026-05-18T02:51:00.566592Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:51:00.566592Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1405.0724","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":"2026-05-18T02:51:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DEb4iFflP4vLK/CZqV9OKHyisnT+h3Y/GUxhfyUcW7kfuaibnac+bEQSPy2Gg0RHZ7ug1n2zGP35GSJfOHyOCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-19T23:00:16.365931Z"},"content_sha256":"58326b94d67a0ef8b6f1f1045a9677d2429daa04884d442591aaa16a650a6540","schema_version":"1.0","event_id":"sha256:58326b94d67a0ef8b6f1f1045a9677d2429daa04884d442591aaa16a650a6540"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:B5GKGUBTKEZKKTYY5NRPDJ6VXY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Rank Matching for Multihop Multiflow","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Hua Sun, Sundar R. Krishnamurthy, Syed A. Jafar","submitted_at":"2014-05-04T17:53:42Z","abstract_excerpt":"We study the degrees of freedom (DoF) of the layered 2 X 2 X 2 MIMO interference channel where each node is equipped with arbitrary number of antennas, the channels between the nodes have arbitrary rank constraints, and subject to the rank-constraints the channel coefficients can take arbitrary values. The DoF outer bounds reveal a fundamental rank-matching phenomenon, reminiscent of impedance matching in circuit theory. It is well known that the maximum power transfer in a circuit is achieved not for the maximum or minimum load impedance but for the load impedance that matches the source impe"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.0724","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":"2026-05-18T02:51:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"t4wGUcFkXX0kkclA/YFXLUZjADdSfEXpwJAdvqCX+bzoE26AIYIYm2Sy5/Oioiz4M84gH0Zmlm2I8noCk2+hAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-19T23:00:16.366274Z"},"content_sha256":"eb8ae6b54f776ce9b817847d13614df067dc4eb67490aa3fb925f51e31eede4e","schema_version":"1.0","event_id":"sha256:eb8ae6b54f776ce9b817847d13614df067dc4eb67490aa3fb925f51e31eede4e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/B5GKGUBTKEZKKTYY5NRPDJ6VXY/bundle.json","state_url":"https://pith.science/pith/B5GKGUBTKEZKKTYY5NRPDJ6VXY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/B5GKGUBTKEZKKTYY5NRPDJ6VXY/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":"2026-06-19T23:00:16Z","links":{"resolver":"https://pith.science/pith/B5GKGUBTKEZKKTYY5NRPDJ6VXY","bundle":"https://pith.science/pith/B5GKGUBTKEZKKTYY5NRPDJ6VXY/bundle.json","state":"https://pith.science/pith/B5GKGUBTKEZKKTYY5NRPDJ6VXY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/B5GKGUBTKEZKKTYY5NRPDJ6VXY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:B5GKGUBTKEZKKTYY5NRPDJ6VXY","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":"f37e777832b474ab9ad442da66d4c31a42f93555ada060d433f5504fd8d8ba52","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2014-05-04T17:53:42Z","title_canon_sha256":"ad755da886c6667947b35f6b2424d1f127824bc9781cf81156ae2df4128d5fc8"},"schema_version":"1.0","source":{"id":"1405.0724","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1405.0724","created_at":"2026-05-18T02:51:00Z"},{"alias_kind":"arxiv_version","alias_value":"1405.0724v2","created_at":"2026-05-18T02:51:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1405.0724","created_at":"2026-05-18T02:51:00Z"},{"alias_kind":"pith_short_12","alias_value":"B5GKGUBTKEZK","created_at":"2026-05-18T12:28:22Z"},{"alias_kind":"pith_short_16","alias_value":"B5GKGUBTKEZKKTYY","created_at":"2026-05-18T12:28:22Z"},{"alias_kind":"pith_short_8","alias_value":"B5GKGUBT","created_at":"2026-05-18T12:28:22Z"}],"graph_snapshots":[{"event_id":"sha256:eb8ae6b54f776ce9b817847d13614df067dc4eb67490aa3fb925f51e31eede4e","target":"graph","created_at":"2026-05-18T02:51:00Z","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 study the degrees of freedom (DoF) of the layered 2 X 2 X 2 MIMO interference channel where each node is equipped with arbitrary number of antennas, the channels between the nodes have arbitrary rank constraints, and subject to the rank-constraints the channel coefficients can take arbitrary values. The DoF outer bounds reveal a fundamental rank-matching phenomenon, reminiscent of impedance matching in circuit theory. It is well known that the maximum power transfer in a circuit is achieved not for the maximum or minimum load impedance but for the load impedance that matches the source impe","authors_text":"Hua Sun, Sundar R. Krishnamurthy, Syed A. Jafar","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2014-05-04T17:53:42Z","title":"Rank Matching for Multihop Multiflow"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.0724","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":"sha256:58326b94d67a0ef8b6f1f1045a9677d2429daa04884d442591aaa16a650a6540","target":"record","created_at":"2026-05-18T02:51:00Z","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":"f37e777832b474ab9ad442da66d4c31a42f93555ada060d433f5504fd8d8ba52","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2014-05-04T17:53:42Z","title_canon_sha256":"ad755da886c6667947b35f6b2424d1f127824bc9781cf81156ae2df4128d5fc8"},"schema_version":"1.0","source":{"id":"1405.0724","kind":"arxiv","version":2}},"canonical_sha256":"0f4ca350335132a54f18eb62f1a7d5be0a527cd1142e9c7f8388b663d480a2ed","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0f4ca350335132a54f18eb62f1a7d5be0a527cd1142e9c7f8388b663d480a2ed","first_computed_at":"2026-05-18T02:51:00.566592Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:51:00.566592Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"oFmEY/UyL7I2zJFP4HlCOXNDIByff44WKFsunevmEeX+r45LdT35wyhl0GljGgfwYSnUlXyLpivdNT3QMaXMBw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:51:00.567012Z","signed_message":"canonical_sha256_bytes"},"source_id":"1405.0724","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:58326b94d67a0ef8b6f1f1045a9677d2429daa04884d442591aaa16a650a6540","sha256:eb8ae6b54f776ce9b817847d13614df067dc4eb67490aa3fb925f51e31eede4e"],"state_sha256":"09239303b8adbb6ca5eef9d60815cb00e3c31acca0f0b52ccdb0e9c67025e7c0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gOr4aYXfppSlZihEZSpSWB7CjiItwa5l/ZpXBV3aLENeA7J03fqM5jyFTywy5mRh+C178QkqKkgpjBMZ+Rl4BA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-19T23:00:16.368337Z","bundle_sha256":"173ac5f790860be4f82938d2cac986564ded530bd253d18ff94b1dff1d3aeb23"}}