{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:HJZ5NI23NET7NBEYLUYXHC7OG3","short_pith_number":"pith:HJZ5NI23","canonical_record":{"source":{"id":"1012.2350","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2010-12-10T19:08:39Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"25b59bd037c01945f7d5fd48e8cf1a1da9338cbf562202ddfb4235918bbe5520","abstract_canon_sha256":"4c2918390cee962d0a6b24abb8b6046a6b68018658e28462772dfbf512582b6c"},"schema_version":"1.0"},"canonical_sha256":"3a73d6a35b6927f684985d31738bee36c84d9a50057d5d00ecfb68d6a8c53682","source":{"kind":"arxiv","id":"1012.2350","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1012.2350","created_at":"2026-05-18T04:33:38Z"},{"alias_kind":"arxiv_version","alias_value":"1012.2350v1","created_at":"2026-05-18T04:33:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1012.2350","created_at":"2026-05-18T04:33:38Z"},{"alias_kind":"pith_short_12","alias_value":"HJZ5NI23NET7","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_16","alias_value":"HJZ5NI23NET7NBEY","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_8","alias_value":"HJZ5NI23","created_at":"2026-05-18T12:26:07Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:HJZ5NI23NET7NBEYLUYXHC7OG3","target":"record","payload":{"canonical_record":{"source":{"id":"1012.2350","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2010-12-10T19:08:39Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"25b59bd037c01945f7d5fd48e8cf1a1da9338cbf562202ddfb4235918bbe5520","abstract_canon_sha256":"4c2918390cee962d0a6b24abb8b6046a6b68018658e28462772dfbf512582b6c"},"schema_version":"1.0"},"canonical_sha256":"3a73d6a35b6927f684985d31738bee36c84d9a50057d5d00ecfb68d6a8c53682","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:33:38.042106Z","signature_b64":"uP/40aK3k+tFPK9OXlPjFzmwiOR6Aq2MJx7+dyaxPOCQVHqwmYcfjTwLOPjq6pv4kxGyEqWNohcElWe1NZaLBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3a73d6a35b6927f684985d31738bee36c84d9a50057d5d00ecfb68d6a8c53682","last_reissued_at":"2026-05-18T04:33:38.041514Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:33:38.041514Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1012.2350","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":"2026-05-18T04:33:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"te5OVQN+Pom8Mkx5w3CnLrOnLmmsHJAIuuTfQQbte8ReMxq/BsXnFx39NLdHU3swIWyqEl18lCsBRTHvE4SXCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T17:32:04.578213Z"},"content_sha256":"4ff42c00c285019f99c6c58531b65c0e98074db394a07e0c78b069408a12fcf8","schema_version":"1.0","event_id":"sha256:4ff42c00c285019f99c6c58531b65c0e98074db394a07e0c78b069408a12fcf8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:HJZ5NI23NET7NBEYLUYXHC7OG3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Aligned Interference Neutralization and the Degrees of Freedom of the 2x2x2 Interference Channel","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Sae-Young Chung, Sang-Woon Jeon, Syed A. Jafar, Tiangao Gou","submitted_at":"2010-12-10T19:08:39Z","abstract_excerpt":"We show that the 2x2x2 interference channel, i.e., the multihop interference channel formed by concatenation of two 2-user interference channels achieves the min-cut outer bound value of 2 DoF, for almost all values of channel coefficients, for both time-varying or fixed channel coefficients. The key to this result is a new idea, called aligned interference neutralization, that provides a way to align interference terms over each hop in a manner that allows them to be cancelled over the air at the last hop."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1012.2350","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":"2026-05-18T04:33:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dqak4pvI6PGS7auhjeZKON6C2tiXVxQBTOz70a0c75zkQRKQ0Oa/De0+tjU8xC/0qgsqyaELPNO0Z2RAtiPmAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T17:32:04.578956Z"},"content_sha256":"8b4ab886109c87e9a19ec6f41cd337f098e507903ccedfb43a94691df5325276","schema_version":"1.0","event_id":"sha256:8b4ab886109c87e9a19ec6f41cd337f098e507903ccedfb43a94691df5325276"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HJZ5NI23NET7NBEYLUYXHC7OG3/bundle.json","state_url":"https://pith.science/pith/HJZ5NI23NET7NBEYLUYXHC7OG3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HJZ5NI23NET7NBEYLUYXHC7OG3/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":"2026-06-09T17:32:04Z","links":{"resolver":"https://pith.science/pith/HJZ5NI23NET7NBEYLUYXHC7OG3","bundle":"https://pith.science/pith/HJZ5NI23NET7NBEYLUYXHC7OG3/bundle.json","state":"https://pith.science/pith/HJZ5NI23NET7NBEYLUYXHC7OG3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HJZ5NI23NET7NBEYLUYXHC7OG3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:HJZ5NI23NET7NBEYLUYXHC7OG3","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":"4c2918390cee962d0a6b24abb8b6046a6b68018658e28462772dfbf512582b6c","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2010-12-10T19:08:39Z","title_canon_sha256":"25b59bd037c01945f7d5fd48e8cf1a1da9338cbf562202ddfb4235918bbe5520"},"schema_version":"1.0","source":{"id":"1012.2350","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1012.2350","created_at":"2026-05-18T04:33:38Z"},{"alias_kind":"arxiv_version","alias_value":"1012.2350v1","created_at":"2026-05-18T04:33:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1012.2350","created_at":"2026-05-18T04:33:38Z"},{"alias_kind":"pith_short_12","alias_value":"HJZ5NI23NET7","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_16","alias_value":"HJZ5NI23NET7NBEY","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_8","alias_value":"HJZ5NI23","created_at":"2026-05-18T12:26:07Z"}],"graph_snapshots":[{"event_id":"sha256:8b4ab886109c87e9a19ec6f41cd337f098e507903ccedfb43a94691df5325276","target":"graph","created_at":"2026-05-18T04:33:38Z","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 show that the 2x2x2 interference channel, i.e., the multihop interference channel formed by concatenation of two 2-user interference channels achieves the min-cut outer bound value of 2 DoF, for almost all values of channel coefficients, for both time-varying or fixed channel coefficients. The key to this result is a new idea, called aligned interference neutralization, that provides a way to align interference terms over each hop in a manner that allows them to be cancelled over the air at the last hop.","authors_text":"Sae-Young Chung, Sang-Woon Jeon, Syed A. Jafar, Tiangao Gou","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2010-12-10T19:08:39Z","title":"Aligned Interference Neutralization and the Degrees of Freedom of the 2x2x2 Interference Channel"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1012.2350","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":"sha256:4ff42c00c285019f99c6c58531b65c0e98074db394a07e0c78b069408a12fcf8","target":"record","created_at":"2026-05-18T04:33:38Z","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":"4c2918390cee962d0a6b24abb8b6046a6b68018658e28462772dfbf512582b6c","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2010-12-10T19:08:39Z","title_canon_sha256":"25b59bd037c01945f7d5fd48e8cf1a1da9338cbf562202ddfb4235918bbe5520"},"schema_version":"1.0","source":{"id":"1012.2350","kind":"arxiv","version":1}},"canonical_sha256":"3a73d6a35b6927f684985d31738bee36c84d9a50057d5d00ecfb68d6a8c53682","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3a73d6a35b6927f684985d31738bee36c84d9a50057d5d00ecfb68d6a8c53682","first_computed_at":"2026-05-18T04:33:38.041514Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:33:38.041514Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"uP/40aK3k+tFPK9OXlPjFzmwiOR6Aq2MJx7+dyaxPOCQVHqwmYcfjTwLOPjq6pv4kxGyEqWNohcElWe1NZaLBA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:33:38.042106Z","signed_message":"canonical_sha256_bytes"},"source_id":"1012.2350","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4ff42c00c285019f99c6c58531b65c0e98074db394a07e0c78b069408a12fcf8","sha256:8b4ab886109c87e9a19ec6f41cd337f098e507903ccedfb43a94691df5325276"],"state_sha256":"2f2e597763f66d66592b207057f212324722a4094436654bd5b830bb9db01bc7"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"m42C5w7Hc59AVXJxXT/2orUzp5GRI01zoMdlyebh0nEu5HnvmZ9xW5Qjfg2EV11WHKBIKpsbglA07YjXfNIpAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T17:32:04.582945Z","bundle_sha256":"3d4350affb345a6b33fae5240419b53e0bb890ba7f8b72d9fae80f50f0f16001"}}