{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2009:JJKQIPFLSPOU25CN3U66IGOUHC","short_pith_number":"pith:JJKQIPFL","canonical_record":{"source":{"id":"0901.4379","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2009-01-28T00:29:28Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"d5126eeed355d00a769cceb71a988aed36b3722f8b6122887979cf85b527cf49","abstract_canon_sha256":"bcf128cdcd708433aebdad2a944ae77113362d37df6ae8aa90bd58f9fea32db9"},"schema_version":"1.0"},"canonical_sha256":"4a55043cab93dd4d744ddd3de419d438ba0f324bac1253c7431d0a165b44fe98","source":{"kind":"arxiv","id":"0901.4379","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0901.4379","created_at":"2026-05-18T03:53:29Z"},{"alias_kind":"arxiv_version","alias_value":"0901.4379v3","created_at":"2026-05-18T03:53:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0901.4379","created_at":"2026-05-18T03:53:29Z"},{"alias_kind":"pith_short_12","alias_value":"JJKQIPFLSPOU","created_at":"2026-05-18T12:26:00Z"},{"alias_kind":"pith_short_16","alias_value":"JJKQIPFLSPOU25CN","created_at":"2026-05-18T12:26:00Z"},{"alias_kind":"pith_short_8","alias_value":"JJKQIPFL","created_at":"2026-05-18T12:26:00Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2009:JJKQIPFLSPOU25CN3U66IGOUHC","target":"record","payload":{"canonical_record":{"source":{"id":"0901.4379","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2009-01-28T00:29:28Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"d5126eeed355d00a769cceb71a988aed36b3722f8b6122887979cf85b527cf49","abstract_canon_sha256":"bcf128cdcd708433aebdad2a944ae77113362d37df6ae8aa90bd58f9fea32db9"},"schema_version":"1.0"},"canonical_sha256":"4a55043cab93dd4d744ddd3de419d438ba0f324bac1253c7431d0a165b44fe98","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:53:29.796820Z","signature_b64":"nPoi+FYo26eCiC3GBW3QObZVOjYTUqQq8f6CH/+7zt/bxT8haPbvjuVRRGexCCYnYpSWVOIWM0cfimtNGmOvBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4a55043cab93dd4d744ddd3de419d438ba0f324bac1253c7431d0a165b44fe98","last_reissued_at":"2026-05-18T03:53:29.795747Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:53:29.795747Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0901.4379","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:53:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"x5Xy+IfcJYf6zXceLqFIbZs3DvBOiLnLRLKFIGsNsoF4vc5kz29zBivLPEs5eegJUhkN7MWQrERuFmeTJzvHDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T05:41:46.572761Z"},"content_sha256":"186c9892a5fcf4d801bae26d710a495d8a3b172a719aacc20c2e7fc57c25a3fd","schema_version":"1.0","event_id":"sha256:186c9892a5fcf4d801bae26d710a495d8a3b172a719aacc20c2e7fc57c25a3fd"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2009:JJKQIPFLSPOU25CN3U66IGOUHC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Ergodic Interference Alignment","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Bobak Nazer, Michael Gastpar, Sriram Vishwanath, Syed A. Jafar","submitted_at":"2009-01-28T00:29:28Z","abstract_excerpt":"This paper develops a new communication strategy, ergodic interference alignment, for the K-user interference channel with time-varying fading. At any particular time, each receiver will see a superposition of the transmitted signals plus noise. The standard approach to such a scenario results in each transmitter-receiver pair achieving a rate proportional to 1/K its interference-free ergodic capacity. However, given two well-chosen time indices, the channel coefficients from interfering users can be made to exactly cancel. By adding up these two observations, each receiver can obtain its desi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0901.4379","kind":"arxiv","version":3},"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":"2026-05-18T03:53:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MN/jxUPLQ8wH/Ku9ww+9tVZws8FySR57Yp1Af+s2OknsG7SAS4AjPeQhsfCHtG+lWjGAdgDwDFoLS0CMoy5rCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T05:41:46.573434Z"},"content_sha256":"15d54aaf701b9b4800b0ba31da85e28c07119d53e3cbcc2524733f8373fc86e9","schema_version":"1.0","event_id":"sha256:15d54aaf701b9b4800b0ba31da85e28c07119d53e3cbcc2524733f8373fc86e9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JJKQIPFLSPOU25CN3U66IGOUHC/bundle.json","state_url":"https://pith.science/pith/JJKQIPFLSPOU25CN3U66IGOUHC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JJKQIPFLSPOU25CN3U66IGOUHC/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":"2026-05-31T05:41:46Z","links":{"resolver":"https://pith.science/pith/JJKQIPFLSPOU25CN3U66IGOUHC","bundle":"https://pith.science/pith/JJKQIPFLSPOU25CN3U66IGOUHC/bundle.json","state":"https://pith.science/pith/JJKQIPFLSPOU25CN3U66IGOUHC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JJKQIPFLSPOU25CN3U66IGOUHC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:JJKQIPFLSPOU25CN3U66IGOUHC","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":"bcf128cdcd708433aebdad2a944ae77113362d37df6ae8aa90bd58f9fea32db9","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2009-01-28T00:29:28Z","title_canon_sha256":"d5126eeed355d00a769cceb71a988aed36b3722f8b6122887979cf85b527cf49"},"schema_version":"1.0","source":{"id":"0901.4379","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0901.4379","created_at":"2026-05-18T03:53:29Z"},{"alias_kind":"arxiv_version","alias_value":"0901.4379v3","created_at":"2026-05-18T03:53:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0901.4379","created_at":"2026-05-18T03:53:29Z"},{"alias_kind":"pith_short_12","alias_value":"JJKQIPFLSPOU","created_at":"2026-05-18T12:26:00Z"},{"alias_kind":"pith_short_16","alias_value":"JJKQIPFLSPOU25CN","created_at":"2026-05-18T12:26:00Z"},{"alias_kind":"pith_short_8","alias_value":"JJKQIPFL","created_at":"2026-05-18T12:26:00Z"}],"graph_snapshots":[{"event_id":"sha256:15d54aaf701b9b4800b0ba31da85e28c07119d53e3cbcc2524733f8373fc86e9","target":"graph","created_at":"2026-05-18T03:53:29Z","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":"This paper develops a new communication strategy, ergodic interference alignment, for the K-user interference channel with time-varying fading. At any particular time, each receiver will see a superposition of the transmitted signals plus noise. The standard approach to such a scenario results in each transmitter-receiver pair achieving a rate proportional to 1/K its interference-free ergodic capacity. However, given two well-chosen time indices, the channel coefficients from interfering users can be made to exactly cancel. By adding up these two observations, each receiver can obtain its desi","authors_text":"Bobak Nazer, Michael Gastpar, Sriram Vishwanath, Syed A. Jafar","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2009-01-28T00:29:28Z","title":"Ergodic Interference Alignment"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0901.4379","kind":"arxiv","version":3},"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":"sha256:186c9892a5fcf4d801bae26d710a495d8a3b172a719aacc20c2e7fc57c25a3fd","target":"record","created_at":"2026-05-18T03:53:29Z","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":"bcf128cdcd708433aebdad2a944ae77113362d37df6ae8aa90bd58f9fea32db9","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2009-01-28T00:29:28Z","title_canon_sha256":"d5126eeed355d00a769cceb71a988aed36b3722f8b6122887979cf85b527cf49"},"schema_version":"1.0","source":{"id":"0901.4379","kind":"arxiv","version":3}},"canonical_sha256":"4a55043cab93dd4d744ddd3de419d438ba0f324bac1253c7431d0a165b44fe98","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4a55043cab93dd4d744ddd3de419d438ba0f324bac1253c7431d0a165b44fe98","first_computed_at":"2026-05-18T03:53:29.795747Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:53:29.795747Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"nPoi+FYo26eCiC3GBW3QObZVOjYTUqQq8f6CH/+7zt/bxT8haPbvjuVRRGexCCYnYpSWVOIWM0cfimtNGmOvBw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:53:29.796820Z","signed_message":"canonical_sha256_bytes"},"source_id":"0901.4379","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:186c9892a5fcf4d801bae26d710a495d8a3b172a719aacc20c2e7fc57c25a3fd","sha256:15d54aaf701b9b4800b0ba31da85e28c07119d53e3cbcc2524733f8373fc86e9"],"state_sha256":"451fb9d25579c2493108aff4371efbf1e36b415f0e52c0c27b3959ccbe2c071b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Go1RPTdkSYcrDtPc37VnM40UH2PdUB6XKii0NWSF1l0kBZfZkvT52aevY0SpGs5cdYEP2/u6m10eEGOHqTRRAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T05:41:46.576025Z","bundle_sha256":"a26779a8cef1ba4a58401b6c9b6e7b5ae389aa1d12552905fe7a60f94fcb02ec"}}