{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:T6JLUHSCUPQIRY33DI22IZMIAQ","short_pith_number":"pith:T6JLUHSC","canonical_record":{"source":{"id":"2606.22301","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.IT","submitted_at":"2026-06-21T02:03:53Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"f9e191bc72b00dbdab5904869fd184e1301781573dcbe172a18246616c4ad81c","abstract_canon_sha256":"d52c5f3d8aa150a8a49ff7c45296f57b85002a84cd7119bb190aefdbe7d29b2a"},"schema_version":"1.0"},"canonical_sha256":"9f92ba1e42a3e088e37b1a35a46588042385bdbb0d6c272467560178ac3b7dc4","source":{"kind":"arxiv","id":"2606.22301","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.22301","created_at":"2026-06-23T02:13:34Z"},{"alias_kind":"arxiv_version","alias_value":"2606.22301v1","created_at":"2026-06-23T02:13:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.22301","created_at":"2026-06-23T02:13:34Z"},{"alias_kind":"pith_short_12","alias_value":"T6JLUHSCUPQI","created_at":"2026-06-23T02:13:34Z"},{"alias_kind":"pith_short_16","alias_value":"T6JLUHSCUPQIRY33","created_at":"2026-06-23T02:13:34Z"},{"alias_kind":"pith_short_8","alias_value":"T6JLUHSC","created_at":"2026-06-23T02:13:34Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:T6JLUHSCUPQIRY33DI22IZMIAQ","target":"record","payload":{"canonical_record":{"source":{"id":"2606.22301","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.IT","submitted_at":"2026-06-21T02:03:53Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"f9e191bc72b00dbdab5904869fd184e1301781573dcbe172a18246616c4ad81c","abstract_canon_sha256":"d52c5f3d8aa150a8a49ff7c45296f57b85002a84cd7119bb190aefdbe7d29b2a"},"schema_version":"1.0"},"canonical_sha256":"9f92ba1e42a3e088e37b1a35a46588042385bdbb0d6c272467560178ac3b7dc4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-23T02:13:34.355868Z","signature_b64":"zQ4w9sdqh9QvK9e59aC2U6hPv/lCyanIZK03w2P7+/31tN9RzLmcrfDh3HMv7Ov+RamfOl5mZi7E5K9zqPjCBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9f92ba1e42a3e088e37b1a35a46588042385bdbb0d6c272467560178ac3b7dc4","last_reissued_at":"2026-06-23T02:13:34.355485Z","signature_status":"signed_v1","first_computed_at":"2026-06-23T02:13:34.355485Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2606.22301","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":"2026-06-23T02:13:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kuhZ5gGVo1gNbDno1kugrosrFLnNoLGi4AAuMfxmVU9BAjTJUjRWWpLADM/1PJxluCi1DJRTQa9M6wpKw4TDAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-28T09:19:25.513836Z"},"content_sha256":"271fb75ae5683acfe74c3d1b9ef5e93626dfa6412f4e03b645c8afc11e1bd106","schema_version":"1.0","event_id":"sha256:271fb75ae5683acfe74c3d1b9ef5e93626dfa6412f4e03b645c8afc11e1bd106"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:T6JLUHSCUPQIRY33DI22IZMIAQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Differentiable Conditional Mutual Information for Multi-Terminal Linear Gaussian Wireless Networks","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Siqi Na, Tadashi Wadayama","submitted_at":"2026-06-21T02:03:53Z","abstract_excerpt":"The rate regions of multi-terminal Gaussian channels (multiple-access, broadcast, interference, relay) are delimited by conditional mutual informations $I(V_A;V_B\\,|\\,V_C)$ among groups of input and output nodes; bringing such channels under differentiable physical-layer design therefore hinges on evaluating any such conditional MI, and its gradient, on a unified computation graph. Modeling the network as a linear Gaussian directed acyclic graph (Gaussian-DAG), we obtain $I(V_A;V_B\\,|\\,V_C)$ in closed form: from the node-pair covariances produced by one K-recursion forward pass, it is a log-de"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.22301","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.22301/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-06-23T02:13:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ugKe4ZW7GvHuQ9JM7baN8fG/maELs8WqtVABo7Wj699bbW0o7vmxAbWKHxNsVQsbf9AnNse0kElysaYKKJoTAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-28T09:19:25.514222Z"},"content_sha256":"b98aff12b0f6f3451a5a5838a9a0ea1ee1889e65744870bf9fcea9477b252eab","schema_version":"1.0","event_id":"sha256:b98aff12b0f6f3451a5a5838a9a0ea1ee1889e65744870bf9fcea9477b252eab"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/T6JLUHSCUPQIRY33DI22IZMIAQ/bundle.json","state_url":"https://pith.science/pith/T6JLUHSCUPQIRY33DI22IZMIAQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/T6JLUHSCUPQIRY33DI22IZMIAQ/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":"2026-06-28T09:19:25Z","links":{"resolver":"https://pith.science/pith/T6JLUHSCUPQIRY33DI22IZMIAQ","bundle":"https://pith.science/pith/T6JLUHSCUPQIRY33DI22IZMIAQ/bundle.json","state":"https://pith.science/pith/T6JLUHSCUPQIRY33DI22IZMIAQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/T6JLUHSCUPQIRY33DI22IZMIAQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:T6JLUHSCUPQIRY33DI22IZMIAQ","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":"d52c5f3d8aa150a8a49ff7c45296f57b85002a84cd7119bb190aefdbe7d29b2a","cross_cats_sorted":["math.IT"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.IT","submitted_at":"2026-06-21T02:03:53Z","title_canon_sha256":"f9e191bc72b00dbdab5904869fd184e1301781573dcbe172a18246616c4ad81c"},"schema_version":"1.0","source":{"id":"2606.22301","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.22301","created_at":"2026-06-23T02:13:34Z"},{"alias_kind":"arxiv_version","alias_value":"2606.22301v1","created_at":"2026-06-23T02:13:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.22301","created_at":"2026-06-23T02:13:34Z"},{"alias_kind":"pith_short_12","alias_value":"T6JLUHSCUPQI","created_at":"2026-06-23T02:13:34Z"},{"alias_kind":"pith_short_16","alias_value":"T6JLUHSCUPQIRY33","created_at":"2026-06-23T02:13:34Z"},{"alias_kind":"pith_short_8","alias_value":"T6JLUHSC","created_at":"2026-06-23T02:13:34Z"}],"graph_snapshots":[{"event_id":"sha256:b98aff12b0f6f3451a5a5838a9a0ea1ee1889e65744870bf9fcea9477b252eab","target":"graph","created_at":"2026-06-23T02:13:34Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2606.22301/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The rate regions of multi-terminal Gaussian channels (multiple-access, broadcast, interference, relay) are delimited by conditional mutual informations $I(V_A;V_B\\,|\\,V_C)$ among groups of input and output nodes; bringing such channels under differentiable physical-layer design therefore hinges on evaluating any such conditional MI, and its gradient, on a unified computation graph. Modeling the network as a linear Gaussian directed acyclic graph (Gaussian-DAG), we obtain $I(V_A;V_B\\,|\\,V_C)$ in closed form: from the node-pair covariances produced by one K-recursion forward pass, it is a log-de","authors_text":"Siqi Na, Tadashi Wadayama","cross_cats":["math.IT"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.IT","submitted_at":"2026-06-21T02:03:53Z","title":"Differentiable Conditional Mutual Information for Multi-Terminal Linear Gaussian Wireless Networks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.22301","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":"sha256:271fb75ae5683acfe74c3d1b9ef5e93626dfa6412f4e03b645c8afc11e1bd106","target":"record","created_at":"2026-06-23T02:13:34Z","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":"d52c5f3d8aa150a8a49ff7c45296f57b85002a84cd7119bb190aefdbe7d29b2a","cross_cats_sorted":["math.IT"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.IT","submitted_at":"2026-06-21T02:03:53Z","title_canon_sha256":"f9e191bc72b00dbdab5904869fd184e1301781573dcbe172a18246616c4ad81c"},"schema_version":"1.0","source":{"id":"2606.22301","kind":"arxiv","version":1}},"canonical_sha256":"9f92ba1e42a3e088e37b1a35a46588042385bdbb0d6c272467560178ac3b7dc4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9f92ba1e42a3e088e37b1a35a46588042385bdbb0d6c272467560178ac3b7dc4","first_computed_at":"2026-06-23T02:13:34.355485Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-23T02:13:34.355485Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"zQ4w9sdqh9QvK9e59aC2U6hPv/lCyanIZK03w2P7+/31tN9RzLmcrfDh3HMv7Ov+RamfOl5mZi7E5K9zqPjCBA==","signature_status":"signed_v1","signed_at":"2026-06-23T02:13:34.355868Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.22301","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:271fb75ae5683acfe74c3d1b9ef5e93626dfa6412f4e03b645c8afc11e1bd106","sha256:b98aff12b0f6f3451a5a5838a9a0ea1ee1889e65744870bf9fcea9477b252eab"],"state_sha256":"53b706e5d6fc08acdaf5b6ecbbeb634772f004e10c9c2b44589b71c05e4b1936"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9evnvbkMomXQ4o8HqR5HvuDP4Z3syXc5+YEMw1AFJ4o3P//bkuKye25paxvs3a/fmNcgq3tRZ4xFZGnvWSiwBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-28T09:19:25.516471Z","bundle_sha256":"c336b1f70865eab525da5a9d64bd3af2f24da54212ae2ba4484d1330ed30a6fa"}}