{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:7WK2U5EBNXBYC74RCGD2G3IZPK","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":"84ce29487239a5157ff590ee7fc8132f3e37b90898b54158f14bbc4a44660c99","cross_cats_sorted":["math.IT"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.IT","submitted_at":"2026-06-05T07:18:12Z","title_canon_sha256":"9aaa4cfd771ec83bf1f3215ec70361a5478c5eac3ed464f8f19870fb0fd201cb"},"schema_version":"1.0","source":{"id":"2606.06982","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.06982","created_at":"2026-06-08T01:04:39Z"},{"alias_kind":"arxiv_version","alias_value":"2606.06982v1","created_at":"2026-06-08T01:04:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.06982","created_at":"2026-06-08T01:04:39Z"},{"alias_kind":"pith_short_12","alias_value":"7WK2U5EBNXBY","created_at":"2026-06-08T01:04:39Z"},{"alias_kind":"pith_short_16","alias_value":"7WK2U5EBNXBYC74R","created_at":"2026-06-08T01:04:39Z"},{"alias_kind":"pith_short_8","alias_value":"7WK2U5EB","created_at":"2026-06-08T01:04:39Z"}],"graph_snapshots":[{"event_id":"sha256:d3368a99d974944f7572677af318c49892b6743b2b5fc7804e960d36442a6077","target":"graph","created_at":"2026-06-08T01:04:39Z","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/2606.06982/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We present a differentiable framework for end-to-end mutual information (MI) optimization over linear Gaussian directed acyclic graphs (DAGs). The framework targets network-wide design under global constraints, such as a total transmit power budget, and covers MIMO precoding, amplify-and-forward relays, RIS-aided channels, and branching/merging topologies within a common linear Gaussian model. Its core ingredient is a \\emph{K-recursion} that analytically propagates all node-pair covariances along the DAG in topological order, including non-adjacent cross-covariances that are necessary for corr","authors_text":"Na Siqi, Tadashi Wadayama","cross_cats":["math.IT"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.IT","submitted_at":"2026-06-05T07:18:12Z","title":"Mutual Information Optimization via K-Recursion and Automatic Differentiation for Linear Gaussian Wireless Networks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.06982","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:c3fac873ca3d64cc1750f55cd5f149e8e0d65cec717f4288ce636d6826ef4c01","target":"record","created_at":"2026-06-08T01:04:39Z","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":"84ce29487239a5157ff590ee7fc8132f3e37b90898b54158f14bbc4a44660c99","cross_cats_sorted":["math.IT"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.IT","submitted_at":"2026-06-05T07:18:12Z","title_canon_sha256":"9aaa4cfd771ec83bf1f3215ec70361a5478c5eac3ed464f8f19870fb0fd201cb"},"schema_version":"1.0","source":{"id":"2606.06982","kind":"arxiv","version":1}},"canonical_sha256":"fd95aa74816dc3817f911187a36d197a845a1871db07d13903a2dd944f5efb69","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fd95aa74816dc3817f911187a36d197a845a1871db07d13903a2dd944f5efb69","first_computed_at":"2026-06-08T01:04:39.414520Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-08T01:04:39.414520Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"HadZjdGvaiIgnbo1jlm731dE/n1Ptm9wGfU3vt81YSt2YZWrYPpQA79TE7rDq0W2kBm7Agp+L80LxiTnCEQBAQ==","signature_status":"signed_v1","signed_at":"2026-06-08T01:04:39.415395Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.06982","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c3fac873ca3d64cc1750f55cd5f149e8e0d65cec717f4288ce636d6826ef4c01","sha256:d3368a99d974944f7572677af318c49892b6743b2b5fc7804e960d36442a6077"],"state_sha256":"1b808d096772bf6f234d2d34d10ef31e818094490fac3d66ecbe81c548305981"}