{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:F2TOS3NT2C4GWCXGUIRHC7C7DR","short_pith_number":"pith:F2TOS3NT","canonical_record":{"source":{"id":"1202.0898","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2012-02-04T14:49:32Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"084e9b25bfb043b22962ff9c253c8ba71736a537d36372e9696806071d5ce088","abstract_canon_sha256":"705df3683b9ac3517ce749f9fe092ce609fa62406e64e4b95ffd80c784329d8b"},"schema_version":"1.0"},"canonical_sha256":"2ea6e96db3d0b86b0ae6a222717c5f1c75c95aa1c942f93943048519a42e1613","source":{"kind":"arxiv","id":"1202.0898","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1202.0898","created_at":"2026-05-18T04:03:05Z"},{"alias_kind":"arxiv_version","alias_value":"1202.0898v1","created_at":"2026-05-18T04:03:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1202.0898","created_at":"2026-05-18T04:03:05Z"},{"alias_kind":"pith_short_12","alias_value":"F2TOS3NT2C4G","created_at":"2026-05-18T12:27:04Z"},{"alias_kind":"pith_short_16","alias_value":"F2TOS3NT2C4GWCXG","created_at":"2026-05-18T12:27:04Z"},{"alias_kind":"pith_short_8","alias_value":"F2TOS3NT","created_at":"2026-05-18T12:27:04Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:F2TOS3NT2C4GWCXGUIRHC7C7DR","target":"record","payload":{"canonical_record":{"source":{"id":"1202.0898","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2012-02-04T14:49:32Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"084e9b25bfb043b22962ff9c253c8ba71736a537d36372e9696806071d5ce088","abstract_canon_sha256":"705df3683b9ac3517ce749f9fe092ce609fa62406e64e4b95ffd80c784329d8b"},"schema_version":"1.0"},"canonical_sha256":"2ea6e96db3d0b86b0ae6a222717c5f1c75c95aa1c942f93943048519a42e1613","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:03:05.837129Z","signature_b64":"5SSCN8GReS9V/txoGUqV/5XCht99wMnyzuKxm1qos1ylTd5tGUKXP0xtLGimdbMty2jrzKa8Rsj3+/+yVDMUAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2ea6e96db3d0b86b0ae6a222717c5f1c75c95aa1c942f93943048519a42e1613","last_reissued_at":"2026-05-18T04:03:05.836506Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:03:05.836506Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1202.0898","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":"2026-05-18T04:03:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"D5LCu1MO5OxtyqVY9+yXReljfrJOcG6ZMMpwTL7syJXnu2ewoWrtuVMxxPfhr3IeLl1TNxIJWldmw7L2QImnDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T04:38:17.187923Z"},"content_sha256":"b1f12ae14777fb7239abf894f3e5a9b759cb2b9071fe029e306ef939cb5e10da","schema_version":"1.0","event_id":"sha256:b1f12ae14777fb7239abf894f3e5a9b759cb2b9071fe029e306ef939cb5e10da"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:F2TOS3NT2C4GWCXGUIRHC7C7DR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On Marton's inner bound for broadcast channels","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Amin Gohari, Chandra Nair, Venkat Anantharam","submitted_at":"2012-02-04T14:49:32Z","abstract_excerpt":"Marton's inner bound is the best known achievable region for a general discrete memoryless broadcast channel. To compute Marton's inner bound one has to solve an optimization problem over a set of joint distributions on the input and auxiliary random variables. The optimizers turn out to be structured in many cases. Finding properties of optimizers not only results in efficient evaluation of the region, but it may also help one to prove factorization of Marton's inner bound (and thus its optimality). The first part of this paper formulates this factorization approach explicitly and states some"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.0898","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":"2026-05-18T04:03:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YxS2uRyLhA8q+DBry5cMjRU2INAXXhkBAWtGcHwkYAEfoAdp4hGA7xhDxk/MZbitx58fD/dff9TVC4br9IZuCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T04:38:17.188480Z"},"content_sha256":"d801c34cc9efaabce7b5295bd2c2b1a7f7ffab941a6c07483034fce9a80993dd","schema_version":"1.0","event_id":"sha256:d801c34cc9efaabce7b5295bd2c2b1a7f7ffab941a6c07483034fce9a80993dd"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/F2TOS3NT2C4GWCXGUIRHC7C7DR/bundle.json","state_url":"https://pith.science/pith/F2TOS3NT2C4GWCXGUIRHC7C7DR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/F2TOS3NT2C4GWCXGUIRHC7C7DR/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":"2026-06-03T04:38:17Z","links":{"resolver":"https://pith.science/pith/F2TOS3NT2C4GWCXGUIRHC7C7DR","bundle":"https://pith.science/pith/F2TOS3NT2C4GWCXGUIRHC7C7DR/bundle.json","state":"https://pith.science/pith/F2TOS3NT2C4GWCXGUIRHC7C7DR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/F2TOS3NT2C4GWCXGUIRHC7C7DR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:F2TOS3NT2C4GWCXGUIRHC7C7DR","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":"705df3683b9ac3517ce749f9fe092ce609fa62406e64e4b95ffd80c784329d8b","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2012-02-04T14:49:32Z","title_canon_sha256":"084e9b25bfb043b22962ff9c253c8ba71736a537d36372e9696806071d5ce088"},"schema_version":"1.0","source":{"id":"1202.0898","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1202.0898","created_at":"2026-05-18T04:03:05Z"},{"alias_kind":"arxiv_version","alias_value":"1202.0898v1","created_at":"2026-05-18T04:03:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1202.0898","created_at":"2026-05-18T04:03:05Z"},{"alias_kind":"pith_short_12","alias_value":"F2TOS3NT2C4G","created_at":"2026-05-18T12:27:04Z"},{"alias_kind":"pith_short_16","alias_value":"F2TOS3NT2C4GWCXG","created_at":"2026-05-18T12:27:04Z"},{"alias_kind":"pith_short_8","alias_value":"F2TOS3NT","created_at":"2026-05-18T12:27:04Z"}],"graph_snapshots":[{"event_id":"sha256:d801c34cc9efaabce7b5295bd2c2b1a7f7ffab941a6c07483034fce9a80993dd","target":"graph","created_at":"2026-05-18T04:03:05Z","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":"Marton's inner bound is the best known achievable region for a general discrete memoryless broadcast channel. To compute Marton's inner bound one has to solve an optimization problem over a set of joint distributions on the input and auxiliary random variables. The optimizers turn out to be structured in many cases. Finding properties of optimizers not only results in efficient evaluation of the region, but it may also help one to prove factorization of Marton's inner bound (and thus its optimality). The first part of this paper formulates this factorization approach explicitly and states some","authors_text":"Amin Gohari, Chandra Nair, Venkat Anantharam","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2012-02-04T14:49:32Z","title":"On Marton's inner bound for broadcast channels"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.0898","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:b1f12ae14777fb7239abf894f3e5a9b759cb2b9071fe029e306ef939cb5e10da","target":"record","created_at":"2026-05-18T04:03:05Z","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":"705df3683b9ac3517ce749f9fe092ce609fa62406e64e4b95ffd80c784329d8b","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2012-02-04T14:49:32Z","title_canon_sha256":"084e9b25bfb043b22962ff9c253c8ba71736a537d36372e9696806071d5ce088"},"schema_version":"1.0","source":{"id":"1202.0898","kind":"arxiv","version":1}},"canonical_sha256":"2ea6e96db3d0b86b0ae6a222717c5f1c75c95aa1c942f93943048519a42e1613","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2ea6e96db3d0b86b0ae6a222717c5f1c75c95aa1c942f93943048519a42e1613","first_computed_at":"2026-05-18T04:03:05.836506Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:03:05.836506Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5SSCN8GReS9V/txoGUqV/5XCht99wMnyzuKxm1qos1ylTd5tGUKXP0xtLGimdbMty2jrzKa8Rsj3+/+yVDMUAw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:03:05.837129Z","signed_message":"canonical_sha256_bytes"},"source_id":"1202.0898","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b1f12ae14777fb7239abf894f3e5a9b759cb2b9071fe029e306ef939cb5e10da","sha256:d801c34cc9efaabce7b5295bd2c2b1a7f7ffab941a6c07483034fce9a80993dd"],"state_sha256":"4fa5a789ff8370f3496d179f813ba3b2597c9e514585be1742638f26853ed6e2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DlQQ2gvIDuzOxrc1bpb3+bD5ClEvP2t6FlRnCwGxeKXK25GbThayY4L7L2WQOIWGZszQOUXmb0CZLW1jhoiKDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T04:38:17.191104Z","bundle_sha256":"62b0aaeac5e77af648c7ae32a0646506c5383220d42011f210952c4bd3f1b180"}}