{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:FUQVTUU5E52UXHRNGMT5WXRC37","short_pith_number":"pith:FUQVTUU5","canonical_record":{"source":{"id":"1501.05994","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-01-24T03:07:38Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"3114e850822cf8653bf434ca6e74425af84e04179dd0db937c111d588a20eb72","abstract_canon_sha256":"f78dc2ce391dfbcf49dfd9d72b413ba1fe8db641e165750d13f22cd9e453139e"},"schema_version":"1.0"},"canonical_sha256":"2d2159d29d27754b9e2d3327db5e22dfe00662f5d5ade3dafb9c37707cc985fa","source":{"kind":"arxiv","id":"1501.05994","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1501.05994","created_at":"2026-05-18T02:26:12Z"},{"alias_kind":"arxiv_version","alias_value":"1501.05994v2","created_at":"2026-05-18T02:26:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.05994","created_at":"2026-05-18T02:26:12Z"},{"alias_kind":"pith_short_12","alias_value":"FUQVTUU5E52U","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_16","alias_value":"FUQVTUU5E52UXHRN","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_8","alias_value":"FUQVTUU5","created_at":"2026-05-18T12:29:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:FUQVTUU5E52UXHRNGMT5WXRC37","target":"record","payload":{"canonical_record":{"source":{"id":"1501.05994","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-01-24T03:07:38Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"3114e850822cf8653bf434ca6e74425af84e04179dd0db937c111d588a20eb72","abstract_canon_sha256":"f78dc2ce391dfbcf49dfd9d72b413ba1fe8db641e165750d13f22cd9e453139e"},"schema_version":"1.0"},"canonical_sha256":"2d2159d29d27754b9e2d3327db5e22dfe00662f5d5ade3dafb9c37707cc985fa","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:26:12.374887Z","signature_b64":"NmdSwCU8FJyTzFDgaydcQh6dZ19fX8Dt6ciwOMwJ4BPd6xqSniUjU8NjSdiYohBPko3uBu5JDM9U0C9W8173Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2d2159d29d27754b9e2d3327db5e22dfe00662f5d5ade3dafb9c37707cc985fa","last_reissued_at":"2026-05-18T02:26:12.374342Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:26:12.374342Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1501.05994","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:26:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wk6ECQUZwSGwVwRuKL57T372Fmhc8MP9EUMHMUrFaxsVRxaooCU8jUstZRm5TpNQ4NoYiv21VPFha7O/VrlgCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T23:39:15.414900Z"},"content_sha256":"df984495484f6e45a462adecf18183ad309bf6fc8e92dc9c60244c4ca8c6ee8a","schema_version":"1.0","event_id":"sha256:df984495484f6e45a462adecf18183ad309bf6fc8e92dc9c60244c4ca8c6ee8a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:FUQVTUU5E52UXHRNGMT5WXRC37","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On MMSE Properties of Codes for the Gaussian Broadcast and Wiretap Channels","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"H. Vincent Poor, Rafael F. Schaefer, Ronit Bustin, Shlomo Shamai","submitted_at":"2015-01-24T03:07:38Z","abstract_excerpt":"This work concerns the behavior of \"good\" (capacity achieving) codes in several multi-user settings in the Gaussian regime, in terms of their minimum mean-square error (MMSE) behavior. The settings investigated in this context include the Gaussian wiretap channel, the Gaussian broadcast channel (BC) and the Gaussian BC with confidential messages (BCC). In particular this work addresses the effects of transmitting such codes on unintended receivers, that is, receivers that neither require reliable decoding of the transmitted messages nor are they eavesdroppers that must be kept ignorant, to som"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.05994","kind":"arxiv","version":2},"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":"2026-05-18T02:26:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CNgNxPR9ee61X3w7axTRy1Wy/cocciUOUPdVuRQwHZq1h7DWiwPID4D0d9rJHXRN+4YmEcQ5ZiVrrvQWJtkyDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T23:39:15.415606Z"},"content_sha256":"6a71da029ef559757750d54c9eea2a6939f3b9b56a37be96c34129a57b5dba1e","schema_version":"1.0","event_id":"sha256:6a71da029ef559757750d54c9eea2a6939f3b9b56a37be96c34129a57b5dba1e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FUQVTUU5E52UXHRNGMT5WXRC37/bundle.json","state_url":"https://pith.science/pith/FUQVTUU5E52UXHRNGMT5WXRC37/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FUQVTUU5E52UXHRNGMT5WXRC37/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":"2026-05-28T23:39:15Z","links":{"resolver":"https://pith.science/pith/FUQVTUU5E52UXHRNGMT5WXRC37","bundle":"https://pith.science/pith/FUQVTUU5E52UXHRNGMT5WXRC37/bundle.json","state":"https://pith.science/pith/FUQVTUU5E52UXHRNGMT5WXRC37/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FUQVTUU5E52UXHRNGMT5WXRC37/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:FUQVTUU5E52UXHRNGMT5WXRC37","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":"f78dc2ce391dfbcf49dfd9d72b413ba1fe8db641e165750d13f22cd9e453139e","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-01-24T03:07:38Z","title_canon_sha256":"3114e850822cf8653bf434ca6e74425af84e04179dd0db937c111d588a20eb72"},"schema_version":"1.0","source":{"id":"1501.05994","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1501.05994","created_at":"2026-05-18T02:26:12Z"},{"alias_kind":"arxiv_version","alias_value":"1501.05994v2","created_at":"2026-05-18T02:26:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.05994","created_at":"2026-05-18T02:26:12Z"},{"alias_kind":"pith_short_12","alias_value":"FUQVTUU5E52U","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_16","alias_value":"FUQVTUU5E52UXHRN","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_8","alias_value":"FUQVTUU5","created_at":"2026-05-18T12:29:22Z"}],"graph_snapshots":[{"event_id":"sha256:6a71da029ef559757750d54c9eea2a6939f3b9b56a37be96c34129a57b5dba1e","target":"graph","created_at":"2026-05-18T02:26:12Z","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 work concerns the behavior of \"good\" (capacity achieving) codes in several multi-user settings in the Gaussian regime, in terms of their minimum mean-square error (MMSE) behavior. The settings investigated in this context include the Gaussian wiretap channel, the Gaussian broadcast channel (BC) and the Gaussian BC with confidential messages (BCC). In particular this work addresses the effects of transmitting such codes on unintended receivers, that is, receivers that neither require reliable decoding of the transmitted messages nor are they eavesdroppers that must be kept ignorant, to som","authors_text":"H. Vincent Poor, Rafael F. Schaefer, Ronit Bustin, Shlomo Shamai","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-01-24T03:07:38Z","title":"On MMSE Properties of Codes for the Gaussian Broadcast and Wiretap Channels"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.05994","kind":"arxiv","version":2},"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:df984495484f6e45a462adecf18183ad309bf6fc8e92dc9c60244c4ca8c6ee8a","target":"record","created_at":"2026-05-18T02:26:12Z","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":"f78dc2ce391dfbcf49dfd9d72b413ba1fe8db641e165750d13f22cd9e453139e","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-01-24T03:07:38Z","title_canon_sha256":"3114e850822cf8653bf434ca6e74425af84e04179dd0db937c111d588a20eb72"},"schema_version":"1.0","source":{"id":"1501.05994","kind":"arxiv","version":2}},"canonical_sha256":"2d2159d29d27754b9e2d3327db5e22dfe00662f5d5ade3dafb9c37707cc985fa","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2d2159d29d27754b9e2d3327db5e22dfe00662f5d5ade3dafb9c37707cc985fa","first_computed_at":"2026-05-18T02:26:12.374342Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:26:12.374342Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"NmdSwCU8FJyTzFDgaydcQh6dZ19fX8Dt6ciwOMwJ4BPd6xqSniUjU8NjSdiYohBPko3uBu5JDM9U0C9W8173Aw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:26:12.374887Z","signed_message":"canonical_sha256_bytes"},"source_id":"1501.05994","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:df984495484f6e45a462adecf18183ad309bf6fc8e92dc9c60244c4ca8c6ee8a","sha256:6a71da029ef559757750d54c9eea2a6939f3b9b56a37be96c34129a57b5dba1e"],"state_sha256":"bfe9f9af0f0368e32e4754374347f8da275cfea4adc807bba87e8c540f42e07d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1mNEIofzGf9ey4Dz49yfG4xKrrkO3Xl40JfjWg5sloKaPFAX9HZ0jH+On8MRqxxas1DG75kbv77GERGcwtqHCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T23:39:15.419232Z","bundle_sha256":"ecc230c18b4408cd1c262d7b7cead6ecbc74562a1cb94f427f84fd99aa6abbef"}}