{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2022:6JZ3DXEGCK6Z6SQUTBHEFYWEVO","short_pith_number":"pith:6JZ3DXEG","canonical_record":{"source":{"id":"2209.15318","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"cs.IT","submitted_at":"2022-09-30T08:48:49Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"18067448a7e655bd825dd7eccf5ee8eb1ed998a320ec7b5a905a26ca7aeacc54","abstract_canon_sha256":"b8c8021aa28c403e4d7054874cc2009e91b9c1efac7019dd86fba125f6a7547f"},"schema_version":"1.0"},"canonical_sha256":"f273b1dc8612bd9f4a14984e42e2c4ab9bca63afc0ceec56b2f034bc40e70e07","source":{"kind":"arxiv","id":"2209.15318","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2209.15318","created_at":"2026-07-05T05:02:18Z"},{"alias_kind":"arxiv_version","alias_value":"2209.15318v1","created_at":"2026-07-05T05:02:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2209.15318","created_at":"2026-07-05T05:02:18Z"},{"alias_kind":"pith_short_12","alias_value":"6JZ3DXEGCK6Z","created_at":"2026-07-05T05:02:18Z"},{"alias_kind":"pith_short_16","alias_value":"6JZ3DXEGCK6Z6SQU","created_at":"2026-07-05T05:02:18Z"},{"alias_kind":"pith_short_8","alias_value":"6JZ3DXEG","created_at":"2026-07-05T05:02:18Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2022:6JZ3DXEGCK6Z6SQUTBHEFYWEVO","target":"record","payload":{"canonical_record":{"source":{"id":"2209.15318","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"cs.IT","submitted_at":"2022-09-30T08:48:49Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"18067448a7e655bd825dd7eccf5ee8eb1ed998a320ec7b5a905a26ca7aeacc54","abstract_canon_sha256":"b8c8021aa28c403e4d7054874cc2009e91b9c1efac7019dd86fba125f6a7547f"},"schema_version":"1.0"},"canonical_sha256":"f273b1dc8612bd9f4a14984e42e2c4ab9bca63afc0ceec56b2f034bc40e70e07","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T05:02:18.903720Z","signature_b64":"pBlx/Fwj0zXQbmEEtZHusMI3sgJ0KeZJN1iLsFmn8sfRLAXoROJgpizpl5Qm+nMu3/qbRHvHc0FpXjKuY5pRBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f273b1dc8612bd9f4a14984e42e2c4ab9bca63afc0ceec56b2f034bc40e70e07","last_reissued_at":"2026-07-05T05:02:18.903296Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T05:02:18.903296Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2209.15318","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":"2026-07-05T05:02:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fQl6O1HMdkej7gbFV18a/LcGFtVewVqP68Yf6f524Emb7I0O5DVcVtBseJ31g1bpplXVGQor6I/maBPXxLAGAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-23T15:49:14.554448Z"},"content_sha256":"61042675ae7ee7c69dc3edf4bc88aa293c550108a4fd3205bc2acbd05de4d766","schema_version":"1.0","event_id":"sha256:61042675ae7ee7c69dc3edf4bc88aa293c550108a4fd3205bc2acbd05de4d766"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2022:6JZ3DXEGCK6Z6SQUTBHEFYWEVO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Extensions on `A Convex Scheme for the Secrecy Capacity of a MIMO Wiretap Channel with a Single Antenna Eavesdropper'","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Jennifer Chakravarty, Oliver Johnson, Robert Piechocki","submitted_at":"2022-09-30T08:48:49Z","abstract_excerpt":"One key metric for physical layer security is the secrecy capacity. This is the maximum rate that a system can transmit with perfect secrecy. For a Multiple Input Multiple Output (MIMO) system (a newer technology for 5G, 6G and beyond) the secrecy capacity is not fully understood. For a Gaussian MIMO channel, the secrecy capacity is a non-convex optimisation problem for which a general solution is not available.\n  Previous work by the authors showed that the secrecy capacity of a MIMO system with a single eavesdrop antenna is concave to a cut off point. In this work, which extends the previous"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2209.15318","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/2209.15318/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":"2026-07-05T05:02:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PrW35PXhvJ+qsu/JMzAFM7/YlpL7HJt8Dt/adrPunIzYzEQigvi/SoJXgWXcQps9NO734R87BUHUwGTIG19kAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-23T15:49:14.555039Z"},"content_sha256":"49dade0a03f7a7d93243a728ed110ade024372590743ae66dcd948a46952d2e2","schema_version":"1.0","event_id":"sha256:49dade0a03f7a7d93243a728ed110ade024372590743ae66dcd948a46952d2e2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6JZ3DXEGCK6Z6SQUTBHEFYWEVO/bundle.json","state_url":"https://pith.science/pith/6JZ3DXEGCK6Z6SQUTBHEFYWEVO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6JZ3DXEGCK6Z6SQUTBHEFYWEVO/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":"2026-08-23T15:49:14Z","links":{"resolver":"https://pith.science/pith/6JZ3DXEGCK6Z6SQUTBHEFYWEVO","bundle":"https://pith.science/pith/6JZ3DXEGCK6Z6SQUTBHEFYWEVO/bundle.json","state":"https://pith.science/pith/6JZ3DXEGCK6Z6SQUTBHEFYWEVO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6JZ3DXEGCK6Z6SQUTBHEFYWEVO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:6JZ3DXEGCK6Z6SQUTBHEFYWEVO","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":"b8c8021aa28c403e4d7054874cc2009e91b9c1efac7019dd86fba125f6a7547f","cross_cats_sorted":["math.IT"],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"cs.IT","submitted_at":"2022-09-30T08:48:49Z","title_canon_sha256":"18067448a7e655bd825dd7eccf5ee8eb1ed998a320ec7b5a905a26ca7aeacc54"},"schema_version":"1.0","source":{"id":"2209.15318","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2209.15318","created_at":"2026-07-05T05:02:18Z"},{"alias_kind":"arxiv_version","alias_value":"2209.15318v1","created_at":"2026-07-05T05:02:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2209.15318","created_at":"2026-07-05T05:02:18Z"},{"alias_kind":"pith_short_12","alias_value":"6JZ3DXEGCK6Z","created_at":"2026-07-05T05:02:18Z"},{"alias_kind":"pith_short_16","alias_value":"6JZ3DXEGCK6Z6SQU","created_at":"2026-07-05T05:02:18Z"},{"alias_kind":"pith_short_8","alias_value":"6JZ3DXEG","created_at":"2026-07-05T05:02:18Z"}],"graph_snapshots":[{"event_id":"sha256:49dade0a03f7a7d93243a728ed110ade024372590743ae66dcd948a46952d2e2","target":"graph","created_at":"2026-07-05T05:02:18Z","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/2209.15318/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"One key metric for physical layer security is the secrecy capacity. This is the maximum rate that a system can transmit with perfect secrecy. For a Multiple Input Multiple Output (MIMO) system (a newer technology for 5G, 6G and beyond) the secrecy capacity is not fully understood. For a Gaussian MIMO channel, the secrecy capacity is a non-convex optimisation problem for which a general solution is not available.\n  Previous work by the authors showed that the secrecy capacity of a MIMO system with a single eavesdrop antenna is concave to a cut off point. In this work, which extends the previous","authors_text":"Jennifer Chakravarty, Oliver Johnson, Robert Piechocki","cross_cats":["math.IT"],"headline":"","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"cs.IT","submitted_at":"2022-09-30T08:48:49Z","title":"Extensions on `A Convex Scheme for the Secrecy Capacity of a MIMO Wiretap Channel with a Single Antenna Eavesdropper'"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2209.15318","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":"sha256:61042675ae7ee7c69dc3edf4bc88aa293c550108a4fd3205bc2acbd05de4d766","target":"record","created_at":"2026-07-05T05:02:18Z","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":"b8c8021aa28c403e4d7054874cc2009e91b9c1efac7019dd86fba125f6a7547f","cross_cats_sorted":["math.IT"],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"cs.IT","submitted_at":"2022-09-30T08:48:49Z","title_canon_sha256":"18067448a7e655bd825dd7eccf5ee8eb1ed998a320ec7b5a905a26ca7aeacc54"},"schema_version":"1.0","source":{"id":"2209.15318","kind":"arxiv","version":1}},"canonical_sha256":"f273b1dc8612bd9f4a14984e42e2c4ab9bca63afc0ceec56b2f034bc40e70e07","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f273b1dc8612bd9f4a14984e42e2c4ab9bca63afc0ceec56b2f034bc40e70e07","first_computed_at":"2026-07-05T05:02:18.903296Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T05:02:18.903296Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"pBlx/Fwj0zXQbmEEtZHusMI3sgJ0KeZJN1iLsFmn8sfRLAXoROJgpizpl5Qm+nMu3/qbRHvHc0FpXjKuY5pRBA==","signature_status":"signed_v1","signed_at":"2026-07-05T05:02:18.903720Z","signed_message":"canonical_sha256_bytes"},"source_id":"2209.15318","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:61042675ae7ee7c69dc3edf4bc88aa293c550108a4fd3205bc2acbd05de4d766","sha256:49dade0a03f7a7d93243a728ed110ade024372590743ae66dcd948a46952d2e2"],"state_sha256":"af70a39313db7a420dcca6345bc880405ebc8744035f3880e0860e353c59a85a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"liF8IVF2sq+/7zk466ebNaHbXzW/hphEmBYa4PdcD6vYdteM+bkwHeOx8Ochux0q4LwhKDNW3ZIFujTkd3TDDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-23T15:49:14.559885Z","bundle_sha256":"aa3d8392817ed09eb6ec86e653b3ae39cced71794374bfce0acfd4e9375d23db"}}