{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:I6VBVLZV7XP347QGGH5E2AJW73","short_pith_number":"pith:I6VBVLZV","canonical_record":{"source":{"id":"1904.11178","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2019-04-25T07:00:38Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"9e3cbc794ee06410e09a0511abf19d73a9553c8c9de3f176376710dfd71e7123","abstract_canon_sha256":"4d64c1d7973d91bcd111d47e57a7037ab9f194f7fc711289ea7b039f070a563c"},"schema_version":"1.0"},"canonical_sha256":"47aa1aaf35fddfbe7e0631fa4d0136fef2c7f014be9e67325201607737437fc0","source":{"kind":"arxiv","id":"1904.11178","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1904.11178","created_at":"2026-05-17T23:47:45Z"},{"alias_kind":"arxiv_version","alias_value":"1904.11178v1","created_at":"2026-05-17T23:47:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1904.11178","created_at":"2026-05-17T23:47:45Z"},{"alias_kind":"pith_short_12","alias_value":"I6VBVLZV7XP3","created_at":"2026-05-18T12:33:18Z"},{"alias_kind":"pith_short_16","alias_value":"I6VBVLZV7XP347QG","created_at":"2026-05-18T12:33:18Z"},{"alias_kind":"pith_short_8","alias_value":"I6VBVLZV","created_at":"2026-05-18T12:33:18Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:I6VBVLZV7XP347QGGH5E2AJW73","target":"record","payload":{"canonical_record":{"source":{"id":"1904.11178","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2019-04-25T07:00:38Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"9e3cbc794ee06410e09a0511abf19d73a9553c8c9de3f176376710dfd71e7123","abstract_canon_sha256":"4d64c1d7973d91bcd111d47e57a7037ab9f194f7fc711289ea7b039f070a563c"},"schema_version":"1.0"},"canonical_sha256":"47aa1aaf35fddfbe7e0631fa4d0136fef2c7f014be9e67325201607737437fc0","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:47:45.594531Z","signature_b64":"WFpRBzBF+cLilGJeNwBGPErtEDQDJezqEFX+bpmf2IwjrHKJK+yzMw4od+ntl1/5DKcg02AxaMXdw3yIWqa7BA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"47aa1aaf35fddfbe7e0631fa4d0136fef2c7f014be9e67325201607737437fc0","last_reissued_at":"2026-05-17T23:47:45.594075Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:47:45.594075Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1904.11178","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":"2026-05-17T23:47:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QWiSi3PDB22OmfQWISMVSLhtpZR0i9EfF6GUrjVdTb+KWUQRecpLgQXc+n82GLTAivCPV1R1kbPMrdKWXdkDCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T18:29:05.662297Z"},"content_sha256":"957b57be704d8e219d2c9ca4c53b08de53beef2f221863375e4c070137d2d8fa","schema_version":"1.0","event_id":"sha256:957b57be704d8e219d2c9ca4c53b08de53beef2f221863375e4c070137d2d8fa"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:I6VBVLZV7XP347QGGH5E2AJW73","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Weak-Noise Modulation-Estimation of Vector Parameters","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Neri Merhav","submitted_at":"2019-04-25T07:00:38Z","abstract_excerpt":"We address the problem of modulating a parameter onto a power-limited signal, transmitted over a discrete-time Gaussian channel and estimating this parameter at the receiver. Continuing an earlier work, where the optimal trade-off between the weak-noise estimation performance and the outage probability (threshold-effect breakdown) was studied for a single (scalar) parameter, here we extend the derivation of the weak-noise estimation performance to the case of a multi-dimensional vector parameter. This turns out to be a non-trivial extension, that provides a few insights and it has some interes"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.11178","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":"2026-05-17T23:47:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZdJ0XepnbtrInn9QuLFWi8hQxYa8KR2YshNfgjYB4XVQXyyGpufZeDSMeTi1bHkf7yi2t4T6g79Gbx0U9HK2BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T18:29:05.662978Z"},"content_sha256":"ea1e58f5c54c561ecc54bcf820037e0651ffbd89c4e4e387caa618d70116b771","schema_version":"1.0","event_id":"sha256:ea1e58f5c54c561ecc54bcf820037e0651ffbd89c4e4e387caa618d70116b771"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/I6VBVLZV7XP347QGGH5E2AJW73/bundle.json","state_url":"https://pith.science/pith/I6VBVLZV7XP347QGGH5E2AJW73/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/I6VBVLZV7XP347QGGH5E2AJW73/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":"2026-05-27T18:29:05Z","links":{"resolver":"https://pith.science/pith/I6VBVLZV7XP347QGGH5E2AJW73","bundle":"https://pith.science/pith/I6VBVLZV7XP347QGGH5E2AJW73/bundle.json","state":"https://pith.science/pith/I6VBVLZV7XP347QGGH5E2AJW73/state.json","well_known_bundle":"https://pith.science/.well-known/pith/I6VBVLZV7XP347QGGH5E2AJW73/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:I6VBVLZV7XP347QGGH5E2AJW73","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":"4d64c1d7973d91bcd111d47e57a7037ab9f194f7fc711289ea7b039f070a563c","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2019-04-25T07:00:38Z","title_canon_sha256":"9e3cbc794ee06410e09a0511abf19d73a9553c8c9de3f176376710dfd71e7123"},"schema_version":"1.0","source":{"id":"1904.11178","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1904.11178","created_at":"2026-05-17T23:47:45Z"},{"alias_kind":"arxiv_version","alias_value":"1904.11178v1","created_at":"2026-05-17T23:47:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1904.11178","created_at":"2026-05-17T23:47:45Z"},{"alias_kind":"pith_short_12","alias_value":"I6VBVLZV7XP3","created_at":"2026-05-18T12:33:18Z"},{"alias_kind":"pith_short_16","alias_value":"I6VBVLZV7XP347QG","created_at":"2026-05-18T12:33:18Z"},{"alias_kind":"pith_short_8","alias_value":"I6VBVLZV","created_at":"2026-05-18T12:33:18Z"}],"graph_snapshots":[{"event_id":"sha256:ea1e58f5c54c561ecc54bcf820037e0651ffbd89c4e4e387caa618d70116b771","target":"graph","created_at":"2026-05-17T23:47:45Z","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":"We address the problem of modulating a parameter onto a power-limited signal, transmitted over a discrete-time Gaussian channel and estimating this parameter at the receiver. Continuing an earlier work, where the optimal trade-off between the weak-noise estimation performance and the outage probability (threshold-effect breakdown) was studied for a single (scalar) parameter, here we extend the derivation of the weak-noise estimation performance to the case of a multi-dimensional vector parameter. This turns out to be a non-trivial extension, that provides a few insights and it has some interes","authors_text":"Neri Merhav","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2019-04-25T07:00:38Z","title":"Weak-Noise Modulation-Estimation of Vector Parameters"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.11178","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":"sha256:957b57be704d8e219d2c9ca4c53b08de53beef2f221863375e4c070137d2d8fa","target":"record","created_at":"2026-05-17T23:47:45Z","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":"4d64c1d7973d91bcd111d47e57a7037ab9f194f7fc711289ea7b039f070a563c","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2019-04-25T07:00:38Z","title_canon_sha256":"9e3cbc794ee06410e09a0511abf19d73a9553c8c9de3f176376710dfd71e7123"},"schema_version":"1.0","source":{"id":"1904.11178","kind":"arxiv","version":1}},"canonical_sha256":"47aa1aaf35fddfbe7e0631fa4d0136fef2c7f014be9e67325201607737437fc0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"47aa1aaf35fddfbe7e0631fa4d0136fef2c7f014be9e67325201607737437fc0","first_computed_at":"2026-05-17T23:47:45.594075Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:47:45.594075Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"WFpRBzBF+cLilGJeNwBGPErtEDQDJezqEFX+bpmf2IwjrHKJK+yzMw4od+ntl1/5DKcg02AxaMXdw3yIWqa7BA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:47:45.594531Z","signed_message":"canonical_sha256_bytes"},"source_id":"1904.11178","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:957b57be704d8e219d2c9ca4c53b08de53beef2f221863375e4c070137d2d8fa","sha256:ea1e58f5c54c561ecc54bcf820037e0651ffbd89c4e4e387caa618d70116b771"],"state_sha256":"0d8965798718ef000fc9e46f6b74cba08ce1f118eddff7ed139c0fb19cfe0e62"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wV6I+M5ZO/328Lmri4suR1ymnostmF3KRDVmjT+1RTZcmzJDSQpOT+cYWrqBAegMaVTeBPIsdEUHIYMZumb7BA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T18:29:05.666570Z","bundle_sha256":"31f9f6680ce8c7146ea4ff99d7409153155a1eef8aa90423c9d97ac510a7b27d"}}