{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2023:QKAZPPJYTZVEL3OCPWCIYQKKOE","short_pith_number":"pith:QKAZPPJY","canonical_record":{"source":{"id":"2304.12264","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2023-04-24T17:04:04Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"8c26394e740a7c404a46940d3b3a820cb4a06cc50b2ba4fde57f32add60e9d5d","abstract_canon_sha256":"b6de3768240846f0e4257de862a40771e8f6f81eb55d9b3feed9dddbb17da067"},"schema_version":"1.0"},"canonical_sha256":"828197bd389e6a45edc27d848c414a712f547654cc5a0b72af765a1f4a8be76f","source":{"kind":"arxiv","id":"2304.12264","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2304.12264","created_at":"2026-07-05T06:03:49Z"},{"alias_kind":"arxiv_version","alias_value":"2304.12264v1","created_at":"2026-07-05T06:03:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2304.12264","created_at":"2026-07-05T06:03:49Z"},{"alias_kind":"pith_short_12","alias_value":"QKAZPPJYTZVE","created_at":"2026-07-05T06:03:49Z"},{"alias_kind":"pith_short_16","alias_value":"QKAZPPJYTZVEL3OC","created_at":"2026-07-05T06:03:49Z"},{"alias_kind":"pith_short_8","alias_value":"QKAZPPJY","created_at":"2026-07-05T06:03:49Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2023:QKAZPPJYTZVEL3OCPWCIYQKKOE","target":"record","payload":{"canonical_record":{"source":{"id":"2304.12264","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2023-04-24T17:04:04Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"8c26394e740a7c404a46940d3b3a820cb4a06cc50b2ba4fde57f32add60e9d5d","abstract_canon_sha256":"b6de3768240846f0e4257de862a40771e8f6f81eb55d9b3feed9dddbb17da067"},"schema_version":"1.0"},"canonical_sha256":"828197bd389e6a45edc27d848c414a712f547654cc5a0b72af765a1f4a8be76f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T06:03:49.773004Z","signature_b64":"YOos/53zGIRyj5BHrLKp7TXH1QJO/Vu4cbk08bXJLJhz/9CPyor7hYfANLQE5S7S413mS1ouRqB3QyjC3vBEAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"828197bd389e6a45edc27d848c414a712f547654cc5a0b72af765a1f4a8be76f","last_reissued_at":"2026-07-05T06:03:49.772572Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T06:03:49.772572Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2304.12264","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":"2026-07-05T06:03:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ACpuAFzsoAiWljOnABU8iTvZB0iyiw0jPqjcVCHN/irLRc6B0ta4GhqZhjZXKIEj4jc7PBb67lkKJQrHpztCBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-15T15:34:37.725687Z"},"content_sha256":"835c216cdc9da9c33c51bf581b9aacc55d0e4d9f7f6daaf29145995a93c73e77","schema_version":"1.0","event_id":"sha256:835c216cdc9da9c33c51bf581b9aacc55d0e4d9f7f6daaf29145995a93c73e77"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2023:QKAZPPJYTZVEL3OCPWCIYQKKOE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Rectangular Rotational Invariant Estimator for General Additive Noise Matrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Farzad Pourkamali, Nicolas Macris","submitted_at":"2023-04-24T17:04:04Z","abstract_excerpt":"We propose a rectangular rotational invariant estimator to recover a real matrix from noisy matrix observations coming from an arbitrary additive rotational invariant perturbation, in the large dimension limit. Using the Bayes-optimality of this estimator, we derive the asymptotic minimum mean squared error (MMSE). For the particular case of Gaussian noise, we find an explicit expression for the MMSE in terms of the limiting singular value distribution of the observation matrix. Moreover, we prove a formula linking the asymptotic mutual information and the limit of log-spherical integral of re"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2304.12264","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/2304.12264/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":"2026-07-05T06:03:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mYUxITvkupKWhnTL3Ewp/H+mdCVXfu4bV1yG/L9d/ATgodUlGIsWdwFQ04ENVRLsSyZiZE3Ap3gpb84etfqKAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-15T15:34:37.726196Z"},"content_sha256":"4e78a28c423966054a276ea6a5bedd711f9976413dcd03288eb99e43eedc4b54","schema_version":"1.0","event_id":"sha256:4e78a28c423966054a276ea6a5bedd711f9976413dcd03288eb99e43eedc4b54"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QKAZPPJYTZVEL3OCPWCIYQKKOE/bundle.json","state_url":"https://pith.science/pith/QKAZPPJYTZVEL3OCPWCIYQKKOE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QKAZPPJYTZVEL3OCPWCIYQKKOE/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":"2026-08-15T15:34:37Z","links":{"resolver":"https://pith.science/pith/QKAZPPJYTZVEL3OCPWCIYQKKOE","bundle":"https://pith.science/pith/QKAZPPJYTZVEL3OCPWCIYQKKOE/bundle.json","state":"https://pith.science/pith/QKAZPPJYTZVEL3OCPWCIYQKKOE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QKAZPPJYTZVEL3OCPWCIYQKKOE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:QKAZPPJYTZVEL3OCPWCIYQKKOE","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":"b6de3768240846f0e4257de862a40771e8f6f81eb55d9b3feed9dddbb17da067","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2023-04-24T17:04:04Z","title_canon_sha256":"8c26394e740a7c404a46940d3b3a820cb4a06cc50b2ba4fde57f32add60e9d5d"},"schema_version":"1.0","source":{"id":"2304.12264","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2304.12264","created_at":"2026-07-05T06:03:49Z"},{"alias_kind":"arxiv_version","alias_value":"2304.12264v1","created_at":"2026-07-05T06:03:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2304.12264","created_at":"2026-07-05T06:03:49Z"},{"alias_kind":"pith_short_12","alias_value":"QKAZPPJYTZVE","created_at":"2026-07-05T06:03:49Z"},{"alias_kind":"pith_short_16","alias_value":"QKAZPPJYTZVEL3OC","created_at":"2026-07-05T06:03:49Z"},{"alias_kind":"pith_short_8","alias_value":"QKAZPPJY","created_at":"2026-07-05T06:03:49Z"}],"graph_snapshots":[{"event_id":"sha256:4e78a28c423966054a276ea6a5bedd711f9976413dcd03288eb99e43eedc4b54","target":"graph","created_at":"2026-07-05T06:03:49Z","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/2304.12264/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We propose a rectangular rotational invariant estimator to recover a real matrix from noisy matrix observations coming from an arbitrary additive rotational invariant perturbation, in the large dimension limit. Using the Bayes-optimality of this estimator, we derive the asymptotic minimum mean squared error (MMSE). For the particular case of Gaussian noise, we find an explicit expression for the MMSE in terms of the limiting singular value distribution of the observation matrix. Moreover, we prove a formula linking the asymptotic mutual information and the limit of log-spherical integral of re","authors_text":"Farzad Pourkamali, Nicolas Macris","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2023-04-24T17:04:04Z","title":"Rectangular Rotational Invariant Estimator for General Additive Noise Matrices"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2304.12264","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":"sha256:835c216cdc9da9c33c51bf581b9aacc55d0e4d9f7f6daaf29145995a93c73e77","target":"record","created_at":"2026-07-05T06:03:49Z","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":"b6de3768240846f0e4257de862a40771e8f6f81eb55d9b3feed9dddbb17da067","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2023-04-24T17:04:04Z","title_canon_sha256":"8c26394e740a7c404a46940d3b3a820cb4a06cc50b2ba4fde57f32add60e9d5d"},"schema_version":"1.0","source":{"id":"2304.12264","kind":"arxiv","version":1}},"canonical_sha256":"828197bd389e6a45edc27d848c414a712f547654cc5a0b72af765a1f4a8be76f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"828197bd389e6a45edc27d848c414a712f547654cc5a0b72af765a1f4a8be76f","first_computed_at":"2026-07-05T06:03:49.772572Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T06:03:49.772572Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"YOos/53zGIRyj5BHrLKp7TXH1QJO/Vu4cbk08bXJLJhz/9CPyor7hYfANLQE5S7S413mS1ouRqB3QyjC3vBEAA==","signature_status":"signed_v1","signed_at":"2026-07-05T06:03:49.773004Z","signed_message":"canonical_sha256_bytes"},"source_id":"2304.12264","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:835c216cdc9da9c33c51bf581b9aacc55d0e4d9f7f6daaf29145995a93c73e77","sha256:4e78a28c423966054a276ea6a5bedd711f9976413dcd03288eb99e43eedc4b54"],"state_sha256":"f12c05df51689a1dcb0a9720184deda24f641cc19b5b1e4278c0dd8650cec9b2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"apfh5mCU6mQCyp3BTBSppRiuGGvamxlefujToYTFYv2f1aYJ5MVOSX0XZHba6CkQjMviQpsOPMi9q8ZkGV/XDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-15T15:34:37.730309Z","bundle_sha256":"e0c977eaa030c54111badc57532d2af59a611b27ce0b01ad9ceafc381e9cf765"}}