{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:4E5XVCJ6QXSDWMHDKW5SXS5ISN","short_pith_number":"pith:4E5XVCJ6","canonical_record":{"source":{"id":"2405.20993","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.IT","submitted_at":"2024-05-31T16:38:35Z","cross_cats_sorted":["cond-mat.dis-nn","cs.LG","math.IT","math.ST","stat.TH"],"title_canon_sha256":"f2fc0821daecc4ca0e8c33872a92cd37a8e3609fa000119c468ded6a23f7f69a","abstract_canon_sha256":"401802a044c7e6e337ca46b4d00f49c4d9cd22118896e391a99c6ee61fa66251"},"schema_version":"1.0"},"canonical_sha256":"e13b7a893e85e43b30e355bb2bcba893670e6c01c5c58a19f115631557bed0a5","source":{"kind":"arxiv","id":"2405.20993","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2405.20993","created_at":"2026-07-05T08:41:03Z"},{"alias_kind":"arxiv_version","alias_value":"2405.20993v2","created_at":"2026-07-05T08:41:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2405.20993","created_at":"2026-07-05T08:41:03Z"},{"alias_kind":"pith_short_12","alias_value":"4E5XVCJ6QXSD","created_at":"2026-07-05T08:41:03Z"},{"alias_kind":"pith_short_16","alias_value":"4E5XVCJ6QXSDWMHD","created_at":"2026-07-05T08:41:03Z"},{"alias_kind":"pith_short_8","alias_value":"4E5XVCJ6","created_at":"2026-07-05T08:41:03Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:4E5XVCJ6QXSDWMHDKW5SXS5ISN","target":"record","payload":{"canonical_record":{"source":{"id":"2405.20993","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.IT","submitted_at":"2024-05-31T16:38:35Z","cross_cats_sorted":["cond-mat.dis-nn","cs.LG","math.IT","math.ST","stat.TH"],"title_canon_sha256":"f2fc0821daecc4ca0e8c33872a92cd37a8e3609fa000119c468ded6a23f7f69a","abstract_canon_sha256":"401802a044c7e6e337ca46b4d00f49c4d9cd22118896e391a99c6ee61fa66251"},"schema_version":"1.0"},"canonical_sha256":"e13b7a893e85e43b30e355bb2bcba893670e6c01c5c58a19f115631557bed0a5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:41:03.431369Z","signature_b64":"3S+mv0+L+Yxx59kxXmWLq5BBU/fy1iB9Fg3n8eC0R0puaqjHTEELVqRw4B2XhkmdGS/wQOaZNHtINMx8FiEYAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e13b7a893e85e43b30e355bb2bcba893670e6c01c5c58a19f115631557bed0a5","last_reissued_at":"2026-07-05T08:41:03.430890Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:41:03.430890Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2405.20993","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":"2026-07-05T08:41:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1MY5iKcKaDMEbX7EWm94htWR04EInt40tHtgSPHY9uXqfyN3aohJxmos8OyEHZwmv2udzVc3ikmtMBkgllYmBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-19T08:25:23.929508Z"},"content_sha256":"86e73f59a15706fcbef7d136d7a5107200ef510e75d4aeef0e04aff852c8c95f","schema_version":"1.0","event_id":"sha256:86e73f59a15706fcbef7d136d7a5107200ef510e75d4aeef0e04aff852c8c95f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:4E5XVCJ6QXSDWMHDKW5SXS5ISN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Information limits and Thouless-Anderson-Palmer equations for spiked matrix models with structured noise","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cond-mat.dis-nn","cs.LG","math.IT","math.ST","stat.TH"],"primary_cat":"cs.IT","authors_text":"Francesco Camilli, Jean Barbier, Marco Mondelli, Yizhou Xu","submitted_at":"2024-05-31T16:38:35Z","abstract_excerpt":"We consider a prototypical problem of Bayesian inference for a structured spiked model: a low-rank signal is corrupted by additive noise. While both information-theoretic and algorithmic limits are well understood when the noise is a Gaussian Wigner matrix, the more realistic case of structured noise still proves to be challenging. To capture the structure while maintaining mathematical tractability, a line of work has focused on rotationally invariant noise. However, existing studies either provide sub-optimal algorithms or are limited to special cases of noise ensembles. In this paper, using"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2405.20993","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2405.20993/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":"2026-07-05T08:41:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"v+mkIWVbtFJZgD84iIhUQTrrgKF/+TYikH6RqZt5PRYN+uFJC9dCykbVI0XIh4drfMRjn9hX3GFDtI0WlCT3DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-19T08:25:23.930036Z"},"content_sha256":"7741b2639344c6040290b7557b2c8441a933febfc27a209ba30a0f51dfbf050f","schema_version":"1.0","event_id":"sha256:7741b2639344c6040290b7557b2c8441a933febfc27a209ba30a0f51dfbf050f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4E5XVCJ6QXSDWMHDKW5SXS5ISN/bundle.json","state_url":"https://pith.science/pith/4E5XVCJ6QXSDWMHDKW5SXS5ISN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4E5XVCJ6QXSDWMHDKW5SXS5ISN/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":"2026-08-19T08:25:23Z","links":{"resolver":"https://pith.science/pith/4E5XVCJ6QXSDWMHDKW5SXS5ISN","bundle":"https://pith.science/pith/4E5XVCJ6QXSDWMHDKW5SXS5ISN/bundle.json","state":"https://pith.science/pith/4E5XVCJ6QXSDWMHDKW5SXS5ISN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4E5XVCJ6QXSDWMHDKW5SXS5ISN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:4E5XVCJ6QXSDWMHDKW5SXS5ISN","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":"401802a044c7e6e337ca46b4d00f49c4d9cd22118896e391a99c6ee61fa66251","cross_cats_sorted":["cond-mat.dis-nn","cs.LG","math.IT","math.ST","stat.TH"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.IT","submitted_at":"2024-05-31T16:38:35Z","title_canon_sha256":"f2fc0821daecc4ca0e8c33872a92cd37a8e3609fa000119c468ded6a23f7f69a"},"schema_version":"1.0","source":{"id":"2405.20993","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2405.20993","created_at":"2026-07-05T08:41:03Z"},{"alias_kind":"arxiv_version","alias_value":"2405.20993v2","created_at":"2026-07-05T08:41:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2405.20993","created_at":"2026-07-05T08:41:03Z"},{"alias_kind":"pith_short_12","alias_value":"4E5XVCJ6QXSD","created_at":"2026-07-05T08:41:03Z"},{"alias_kind":"pith_short_16","alias_value":"4E5XVCJ6QXSDWMHD","created_at":"2026-07-05T08:41:03Z"},{"alias_kind":"pith_short_8","alias_value":"4E5XVCJ6","created_at":"2026-07-05T08:41:03Z"}],"graph_snapshots":[{"event_id":"sha256:7741b2639344c6040290b7557b2c8441a933febfc27a209ba30a0f51dfbf050f","target":"graph","created_at":"2026-07-05T08:41:03Z","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/2405.20993/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We consider a prototypical problem of Bayesian inference for a structured spiked model: a low-rank signal is corrupted by additive noise. While both information-theoretic and algorithmic limits are well understood when the noise is a Gaussian Wigner matrix, the more realistic case of structured noise still proves to be challenging. To capture the structure while maintaining mathematical tractability, a line of work has focused on rotationally invariant noise. However, existing studies either provide sub-optimal algorithms or are limited to special cases of noise ensembles. In this paper, using","authors_text":"Francesco Camilli, Jean Barbier, Marco Mondelli, Yizhou Xu","cross_cats":["cond-mat.dis-nn","cs.LG","math.IT","math.ST","stat.TH"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.IT","submitted_at":"2024-05-31T16:38:35Z","title":"Information limits and Thouless-Anderson-Palmer equations for spiked matrix models with structured noise"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2405.20993","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":"sha256:86e73f59a15706fcbef7d136d7a5107200ef510e75d4aeef0e04aff852c8c95f","target":"record","created_at":"2026-07-05T08:41:03Z","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":"401802a044c7e6e337ca46b4d00f49c4d9cd22118896e391a99c6ee61fa66251","cross_cats_sorted":["cond-mat.dis-nn","cs.LG","math.IT","math.ST","stat.TH"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.IT","submitted_at":"2024-05-31T16:38:35Z","title_canon_sha256":"f2fc0821daecc4ca0e8c33872a92cd37a8e3609fa000119c468ded6a23f7f69a"},"schema_version":"1.0","source":{"id":"2405.20993","kind":"arxiv","version":2}},"canonical_sha256":"e13b7a893e85e43b30e355bb2bcba893670e6c01c5c58a19f115631557bed0a5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e13b7a893e85e43b30e355bb2bcba893670e6c01c5c58a19f115631557bed0a5","first_computed_at":"2026-07-05T08:41:03.430890Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T08:41:03.430890Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3S+mv0+L+Yxx59kxXmWLq5BBU/fy1iB9Fg3n8eC0R0puaqjHTEELVqRw4B2XhkmdGS/wQOaZNHtINMx8FiEYAA==","signature_status":"signed_v1","signed_at":"2026-07-05T08:41:03.431369Z","signed_message":"canonical_sha256_bytes"},"source_id":"2405.20993","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:86e73f59a15706fcbef7d136d7a5107200ef510e75d4aeef0e04aff852c8c95f","sha256:7741b2639344c6040290b7557b2c8441a933febfc27a209ba30a0f51dfbf050f"],"state_sha256":"b29c1bf9efc5138d7a8b42d86f0a08135eee5b0fcebacdf77086330b447ac098"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0FrcwybrPRVh70zo/KVMpAtdwesPEDKTejeI0yjqxyvRWFP4t4j6Be2rWHBZQusD9THXQO5nczmfXok4XK3CDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-19T08:25:23.935022Z","bundle_sha256":"55fa50f87bf11f0b1d9c4ea23299749033e201a7739812ccf0b50ec714a5427d"}}