{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:MX3RN6CI5NJOKKDKXMGPCCQL5M","short_pith_number":"pith:MX3RN6CI","schema_version":"1.0","canonical_sha256":"65f716f848eb52e5286abb0cf10a0beb240d0aeb74d096017a49304f35b65c94","source":{"kind":"arxiv","id":"2501.08786","version":1},"attestation_state":"computed","paper":{"title":"Differentiability and overlap concentration in optimal Bayesian inference","license":"http://creativecommons.org/licenses/by-sa/4.0/","headline":"","cross_cats":["cs.IT","math.IT","math.ST","stat.TH"],"primary_cat":"math.PR","authors_text":"Hong-Bin Chen (IHES), Victor Issa (ENS de Lyon)","submitted_at":"2025-01-15T13:16:39Z","abstract_excerpt":"In this short note, we consider models of optimal Bayesian inference of finite-rank tensor products. We add to the model a linear channel parametrized by $h$. We show that at every interior differentiable point $h$ of the free energy (associated with the model), the overlap concentrates at the gradient of the free energy and the minimum mean-square error converges to a related limit. In other words, the model is replica-symmetric at every differentiable point. At any signal-to-noise ratio, such points $h$ form a full-measure set (hence $h=0$ belongs to the closure of these points). For a suffi"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2501.08786","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.PR","submitted_at":"2025-01-15T13:16:39Z","cross_cats_sorted":["cs.IT","math.IT","math.ST","stat.TH"],"title_canon_sha256":"12af7d2bca280aabcc14263b94f0c63946164c2c332a47b6537a130d15fd3fdf","abstract_canon_sha256":"7ca3391fbf7c5c770354d33889a758d66ce7ffb5cd9ebb78362d3860c4edf4c3"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:01:26.038181Z","signature_b64":"rr+eyx5tFyi7+rv+G0oJObuNS4sNbDAurg9Q/AZVGq/vV2wG0XnmH3gpB8KBNrggmMYzJiKSzOYvpf60drWsCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"65f716f848eb52e5286abb0cf10a0beb240d0aeb74d096017a49304f35b65c94","last_reissued_at":"2026-07-05T10:01:26.037766Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:01:26.037766Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Differentiability and overlap concentration in optimal Bayesian inference","license":"http://creativecommons.org/licenses/by-sa/4.0/","headline":"","cross_cats":["cs.IT","math.IT","math.ST","stat.TH"],"primary_cat":"math.PR","authors_text":"Hong-Bin Chen (IHES), Victor Issa (ENS de Lyon)","submitted_at":"2025-01-15T13:16:39Z","abstract_excerpt":"In this short note, we consider models of optimal Bayesian inference of finite-rank tensor products. We add to the model a linear channel parametrized by $h$. We show that at every interior differentiable point $h$ of the free energy (associated with the model), the overlap concentrates at the gradient of the free energy and the minimum mean-square error converges to a related limit. In other words, the model is replica-symmetric at every differentiable point. At any signal-to-noise ratio, such points $h$ form a full-measure set (hence $h=0$ belongs to the closure of these points). For a suffi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2501.08786","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/2501.08786/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2501.08786","created_at":"2026-07-05T10:01:26.037828+00:00"},{"alias_kind":"arxiv_version","alias_value":"2501.08786v1","created_at":"2026-07-05T10:01:26.037828+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2501.08786","created_at":"2026-07-05T10:01:26.037828+00:00"},{"alias_kind":"pith_short_12","alias_value":"MX3RN6CI5NJO","created_at":"2026-07-05T10:01:26.037828+00:00"},{"alias_kind":"pith_short_16","alias_value":"MX3RN6CI5NJOKKDK","created_at":"2026-07-05T10:01:26.037828+00:00"},{"alias_kind":"pith_short_8","alias_value":"MX3RN6CI","created_at":"2026-07-05T10:01:26.037828+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2506.06749","citing_title":"Statistical Limits for Finite-Rank Tensor Estimation","ref_index":14,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/MX3RN6CI5NJOKKDKXMGPCCQL5M","json":"https://pith.science/pith/MX3RN6CI5NJOKKDKXMGPCCQL5M.json","graph_json":"https://pith.science/api/pith-number/MX3RN6CI5NJOKKDKXMGPCCQL5M/graph.json","events_json":"https://pith.science/api/pith-number/MX3RN6CI5NJOKKDKXMGPCCQL5M/events.json","paper":"https://pith.science/paper/MX3RN6CI"},"agent_actions":{"view_html":"https://pith.science/pith/MX3RN6CI5NJOKKDKXMGPCCQL5M","download_json":"https://pith.science/pith/MX3RN6CI5NJOKKDKXMGPCCQL5M.json","view_paper":"https://pith.science/paper/MX3RN6CI","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2501.08786&json=true","fetch_graph":"https://pith.science/api/pith-number/MX3RN6CI5NJOKKDKXMGPCCQL5M/graph.json","fetch_events":"https://pith.science/api/pith-number/MX3RN6CI5NJOKKDKXMGPCCQL5M/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/MX3RN6CI5NJOKKDKXMGPCCQL5M/action/timestamp_anchor","attest_storage":"https://pith.science/pith/MX3RN6CI5NJOKKDKXMGPCCQL5M/action/storage_attestation","attest_author":"https://pith.science/pith/MX3RN6CI5NJOKKDKXMGPCCQL5M/action/author_attestation","sign_citation":"https://pith.science/pith/MX3RN6CI5NJOKKDKXMGPCCQL5M/action/citation_signature","submit_replication":"https://pith.science/pith/MX3RN6CI5NJOKKDKXMGPCCQL5M/action/replication_record"}},"created_at":"2026-07-05T10:01:26.037828+00:00","updated_at":"2026-07-05T10:01:26.037828+00:00"}