{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:EFXHWSDX5QRYF6IGYV7BOIZBRX","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":"7d94cf0a2dd7bc6eb1236f6f237481649b53e477c49e43dae13723ab1ab8b810","cross_cats_sorted":["cond-mat.stat-mech","cs.LG"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cond-mat.soft","submitted_at":"2026-06-07T15:48:50Z","title_canon_sha256":"1c316078bd0444d86eec07849c5377304e5646494e37ba6767f02cb466f81074"},"schema_version":"1.0","source":{"id":"2606.08694","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.08694","created_at":"2026-06-09T01:05:47Z"},{"alias_kind":"arxiv_version","alias_value":"2606.08694v1","created_at":"2026-06-09T01:05:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.08694","created_at":"2026-06-09T01:05:47Z"},{"alias_kind":"pith_short_12","alias_value":"EFXHWSDX5QRY","created_at":"2026-06-09T01:05:47Z"},{"alias_kind":"pith_short_16","alias_value":"EFXHWSDX5QRYF6IG","created_at":"2026-06-09T01:05:47Z"},{"alias_kind":"pith_short_8","alias_value":"EFXHWSDX","created_at":"2026-06-09T01:05:47Z"}],"graph_snapshots":[{"event_id":"sha256:77ca449983d77eb4e8a9cf21fed639c8a672822c95d09f23c07f298ae4e0b867","target":"graph","created_at":"2026-06-09T01:05:47Z","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/2606.08694/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Generative models are increasingly used to capture correlations in many-body systems, but the representations they learn remain largely opaque to physical interpretation. Here, we establish an intuitive criterion that quantifies the capacity of a variational autoencoder (VAE) to faithfully reconstruct the joint probability distribution of a many body system. In a nutshell, a bound on the VAE capacity is obtained by comparing the rate of the latent channel to the bipartite mutual information of the data. Using this bound, we show that the conditionally independent decoder of any successful VAE ","authors_text":"Marco Biroli, Max Welling, Vincenzo Vitelli","cross_cats":["cond-mat.stat-mech","cs.LG"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cond-mat.soft","submitted_at":"2026-06-07T15:48:50Z","title":"Discovering and decoding latent mean-field structure with variational autoencoders"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.08694","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:e7aa9c09c27e1760e8fabc3773b9b0dfca8c8b9db7298efc8462b446b623a87a","target":"record","created_at":"2026-06-09T01:05:47Z","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":"7d94cf0a2dd7bc6eb1236f6f237481649b53e477c49e43dae13723ab1ab8b810","cross_cats_sorted":["cond-mat.stat-mech","cs.LG"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cond-mat.soft","submitted_at":"2026-06-07T15:48:50Z","title_canon_sha256":"1c316078bd0444d86eec07849c5377304e5646494e37ba6767f02cb466f81074"},"schema_version":"1.0","source":{"id":"2606.08694","kind":"arxiv","version":1}},"canonical_sha256":"216e7b4877ec2382f906c57e1723218dce5f9f485ef92aeb80c030c7b6e9de59","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"216e7b4877ec2382f906c57e1723218dce5f9f485ef92aeb80c030c7b6e9de59","first_computed_at":"2026-06-09T01:05:47.670085Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-09T01:05:47.670085Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"jzvfE48vVo3+HG50zNhWIjGWzWpk60qL7z6wnVRGDoW2qTB3lTWbzjDaGqWzG/p39AdeZaI2/5w9BGxJvP+CDQ==","signature_status":"signed_v1","signed_at":"2026-06-09T01:05:47.670607Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.08694","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e7aa9c09c27e1760e8fabc3773b9b0dfca8c8b9db7298efc8462b446b623a87a","sha256:77ca449983d77eb4e8a9cf21fed639c8a672822c95d09f23c07f298ae4e0b867"],"state_sha256":"7285202addac6e7b10000bfcb4fc3187893c18f261b363cb1352ff93a8eafbdf"}