{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:FPYEEFNZD4JENWV54MVLFZ6MTJ","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":"466457aaf777224ce5e8bff1e187250de5ae54b7b8f00215ab6bfc217d53e929","cross_cats_sorted":["math.PR"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2026-06-29T09:57:39Z","title_canon_sha256":"43ac202af63b5325d3896a70ed9bcc6b253b8eaf67cec5f916be280113b7678f"},"schema_version":"1.0","source":{"id":"2606.30064","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.30064","created_at":"2026-06-30T02:17:48Z"},{"alias_kind":"arxiv_version","alias_value":"2606.30064v1","created_at":"2026-06-30T02:17:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.30064","created_at":"2026-06-30T02:17:48Z"},{"alias_kind":"pith_short_12","alias_value":"FPYEEFNZD4JE","created_at":"2026-06-30T02:17:48Z"},{"alias_kind":"pith_short_16","alias_value":"FPYEEFNZD4JENWV5","created_at":"2026-06-30T02:17:48Z"},{"alias_kind":"pith_short_8","alias_value":"FPYEEFNZ","created_at":"2026-06-30T02:17:48Z"}],"graph_snapshots":[{"event_id":"sha256:216ecaaa747b30fb420e13305b7d91d7ebff9bf4294667f12cd07ba850fe2cdf","target":"graph","created_at":"2026-06-30T02:17:48Z","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/2606.30064/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We introduce a data-driven probabilistic framework for learning systems based on Gibbs measures on hierarchical structures. Unlike standard empirical risk minimization, where a dataset is used to identify a single optimal parameter, our approach transforms the empirical loss function into an interaction potential defining an energy-based model. The resulting Gibbs distribution describes a family of equilibrium learning states generated by the data.\n  We formulate the consistency conditions of the associated finite-volume distributions and derive nonlinear integral fixed-point equations whose s","authors_text":"F. Herrera, L.U. Abdullaev, M.V.Velasco, U.A. Rozikov","cross_cats":["math.PR"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2026-06-29T09:57:39Z","title":"Data-Driven Energy-Based Learning via Gibbs Measures on Hierarchical Structures"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.30064","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":"sha256:2dd688b2fe8a15856ba252880eafef481f029962c1e2cf8130c7c4663885e737","target":"record","created_at":"2026-06-30T02:17:48Z","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":"466457aaf777224ce5e8bff1e187250de5ae54b7b8f00215ab6bfc217d53e929","cross_cats_sorted":["math.PR"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2026-06-29T09:57:39Z","title_canon_sha256":"43ac202af63b5325d3896a70ed9bcc6b253b8eaf67cec5f916be280113b7678f"},"schema_version":"1.0","source":{"id":"2606.30064","kind":"arxiv","version":1}},"canonical_sha256":"2bf04215b91f1246dabde32ab2e7cc9a7b7677f83554312c45c866adf235f594","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2bf04215b91f1246dabde32ab2e7cc9a7b7677f83554312c45c866adf235f594","first_computed_at":"2026-06-30T02:17:48.012154Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-30T02:17:48.012154Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Qh6oH2ZzCl8TC+QS3yH/d4ZMqWANjIlb3JTizcIWu6jU2cAIbZNfm6LePJdts5Y/PLlxignHJ18cpu+bTfu4Bg==","signature_status":"signed_v1","signed_at":"2026-06-30T02:17:48.012809Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.30064","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2dd688b2fe8a15856ba252880eafef481f029962c1e2cf8130c7c4663885e737","sha256:216ecaaa747b30fb420e13305b7d91d7ebff9bf4294667f12cd07ba850fe2cdf"],"state_sha256":"34f9f02a37525e58386057dc2e5a22cce19408dce4d4f9665ec4a626908ba817"}