{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:2SBF5TTC6Z2TP3577QXM7XLFBK","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":"0cf62e196a4d0a465421a177f9b58aa7c81cab34176831f96cf7bc4b76f75914","cross_cats_sorted":["cond-mat.stat-mech","cs.IT","math-ph","math.IT","math.MP","math.ST","stat.TH"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2023-11-29T22:03:46Z","title_canon_sha256":"62c1769556e1833f0afc65715a46851ecb4cda1af6878a65a497c8603803c33d"},"schema_version":"1.0","source":{"id":"2312.00071","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2312.00071","created_at":"2026-07-05T07:19:03Z"},{"alias_kind":"arxiv_version","alias_value":"2312.00071v1","created_at":"2026-07-05T07:19:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2312.00071","created_at":"2026-07-05T07:19:03Z"},{"alias_kind":"pith_short_12","alias_value":"2SBF5TTC6Z2T","created_at":"2026-07-05T07:19:03Z"},{"alias_kind":"pith_short_16","alias_value":"2SBF5TTC6Z2TP357","created_at":"2026-07-05T07:19:03Z"},{"alias_kind":"pith_short_8","alias_value":"2SBF5TTC","created_at":"2026-07-05T07:19:03Z"}],"graph_snapshots":[{"event_id":"sha256:0b04568fa57e05ac648a20f0fa1208a98f08dae70c0f67338b768bb791187f08","target":"graph","created_at":"2026-07-05T07:19:03Z","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/2312.00071/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Relying on a recent progress made in studying bilinearly indexed (bli) random processes in \\cite{Stojnicnflgscompyx23,Stojnicsflgscompyx23}, the main foundational principles of fully lifted random duality theory (fl RDT) were established in \\cite{Stojnicflrdt23}. We here study famous Hopfield models and show that their statistical behavior can be characterized via the fl RDT. Due to a nestedly lifted nature, the resulting characterizations and, therefore, the whole analytical machinery that produces them, become fully operational only if one can successfully conduct underlying numerical evalua","authors_text":"Mihailo Stojnic","cross_cats":["cond-mat.stat-mech","cs.IT","math-ph","math.IT","math.MP","math.ST","stat.TH"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2023-11-29T22:03:46Z","title":"Studying Hopfield models via fully lifted random duality theory"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2312.00071","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":"sha256:22b61079e9523bdf502c6466fcdffbce83972a5ce8097c3ba6fbc4eb69d3005a","target":"record","created_at":"2026-07-05T07:19:03Z","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":"0cf62e196a4d0a465421a177f9b58aa7c81cab34176831f96cf7bc4b76f75914","cross_cats_sorted":["cond-mat.stat-mech","cs.IT","math-ph","math.IT","math.MP","math.ST","stat.TH"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2023-11-29T22:03:46Z","title_canon_sha256":"62c1769556e1833f0afc65715a46851ecb4cda1af6878a65a497c8603803c33d"},"schema_version":"1.0","source":{"id":"2312.00071","kind":"arxiv","version":1}},"canonical_sha256":"d4825ece62f67537efbffc2ecfdd650a8fc722f6886ea4341adf6a6d813fceec","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d4825ece62f67537efbffc2ecfdd650a8fc722f6886ea4341adf6a6d813fceec","first_computed_at":"2026-07-05T07:19:03.229052Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T07:19:03.229052Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"o6TJhg8GUsv+XyuSiDp6qd3DloV53ohVQjvRvq7NcU4Dm2KDAjY3w/tLmoMzqFBzVFs9NjzIInJDyLF4/q68Ag==","signature_status":"signed_v1","signed_at":"2026-07-05T07:19:03.229564Z","signed_message":"canonical_sha256_bytes"},"source_id":"2312.00071","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:22b61079e9523bdf502c6466fcdffbce83972a5ce8097c3ba6fbc4eb69d3005a","sha256:0b04568fa57e05ac648a20f0fa1208a98f08dae70c0f67338b768bb791187f08"],"state_sha256":"4af0bafd61a5a60550c665868d57c5ec32e713b6eb60c20a79a89b3df418fdd4"}