{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:3B4P6ZDAD6BWSP3ZWHB4725DIA","short_pith_number":"pith:3B4P6ZDA","canonical_record":{"source":{"id":"2503.04454","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cond-mat.dis-nn","submitted_at":"2025-03-06T14:09:30Z","cross_cats_sorted":["stat.ML"],"title_canon_sha256":"0f49bb07b2350737441846fbdca85ed0b508c6961ce986c1256c7d4d1774967e","abstract_canon_sha256":"41c848b67495d5ee57b032cd7eccd036c323a8979e9b4e2b273e7147791e600d"},"schema_version":"1.0"},"canonical_sha256":"d878ff64601f83693f79b1c3cfeba34038d80fa4dd39313e9ec60589c75c732c","source":{"kind":"arxiv","id":"2503.04454","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2503.04454","created_at":"2026-07-05T10:25:39Z"},{"alias_kind":"arxiv_version","alias_value":"2503.04454v1","created_at":"2026-07-05T10:25:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2503.04454","created_at":"2026-07-05T10:25:39Z"},{"alias_kind":"pith_short_12","alias_value":"3B4P6ZDAD6BW","created_at":"2026-07-05T10:25:39Z"},{"alias_kind":"pith_short_16","alias_value":"3B4P6ZDAD6BWSP3Z","created_at":"2026-07-05T10:25:39Z"},{"alias_kind":"pith_short_8","alias_value":"3B4P6ZDA","created_at":"2026-07-05T10:25:39Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:3B4P6ZDAD6BWSP3ZWHB4725DIA","target":"record","payload":{"canonical_record":{"source":{"id":"2503.04454","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cond-mat.dis-nn","submitted_at":"2025-03-06T14:09:30Z","cross_cats_sorted":["stat.ML"],"title_canon_sha256":"0f49bb07b2350737441846fbdca85ed0b508c6961ce986c1256c7d4d1774967e","abstract_canon_sha256":"41c848b67495d5ee57b032cd7eccd036c323a8979e9b4e2b273e7147791e600d"},"schema_version":"1.0"},"canonical_sha256":"d878ff64601f83693f79b1c3cfeba34038d80fa4dd39313e9ec60589c75c732c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:25:39.144371Z","signature_b64":"hK40tnU1EKGdjPWGdKJxxjOgl+aySYAs1xa4lq1/VAoRpelZz//QRJ5YfVD4Av3e7KL0xIAEF+gcUTVXTb6pDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d878ff64601f83693f79b1c3cfeba34038d80fa4dd39313e9ec60589c75c732c","last_reissued_at":"2026-07-05T10:25:39.143381Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:25:39.143381Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2503.04454","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T10:25:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9V0nIquB7wettZ9cYNYDVvP6ZIIz35an94BJcBAcXdv9Ko/Staec8/DU4o/CNmJPqtpsSFXUA4qTsqfHpEj+CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-18T19:09:58.794977Z"},"content_sha256":"98bccae452691a1432eeb768112fe418a287c13a83670bfb5faea37d37e03267","schema_version":"1.0","event_id":"sha256:98bccae452691a1432eeb768112fe418a287c13a83670bfb5faea37d37e03267"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:3B4P6ZDAD6BWSP3ZWHB4725DIA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Beyond Disorder: Unveiling Cooperativeness in Multidirectional Associative Memories","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["stat.ML"],"primary_cat":"cond-mat.dis-nn","authors_text":"Adriano Barra, Andrea Alessandrelli, Andrea Ladiana, Andrea Lepre, Federico Ricci-Tersenghi","submitted_at":"2025-03-06T14:09:30Z","abstract_excerpt":"By leveraging tools from the statistical mechanics of complex systems, in these short notes we extend the architecture of a neural network for hetero-associative memory (called three-directional associative memories, TAM) to explore supervised and unsupervised learning protocols. In particular, by providing entropic-heterogeneous datasets to its various layers, we predict and quantify a new emergent phenomenon -- that we term {\\em layer's cooperativeness} -- where the interplay of dataset entropies across network's layers enhances their retrieval capabilities Beyond those they would have witho"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2503.04454","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/2503.04454/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":"2026-07-05T10:25:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mAeZ7YQf8kiqTONKtxJeDDGs5FzDEIeC3tvuQSuKXF6mQtdofteLo6sTf2AbdwzmYHtkkkdcVJRF8LDnSClZDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-18T19:09:58.795350Z"},"content_sha256":"3bc2c70bc3c868b97df74ff0413ffeab8f5f2fab021870c76acf38b9e66c36d8","schema_version":"1.0","event_id":"sha256:3bc2c70bc3c868b97df74ff0413ffeab8f5f2fab021870c76acf38b9e66c36d8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3B4P6ZDAD6BWSP3ZWHB4725DIA/bundle.json","state_url":"https://pith.science/pith/3B4P6ZDAD6BWSP3ZWHB4725DIA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3B4P6ZDAD6BWSP3ZWHB4725DIA/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":"2026-08-18T19:09:58Z","links":{"resolver":"https://pith.science/pith/3B4P6ZDAD6BWSP3ZWHB4725DIA","bundle":"https://pith.science/pith/3B4P6ZDAD6BWSP3ZWHB4725DIA/bundle.json","state":"https://pith.science/pith/3B4P6ZDAD6BWSP3ZWHB4725DIA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3B4P6ZDAD6BWSP3ZWHB4725DIA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:3B4P6ZDAD6BWSP3ZWHB4725DIA","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":"41c848b67495d5ee57b032cd7eccd036c323a8979e9b4e2b273e7147791e600d","cross_cats_sorted":["stat.ML"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cond-mat.dis-nn","submitted_at":"2025-03-06T14:09:30Z","title_canon_sha256":"0f49bb07b2350737441846fbdca85ed0b508c6961ce986c1256c7d4d1774967e"},"schema_version":"1.0","source":{"id":"2503.04454","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2503.04454","created_at":"2026-07-05T10:25:39Z"},{"alias_kind":"arxiv_version","alias_value":"2503.04454v1","created_at":"2026-07-05T10:25:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2503.04454","created_at":"2026-07-05T10:25:39Z"},{"alias_kind":"pith_short_12","alias_value":"3B4P6ZDAD6BW","created_at":"2026-07-05T10:25:39Z"},{"alias_kind":"pith_short_16","alias_value":"3B4P6ZDAD6BWSP3Z","created_at":"2026-07-05T10:25:39Z"},{"alias_kind":"pith_short_8","alias_value":"3B4P6ZDA","created_at":"2026-07-05T10:25:39Z"}],"graph_snapshots":[{"event_id":"sha256:3bc2c70bc3c868b97df74ff0413ffeab8f5f2fab021870c76acf38b9e66c36d8","target":"graph","created_at":"2026-07-05T10:25:39Z","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/2503.04454/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"By leveraging tools from the statistical mechanics of complex systems, in these short notes we extend the architecture of a neural network for hetero-associative memory (called three-directional associative memories, TAM) to explore supervised and unsupervised learning protocols. In particular, by providing entropic-heterogeneous datasets to its various layers, we predict and quantify a new emergent phenomenon -- that we term {\\em layer's cooperativeness} -- where the interplay of dataset entropies across network's layers enhances their retrieval capabilities Beyond those they would have witho","authors_text":"Adriano Barra, Andrea Alessandrelli, Andrea Ladiana, Andrea Lepre, Federico Ricci-Tersenghi","cross_cats":["stat.ML"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cond-mat.dis-nn","submitted_at":"2025-03-06T14:09:30Z","title":"Beyond Disorder: Unveiling Cooperativeness in Multidirectional Associative Memories"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2503.04454","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":"sha256:98bccae452691a1432eeb768112fe418a287c13a83670bfb5faea37d37e03267","target":"record","created_at":"2026-07-05T10:25:39Z","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":"41c848b67495d5ee57b032cd7eccd036c323a8979e9b4e2b273e7147791e600d","cross_cats_sorted":["stat.ML"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cond-mat.dis-nn","submitted_at":"2025-03-06T14:09:30Z","title_canon_sha256":"0f49bb07b2350737441846fbdca85ed0b508c6961ce986c1256c7d4d1774967e"},"schema_version":"1.0","source":{"id":"2503.04454","kind":"arxiv","version":1}},"canonical_sha256":"d878ff64601f83693f79b1c3cfeba34038d80fa4dd39313e9ec60589c75c732c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d878ff64601f83693f79b1c3cfeba34038d80fa4dd39313e9ec60589c75c732c","first_computed_at":"2026-07-05T10:25:39.143381Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:25:39.143381Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"hK40tnU1EKGdjPWGdKJxxjOgl+aySYAs1xa4lq1/VAoRpelZz//QRJ5YfVD4Av3e7KL0xIAEF+gcUTVXTb6pDg==","signature_status":"signed_v1","signed_at":"2026-07-05T10:25:39.144371Z","signed_message":"canonical_sha256_bytes"},"source_id":"2503.04454","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:98bccae452691a1432eeb768112fe418a287c13a83670bfb5faea37d37e03267","sha256:3bc2c70bc3c868b97df74ff0413ffeab8f5f2fab021870c76acf38b9e66c36d8"],"state_sha256":"c54e50e6c4bdca40d88d83167ca451717f236abde16e0fb644dfe679b192d095"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GLV1aJuDRTXc52Y+Os+NuifkUTK2J8cDjeFGVfj+moJ+yNFOZoS50dYtCGL3K8woYLPc0NY3oyb2TEeMw3QsBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-18T19:09:58.797843Z","bundle_sha256":"8c757882c0f0be4e17d2aa69f64a934a5a8591e6ffdfa941b866090d8e8ed2bb"}}