{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:A3TATGVZOPTWSNRZLFCDKMGQCH","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":"8a8fa5d0ce97b757bd8d58bd3d380a238f7aecf1313a788147f84960dca8bb06","cross_cats_sorted":["physics.soc-ph"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cond-mat.dis-nn","submitted_at":"2021-10-17T19:49:57Z","title_canon_sha256":"d717e0e2a074a38b25ec837e7318edc4a543ac8c42d2e209ef54800ff200332d"},"schema_version":"1.0","source":{"id":"2110.08907","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2110.08907","created_at":"2026-07-05T09:43:21Z"},{"alias_kind":"arxiv_version","alias_value":"2110.08907v2","created_at":"2026-07-05T09:43:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2110.08907","created_at":"2026-07-05T09:43:21Z"},{"alias_kind":"pith_short_12","alias_value":"A3TATGVZOPTW","created_at":"2026-07-05T09:43:21Z"},{"alias_kind":"pith_short_16","alias_value":"A3TATGVZOPTWSNRZ","created_at":"2026-07-05T09:43:21Z"},{"alias_kind":"pith_short_8","alias_value":"A3TATGVZ","created_at":"2026-07-05T09:43:21Z"}],"graph_snapshots":[{"event_id":"sha256:11fe76fab774cd8b4bcd16c31ba655c23b770c05179ebf9e2d142bf4b7c0ef7f","target":"graph","created_at":"2026-07-05T09:43:21Z","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/2110.08907/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Interdependence is a fundamental ingredient to analyze the stability of many real-world complex systems featuring functional liasons. Yet, physical realizations of this coupling are still unknown, due to the lack of a theoretical framework for their study. To address this gap, we develop an interdependent magnetization framework and show that dependency links between $K-1$ pairwise networks of Ising spins can be rigorously mapped to directed $K$-spin interactions or to adaptive thermal couplings. We adopt the thermal portrait to determine analytically the phase diagram of the model under diffe","authors_text":"Bnaya Gross, Ivan Bonamassa, Shlomo Havlin","cross_cats":["physics.soc-ph"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cond-mat.dis-nn","submitted_at":"2021-10-17T19:49:57Z","title":"Realizing interdependent couplings as thermal or higher-order interactions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2110.08907","kind":"arxiv","version":2},"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":"sha256:3adc35c894b74fd6fad843d2f17e4f1ce57807adb16fe8718c727fe37b772116","target":"record","created_at":"2026-07-05T09:43:21Z","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":"8a8fa5d0ce97b757bd8d58bd3d380a238f7aecf1313a788147f84960dca8bb06","cross_cats_sorted":["physics.soc-ph"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cond-mat.dis-nn","submitted_at":"2021-10-17T19:49:57Z","title_canon_sha256":"d717e0e2a074a38b25ec837e7318edc4a543ac8c42d2e209ef54800ff200332d"},"schema_version":"1.0","source":{"id":"2110.08907","kind":"arxiv","version":2}},"canonical_sha256":"06e6099ab973e769363959443530d011f0496c73246f2588a47e9cef0ce2b875","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"06e6099ab973e769363959443530d011f0496c73246f2588a47e9cef0ce2b875","first_computed_at":"2026-07-05T09:43:21.152634Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:43:21.152634Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"uQ4mDMZUEoahbg1esgZ5YkME5N/Q5pS/61TlUmN6dqOmS8PaITRVvD2boC+zDrrWgDkhCBfjqrJeK0lJzwkaCA==","signature_status":"signed_v1","signed_at":"2026-07-05T09:43:21.153068Z","signed_message":"canonical_sha256_bytes"},"source_id":"2110.08907","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3adc35c894b74fd6fad843d2f17e4f1ce57807adb16fe8718c727fe37b772116","sha256:11fe76fab774cd8b4bcd16c31ba655c23b770c05179ebf9e2d142bf4b7c0ef7f"],"state_sha256":"bf8606f189629daa28de41f8931a58921878bb8d2b46431fec007c56c1f9b42c"}