{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:FJNGWMOFXRD5IFFSJOZ5HDFEDB","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":"5f77251e59373c01167ab24dd01363ae9ccfcdefa324772e3caab4577c650775","cross_cats_sorted":["nlin.AO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2023-12-29T22:54:14Z","title_canon_sha256":"83edbaa9e295c0be6378157254adab8d5a8c389a2956237f062c674786614e1f"},"schema_version":"1.0","source":{"id":"2401.00092","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2401.00092","created_at":"2026-07-05T08:49:27Z"},{"alias_kind":"arxiv_version","alias_value":"2401.00092v3","created_at":"2026-07-05T08:49:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2401.00092","created_at":"2026-07-05T08:49:27Z"},{"alias_kind":"pith_short_12","alias_value":"FJNGWMOFXRD5","created_at":"2026-07-05T08:49:27Z"},{"alias_kind":"pith_short_16","alias_value":"FJNGWMOFXRD5IFFS","created_at":"2026-07-05T08:49:27Z"},{"alias_kind":"pith_short_8","alias_value":"FJNGWMOF","created_at":"2026-07-05T08:49:27Z"}],"graph_snapshots":[{"event_id":"sha256:369477c97eb81f35ef10707a2a149c1b32ff7802f0f893df619522bb8cebf35f","target":"graph","created_at":"2026-07-05T08:49:27Z","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/2401.00092/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We investigate the role of the spectral dimension $d_s$ in determining the universality of phase transitions on a complex network. Due to its structural heterogeneity, a complex network generally acts as a disordered system. Specifically, we study the synchronization and entrainment transitions in the nonequilibrium dynamics of the Kuramoto model and the phase transition of the equilibrium dynamics of the classical $XY$ model, thereby covering a broad spectrum from nonlinear dynamics to statistical and condensed matter physics. Using linear theory, we obtain a general relationship between the ","authors_text":"Mrinal Sarkar, Nicol\\`o Defenu, Tilman Enss","cross_cats":["nlin.AO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2023-12-29T22:54:14Z","title":"Universality of critical dynamics on a complex network"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2401.00092","kind":"arxiv","version":3},"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":"sha256:74cdafaba9756bead3a2baa22babee8cb54580c6d9eacabf68f74a40451f0c97","target":"record","created_at":"2026-07-05T08:49:27Z","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":"5f77251e59373c01167ab24dd01363ae9ccfcdefa324772e3caab4577c650775","cross_cats_sorted":["nlin.AO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2023-12-29T22:54:14Z","title_canon_sha256":"83edbaa9e295c0be6378157254adab8d5a8c389a2956237f062c674786614e1f"},"schema_version":"1.0","source":{"id":"2401.00092","kind":"arxiv","version":3}},"canonical_sha256":"2a5a6b31c5bc47d414b24bb3d38ca418445a44f301528b8483415ea071c88d72","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2a5a6b31c5bc47d414b24bb3d38ca418445a44f301528b8483415ea071c88d72","first_computed_at":"2026-07-05T08:49:27.600525Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T08:49:27.600525Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"P9VZ9m+gZU1nylQI8prdFYec3o8H7WHZmsfYqR1ptPS3B0Flm7H3dx8LYa4yEAdm2HPT9SYMVTDypK376KP8CA==","signature_status":"signed_v1","signed_at":"2026-07-05T08:49:27.600988Z","signed_message":"canonical_sha256_bytes"},"source_id":"2401.00092","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:74cdafaba9756bead3a2baa22babee8cb54580c6d9eacabf68f74a40451f0c97","sha256:369477c97eb81f35ef10707a2a149c1b32ff7802f0f893df619522bb8cebf35f"],"state_sha256":"2ae22a0c4a673724e8984de187eda65b9c33bd2cae8f9f8272426e0a09c9a368"}