{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2023:FJNGWMOFXRD5IFFSJOZ5HDFEDB","short_pith_number":"pith:FJNGWMOF","canonical_record":{"source":{"id":"2401.00092","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2023-12-29T22:54:14Z","cross_cats_sorted":["nlin.AO"],"title_canon_sha256":"83edbaa9e295c0be6378157254adab8d5a8c389a2956237f062c674786614e1f","abstract_canon_sha256":"5f77251e59373c01167ab24dd01363ae9ccfcdefa324772e3caab4577c650775"},"schema_version":"1.0"},"canonical_sha256":"2a5a6b31c5bc47d414b24bb3d38ca418445a44f301528b8483415ea071c88d72","source":{"kind":"arxiv","id":"2401.00092","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"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2023:FJNGWMOFXRD5IFFSJOZ5HDFEDB","target":"record","payload":{"canonical_record":{"source":{"id":"2401.00092","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2023-12-29T22:54:14Z","cross_cats_sorted":["nlin.AO"],"title_canon_sha256":"83edbaa9e295c0be6378157254adab8d5a8c389a2956237f062c674786614e1f","abstract_canon_sha256":"5f77251e59373c01167ab24dd01363ae9ccfcdefa324772e3caab4577c650775"},"schema_version":"1.0"},"canonical_sha256":"2a5a6b31c5bc47d414b24bb3d38ca418445a44f301528b8483415ea071c88d72","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:49:27.600988Z","signature_b64":"P9VZ9m+gZU1nylQI8prdFYec3o8H7WHZmsfYqR1ptPS3B0Flm7H3dx8LYa4yEAdm2HPT9SYMVTDypK376KP8CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2a5a6b31c5bc47d414b24bb3d38ca418445a44f301528b8483415ea071c88d72","last_reissued_at":"2026-07-05T08:49:27.600525Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:49:27.600525Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2401.00092","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T08:49:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"a1dqavIIP1rpnkr4b1RYy4xL5oUo0vayg6k49UNnFHhlKZObTv4UI5W9xqbgEgayc0K2Lr8w100MQXidJD4RBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-07T09:18:31.272887Z"},"content_sha256":"74cdafaba9756bead3a2baa22babee8cb54580c6d9eacabf68f74a40451f0c97","schema_version":"1.0","event_id":"sha256:74cdafaba9756bead3a2baa22babee8cb54580c6d9eacabf68f74a40451f0c97"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2023:FJNGWMOFXRD5IFFSJOZ5HDFEDB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Universality of critical dynamics on a complex network","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["nlin.AO"],"primary_cat":"cond-mat.stat-mech","authors_text":"Mrinal Sarkar, Nicol\\`o Defenu, Tilman Enss","submitted_at":"2023-12-29T22:54:14Z","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 "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2401.00092","kind":"arxiv","version":3},"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/2401.00092/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":"2026-07-05T08:49:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AkatttsSD+zsJLdWZu6Kj9Iv3UGIUpptXxAoNK/2of2C7LUCgMI6HyG6r6yebansRnzYBV+8OQu0zMtlhiV9DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-07T09:18:31.273791Z"},"content_sha256":"369477c97eb81f35ef10707a2a149c1b32ff7802f0f893df619522bb8cebf35f","schema_version":"1.0","event_id":"sha256:369477c97eb81f35ef10707a2a149c1b32ff7802f0f893df619522bb8cebf35f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FJNGWMOFXRD5IFFSJOZ5HDFEDB/bundle.json","state_url":"https://pith.science/pith/FJNGWMOFXRD5IFFSJOZ5HDFEDB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FJNGWMOFXRD5IFFSJOZ5HDFEDB/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":"2026-08-07T09:18:31Z","links":{"resolver":"https://pith.science/pith/FJNGWMOFXRD5IFFSJOZ5HDFEDB","bundle":"https://pith.science/pith/FJNGWMOFXRD5IFFSJOZ5HDFEDB/bundle.json","state":"https://pith.science/pith/FJNGWMOFXRD5IFFSJOZ5HDFEDB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FJNGWMOFXRD5IFFSJOZ5HDFEDB/bundle.json"},"state":{"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"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tB1rVR36VD6Ko0lfE6I9UHq+wb++pJTsacYbHpZ2rXgGnQVlWxKv2Vv+1eO8b3ANy9R/0SBYr0WgI27J32KUAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-07T09:18:31.282772Z","bundle_sha256":"284c7d2eeb591807960f27f6cb8d03a6a33bbacb846c02027e77e1faf5e47d4b"}}