{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:DMGXPUK4MLEUYB223NB4V57B7Y","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":"85161e9ebac931ec472472f98c54d33b68e74c98fec28c9ba21da37cc073d816","cross_cats_sorted":["cond-mat.stat-mech","nlin.PS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2016-10-24T20:20:13Z","title_canon_sha256":"4d882cca50b16e2e68259a89244d252616146f8ca60e3935dd731dc9c6bf88e5"},"schema_version":"1.0","source":{"id":"1610.07635","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.07635","created_at":"2026-05-18T00:20:07Z"},{"alias_kind":"arxiv_version","alias_value":"1610.07635v2","created_at":"2026-05-18T00:20:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.07635","created_at":"2026-05-18T00:20:07Z"},{"alias_kind":"pith_short_12","alias_value":"DMGXPUK4MLEU","created_at":"2026-05-18T12:30:12Z"},{"alias_kind":"pith_short_16","alias_value":"DMGXPUK4MLEUYB22","created_at":"2026-05-18T12:30:12Z"},{"alias_kind":"pith_short_8","alias_value":"DMGXPUK4","created_at":"2026-05-18T12:30:12Z"}],"graph_snapshots":[{"event_id":"sha256:25a28b806cee87393b6b0c6539885b735d4c195b1e9a09846dfc7b91b9362634","target":"graph","created_at":"2026-05-18T00:20:07Z","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"},"paper":{"abstract_excerpt":"We study diffusion-driven pattern-formation in networks of networks, a class of multilayer systems, where different layers have the same topology, but different internal dynamics. Agents are assumed to disperse within a layer by undergoing random walks, while they can be created or destroyed by reactions between or within a layer. We show that the stability of homogeneous steady states can be analyzed with a master stability function approach that reveals a deep analogy between pattern formation in networks and pattern formation in continuous space.For illustration we consider a generalized mo","authors_text":"Andreas Brechtel, Barbara Drossel, Daniel Ritterskamp, Philipp Gramlich, Thilo gross","cross_cats":["cond-mat.stat-mech","nlin.PS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2016-10-24T20:20:13Z","title":"Master stability functions reveal diffusion-driven pattern formation in networks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.07635","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:f474c9b18126e5b90420f71d2cb6a06f9ac5227930b9e0015ecd1320dd7cceb4","target":"record","created_at":"2026-05-18T00:20:07Z","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":"85161e9ebac931ec472472f98c54d33b68e74c98fec28c9ba21da37cc073d816","cross_cats_sorted":["cond-mat.stat-mech","nlin.PS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2016-10-24T20:20:13Z","title_canon_sha256":"4d882cca50b16e2e68259a89244d252616146f8ca60e3935dd731dc9c6bf88e5"},"schema_version":"1.0","source":{"id":"1610.07635","kind":"arxiv","version":2}},"canonical_sha256":"1b0d77d15c62c94c075adb43caf7e1fe27e4625b4765e3163f9df4c416adf0b1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1b0d77d15c62c94c075adb43caf7e1fe27e4625b4765e3163f9df4c416adf0b1","first_computed_at":"2026-05-18T00:20:07.369431Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:20:07.369431Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"t2NdglLxJdkpt4KLWgDxOFVnbI35sprQljCe5+Y/YRXS9awPLDUZR4/ruLW2ANOVpKU8lKeTm6KJxlhq8js1Dw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:20:07.369984Z","signed_message":"canonical_sha256_bytes"},"source_id":"1610.07635","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f474c9b18126e5b90420f71d2cb6a06f9ac5227930b9e0015ecd1320dd7cceb4","sha256:25a28b806cee87393b6b0c6539885b735d4c195b1e9a09846dfc7b91b9362634"],"state_sha256":"2d6678a78dd1bf24663665711b5d6f4a0c02a8da6442d8a692dc547190ad8327"}