{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:F6DKKC4I7ENAPKXQRTZ553AQGJ","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":"da9a4a6889c078108ad62f3a9c9c30ca8023afc734c516521c7f7b52d56e6ca8","cross_cats_sorted":["cond-mat.stat-mech","physics.soc-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.dis-nn","submitted_at":"2019-08-25T21:12:26Z","title_canon_sha256":"36e7f57021128f4f3c839b7e00b9d7fccedc52d4fe03525c14f0b14919ecf94d"},"schema_version":"1.0","source":{"id":"1908.09392","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1908.09392","created_at":"2026-07-05T00:28:12Z"},{"alias_kind":"arxiv_version","alias_value":"1908.09392v2","created_at":"2026-07-05T00:28:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.09392","created_at":"2026-07-05T00:28:12Z"},{"alias_kind":"pith_short_12","alias_value":"F6DKKC4I7ENA","created_at":"2026-07-05T00:28:12Z"},{"alias_kind":"pith_short_16","alias_value":"F6DKKC4I7ENAPKXQ","created_at":"2026-07-05T00:28:12Z"},{"alias_kind":"pith_short_8","alias_value":"F6DKKC4I","created_at":"2026-07-05T00:28:12Z"}],"graph_snapshots":[{"event_id":"sha256:9d747c9476764f875df5332a0d2780c37dfb3a8415e9d761625184388de22144","target":"graph","created_at":"2026-07-05T00:28:12Z","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/1908.09392/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Network geometry has strong effects on network dynamics. In particular, the underlying hyperbolic geometry of discrete manifolds has recently been shown to affect their critical percolation properties. Here we investigate the properties of link percolation in non-amenable two-dimensional branching simplicial and cell complexes, i.e., simplicial and cell complexes in which the boundary scales like the volume. We establish the relation between the equations determining the percolation probability in random branching cell complexes and the equation for interdependent percolation in multiplex netw","authors_text":"Ginestra Bianconi, Ivan Kryven, Robert M. Ziff","cross_cats":["cond-mat.stat-mech","physics.soc-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.dis-nn","submitted_at":"2019-08-25T21:12:26Z","title":"Percolation on branching simplicial and cell complexes and its relation to interdependent percolation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.09392","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":"sha256:1dceb15dc211636ba4d9cb3ff33f1c3f848819c1aec40b8278163df2789b0243","target":"record","created_at":"2026-07-05T00:28:12Z","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":"da9a4a6889c078108ad62f3a9c9c30ca8023afc734c516521c7f7b52d56e6ca8","cross_cats_sorted":["cond-mat.stat-mech","physics.soc-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.dis-nn","submitted_at":"2019-08-25T21:12:26Z","title_canon_sha256":"36e7f57021128f4f3c839b7e00b9d7fccedc52d4fe03525c14f0b14919ecf94d"},"schema_version":"1.0","source":{"id":"1908.09392","kind":"arxiv","version":2}},"canonical_sha256":"2f86a50b88f91a07aaf08cf3deec103241c6c424ae1115c089f30133e5e6fc42","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2f86a50b88f91a07aaf08cf3deec103241c6c424ae1115c089f30133e5e6fc42","first_computed_at":"2026-07-05T00:28:12.264045Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T00:28:12.264045Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9uA045451aymxaFFb6jClhXfSEBRA+iY3L9L9RdXD0nM0wK0kgULRYbl76xbOPUkshPc750Az0SIFz5rQj9DBg==","signature_status":"signed_v1","signed_at":"2026-07-05T00:28:12.264546Z","signed_message":"canonical_sha256_bytes"},"source_id":"1908.09392","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1dceb15dc211636ba4d9cb3ff33f1c3f848819c1aec40b8278163df2789b0243","sha256:9d747c9476764f875df5332a0d2780c37dfb3a8415e9d761625184388de22144"],"state_sha256":"e929a9a61f6e4b3b36d2a392f7b4b1f066d139bd5ac83ad96d9ccba1d6bb47f9"}