{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:OXNUSCKVYYPRX64XFVG7DX64SG","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":"b36a9dea425a0e4711d396b760160bcc6c2f9259e1c8b42b63747a61400e2604","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2018-12-07T00:16:02Z","title_canon_sha256":"3ba418c297a7fb82d5643ff1ffa80556d118884642f33ed48d2b3d7c2416d8be"},"schema_version":"1.0","source":{"id":"1812.02857","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1812.02857","created_at":"2026-05-17T23:58:51Z"},{"alias_kind":"arxiv_version","alias_value":"1812.02857v1","created_at":"2026-05-17T23:58:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1812.02857","created_at":"2026-05-17T23:58:51Z"},{"alias_kind":"pith_short_12","alias_value":"OXNUSCKVYYPR","created_at":"2026-05-18T12:32:43Z"},{"alias_kind":"pith_short_16","alias_value":"OXNUSCKVYYPRX64X","created_at":"2026-05-18T12:32:43Z"},{"alias_kind":"pith_short_8","alias_value":"OXNUSCKV","created_at":"2026-05-18T12:32:43Z"}],"graph_snapshots":[{"event_id":"sha256:ff49c145783182349cdf90c817a6e0c6270f3f9ff7f9298152293e2e610a0039","target":"graph","created_at":"2026-05-17T23:58:51Z","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":"A Cattaneo equation for a comb structure is considered. We present a rigorous analysis of the obtained fractional diffusion equation, and corresponding solutions for the probability distribution function are obtained in the form of the Fox $H$-function and its infinite series. The mean square displacement along the backbone is obtained as well in terms of the infinite series of the Fox $H$-function. The obtained solutions describe the transition from normal diffusion to subdiffusion, which results from the comb geometry.","authors_text":"Alexander Iomin, Trifce Sandev","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2018-12-07T00:16:02Z","title":"Finite-velocity diffusion on a comb"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.02857","kind":"arxiv","version":1},"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":"sha256:1a2b9096ab167dcdc88ca91621fcdfa633c38d00a31a46621aca06d84737c6c0","target":"record","created_at":"2026-05-17T23:58:51Z","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":"b36a9dea425a0e4711d396b760160bcc6c2f9259e1c8b42b63747a61400e2604","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2018-12-07T00:16:02Z","title_canon_sha256":"3ba418c297a7fb82d5643ff1ffa80556d118884642f33ed48d2b3d7c2416d8be"},"schema_version":"1.0","source":{"id":"1812.02857","kind":"arxiv","version":1}},"canonical_sha256":"75db490955c61f1bfb972d4df1dfdc918b3391ccf8a95124fff468782efac3a1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"75db490955c61f1bfb972d4df1dfdc918b3391ccf8a95124fff468782efac3a1","first_computed_at":"2026-05-17T23:58:51.655148Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:58:51.655148Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ewax1ioKJi5hYQ05VaZx//4VzwV4lwZFNyMi+gUpu4MN1Vkb7otCc1zl1Ff5aM0vtRUZ1lNZ2rfOkx7MjeVLAw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:58:51.655692Z","signed_message":"canonical_sha256_bytes"},"source_id":"1812.02857","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1a2b9096ab167dcdc88ca91621fcdfa633c38d00a31a46621aca06d84737c6c0","sha256:ff49c145783182349cdf90c817a6e0c6270f3f9ff7f9298152293e2e610a0039"],"state_sha256":"54f7914811441fd700066fd18a3c99f27fa2ac4ace6e9457ee803f72a9357edf"}