{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:TNJ7WHN643FVOKB2EOA423BWOW","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":"272f9055dab844f691532fe5bcecb20f8d7f3033a9aaf67eb92b0c5d409e5419","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2013-06-28T10:23:50Z","title_canon_sha256":"170e16a36b1006a34a340366f9a50dd09f71ab8faaa2ff5eac5d588a551c1c34"},"schema_version":"1.0","source":{"id":"1306.6781","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1306.6781","created_at":"2026-05-18T03:19:42Z"},{"alias_kind":"arxiv_version","alias_value":"1306.6781v1","created_at":"2026-05-18T03:19:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1306.6781","created_at":"2026-05-18T03:19:42Z"},{"alias_kind":"pith_short_12","alias_value":"TNJ7WHN643FV","created_at":"2026-05-18T12:28:02Z"},{"alias_kind":"pith_short_16","alias_value":"TNJ7WHN643FVOKB2","created_at":"2026-05-18T12:28:02Z"},{"alias_kind":"pith_short_8","alias_value":"TNJ7WHN6","created_at":"2026-05-18T12:28:02Z"}],"graph_snapshots":[{"event_id":"sha256:37c64302464169332dc137639ba7f498821190288dee9315260dac82258c55f6","target":"graph","created_at":"2026-05-18T03:19:42Z","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":"Reaction-diffusion processes in two-dimensional percolating structures are investigated. Two different problems are addressed: reaction spreading on a percolating cluster and front propagation through a percolating channel. For reaction spreading, numerical data and analytical estimates show a power-law behavior of the reaction product as M(t) \\sim t^dl, where dl is the connectivity dimension. In a percolating channel, a statistically stationary traveling wave develops. The speed and the width of the traveling wave are numerically computed. While the front speed is a low-fluctuating quantity a","authors_text":"Angelo Vulpiani, Davide Vergni, Federico Bianco, Sergio Chibbaro","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2013-06-28T10:23:50Z","title":"Reaction spreading on percolating clusters"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.6781","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:eeeb37c5a8444ae68df2a03dae91699f8287e7c7ba85777640baa8828e8e9ca8","target":"record","created_at":"2026-05-18T03:19:42Z","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":"272f9055dab844f691532fe5bcecb20f8d7f3033a9aaf67eb92b0c5d409e5419","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2013-06-28T10:23:50Z","title_canon_sha256":"170e16a36b1006a34a340366f9a50dd09f71ab8faaa2ff5eac5d588a551c1c34"},"schema_version":"1.0","source":{"id":"1306.6781","kind":"arxiv","version":1}},"canonical_sha256":"9b53fb1dbee6cb57283a2381cd6c36758a84b555d21b233ca885ec984badcc8a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9b53fb1dbee6cb57283a2381cd6c36758a84b555d21b233ca885ec984badcc8a","first_computed_at":"2026-05-18T03:19:42.991405Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:19:42.991405Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"sp3cmamwfPfiXwX1OMYLFJgqv9Po0uUUCuBskc3N9ZSkkW5wMIwdMkXShbESJHA1Y849SgE2ZagpNN+oBBtZAw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:19:42.991916Z","signed_message":"canonical_sha256_bytes"},"source_id":"1306.6781","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:eeeb37c5a8444ae68df2a03dae91699f8287e7c7ba85777640baa8828e8e9ca8","sha256:37c64302464169332dc137639ba7f498821190288dee9315260dac82258c55f6"],"state_sha256":"e6a812136842535d61b3b213379acfdf867d0b5b32ff2f1aac87dcaa3bf07e94"}