{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:1998:MHHE7HWAIBIBAPOA426X3MEPIR","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":"a9a61b121c55ad6f6c2ba8b57fc63d14555d36e1b2f90d51f341668d6989f6be","cross_cats_sorted":["nlin.PS","patt-sol"],"license":"","primary_cat":"cond-mat.soft","submitted_at":"1998-03-26T03:03:42Z","title_canon_sha256":"e55051ec6d64be00b5ad7203adc30e44e39a45c177ed2d6ecc6e64931dbf2f20"},"schema_version":"1.0","source":{"id":"cond-mat/9803315","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"cond-mat/9803315","created_at":"2026-05-18T01:39:30Z"},{"alias_kind":"arxiv_version","alias_value":"cond-mat/9803315v1","created_at":"2026-05-18T01:39:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.cond-mat/9803315","created_at":"2026-05-18T01:39:30Z"},{"alias_kind":"pith_short_12","alias_value":"MHHE7HWAIBIB","created_at":"2026-05-18T12:25:49Z"},{"alias_kind":"pith_short_16","alias_value":"MHHE7HWAIBIBAPOA","created_at":"2026-05-18T12:25:49Z"},{"alias_kind":"pith_short_8","alias_value":"MHHE7HWA","created_at":"2026-05-18T12:25:49Z"}],"graph_snapshots":[{"event_id":"sha256:2694ec40e3471289e8904df187b23658118a5f903d145e8e209d24355be550ce","target":"graph","created_at":"2026-05-18T01:39:30Z","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 investigate a class of stochastic growth models involving competition between two phases in which one of the phases has a competitive advantage. The equilibrium populations of the competing phases are calculated using a mean field analysis. Regression probabilities for the extinction of the advantaged phase are calculated in a leading order approximation. The results of the calculations are in good agreement with simulations carried out on a square lattice with periodic boundaries. The class of models are variants of the Williams- Bjerknes model for the growth of tumours in the basal layer ","authors_text":"B.I. Henry, M.T. Batchelor (ANU), S.D. Watt (UNSW)","cross_cats":["nlin.PS","patt-sol"],"headline":"","license":"","primary_cat":"cond-mat.soft","submitted_at":"1998-03-26T03:03:42Z","title":"Mean field analysis of Williams-Bjerknes type growth"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"cond-mat/9803315","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":"sha256:96a043aa88415cca80c81249f87ed54d4f8251a47dc87aa743196bbf6750053c","target":"record","created_at":"2026-05-18T01:39:30Z","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":"a9a61b121c55ad6f6c2ba8b57fc63d14555d36e1b2f90d51f341668d6989f6be","cross_cats_sorted":["nlin.PS","patt-sol"],"license":"","primary_cat":"cond-mat.soft","submitted_at":"1998-03-26T03:03:42Z","title_canon_sha256":"e55051ec6d64be00b5ad7203adc30e44e39a45c177ed2d6ecc6e64931dbf2f20"},"schema_version":"1.0","source":{"id":"cond-mat/9803315","kind":"arxiv","version":1}},"canonical_sha256":"61ce4f9ec04050103dc0e6bd7db08f4465e8e0128592080673ed9b03164f2023","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"61ce4f9ec04050103dc0e6bd7db08f4465e8e0128592080673ed9b03164f2023","first_computed_at":"2026-05-18T01:39:30.881609Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:39:30.881609Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6/n3zZKS9V4UchEyMjKJdKJM/jdbFu51FlSsQjBFO6tfN/chfPWiTLwCNB0JCGCIE6XeFdHl86kczJzGE1VyBA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:39:30.882223Z","signed_message":"canonical_sha256_bytes"},"source_id":"cond-mat/9803315","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:96a043aa88415cca80c81249f87ed54d4f8251a47dc87aa743196bbf6750053c","sha256:2694ec40e3471289e8904df187b23658118a5f903d145e8e209d24355be550ce"],"state_sha256":"30daca6422d89a1a02e942a392e36ded494758bd8a3b440ff1b0f7f2fe563b57"}