{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:HLJVZCYGFITIOXHY3JM6F2HVMD","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":"520d769594ba4c3b6561bda5bc90543f5fc5c7992e0f671e22deea445a0c0016","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-08-21T05:53:50Z","title_canon_sha256":"b40d54ac327fcda3a73b1f1738c74be5139a14a2641bddfa750b2e514754c77c"},"schema_version":"1.0","source":{"id":"1508.05899","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1508.05899","created_at":"2026-05-18T01:20:45Z"},{"alias_kind":"arxiv_version","alias_value":"1508.05899v1","created_at":"2026-05-18T01:20:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.05899","created_at":"2026-05-18T01:20:45Z"},{"alias_kind":"pith_short_12","alias_value":"HLJVZCYGFITI","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_16","alias_value":"HLJVZCYGFITIOXHY","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_8","alias_value":"HLJVZCYG","created_at":"2026-05-18T12:29:25Z"}],"graph_snapshots":[{"event_id":"sha256:8e54e1d6934abdcb3cac710e3ab31522a3334213896d216a3980dcf1a7b5e999","target":"graph","created_at":"2026-05-18T01:20:45Z","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":"Exact solutions for nonlinear Arrhenius reaction-diffusion are constructed in $n$ dimensions. A single relationship between nonlinear diffusivity and the nonlinear reaction term leads to a nonclassical Lie symmetry whose invariant solutions have a heat flux that is exponential in time (either growth or decay), and satisfying a linear Helmholtz equation in space. This construction extends also to heterogeneous diffusion wherein the nonlinear diffusivity factorises to the product of a function of temperature and a function of position. Example solutions are given with applications to heat conduc","authors_text":"B. H. Bradshaw-Hajek, D. Triadis, P. Broadbridge","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-08-21T05:53:50Z","title":"Exact nonclassical symmetry solutions of Arrhenius reaction-diffusion"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.05899","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:fd58de90d2b582b4ca1dc762ddb395b8a48cd04cd79f9dd5f1c3acc6afb5f13c","target":"record","created_at":"2026-05-18T01:20:45Z","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":"520d769594ba4c3b6561bda5bc90543f5fc5c7992e0f671e22deea445a0c0016","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-08-21T05:53:50Z","title_canon_sha256":"b40d54ac327fcda3a73b1f1738c74be5139a14a2641bddfa750b2e514754c77c"},"schema_version":"1.0","source":{"id":"1508.05899","kind":"arxiv","version":1}},"canonical_sha256":"3ad35c8b062a26875cf8da59e2e8f560fafb4ecd4c6998787aa793674855b76c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3ad35c8b062a26875cf8da59e2e8f560fafb4ecd4c6998787aa793674855b76c","first_computed_at":"2026-05-18T01:20:45.329484Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:20:45.329484Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"RmHrL9Xh7w2eHPaapLIG4MMLOAWyrpH/9QI/Cpk6jfH1T8gCSeJx1AKlyQY1inoDwzAV1/iPF7AiYGSnP7i6Ag==","signature_status":"signed_v1","signed_at":"2026-05-18T01:20:45.330020Z","signed_message":"canonical_sha256_bytes"},"source_id":"1508.05899","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fd58de90d2b582b4ca1dc762ddb395b8a48cd04cd79f9dd5f1c3acc6afb5f13c","sha256:8e54e1d6934abdcb3cac710e3ab31522a3334213896d216a3980dcf1a7b5e999"],"state_sha256":"bca9546221acb307b931178ef2c1cdd06ffa654e1e2d26f10220ea45756ad568"}