{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:1994:NTEO3KDMCL2BW7RZNTE4RMGYP3","short_pith_number":"pith:NTEO3KDM","schema_version":"1.0","canonical_sha256":"6cc8eda86c12f41b7e396cc9c8b0d87ee029ad988446fcaa2acd773be94be43b","source":{"kind":"arxiv","id":"patt-sol/9403001","version":1},"attestation_state":"computed","paper":{"title":"On the validity of the linear speed selection mechanism for fronts of the nonlinear diffusion equation","license":"","headline":"","cross_cats":["nlin.PS"],"primary_cat":"patt-sol","authors_text":"Casilla 306, Chile), M. C. Depassier (Facultad de F\\'isica, P. Universidad Cat\\'olica de Chile, R. D. Benguria, Santiago 22","submitted_at":"1994-03-08T18:38:00Z","abstract_excerpt":"We consider the problem of the speed selection mechanism for the one dimensional nonlinear diffusion equation $u_t = u_{xx} + f(u)$. It has been rigorously shown by Aronson and Weinberger that for a wide class of functions $f$, sufficiently localized initial conditions evolve in time into a monotonic front which propagates with speed $c^*$ such that $2 \\sqrt{f'(0)} \\leq c^* < 2 \\sqrt{\\sup(f(u)/u)}$. The lower value $c_L = 2 \\sqrt{f'(0)}$ is that predicted by the linear marginal stability speed selection mechanism. We derive a new lower bound on the the speed of the selected front, this bound d"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"patt-sol/9403001","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"patt-sol","submitted_at":"1994-03-08T18:38:00Z","cross_cats_sorted":["nlin.PS"],"title_canon_sha256":"3bb9b2476b89e71752fedacb77685cce443636a5e7520e15891dd5b3c69f303d","abstract_canon_sha256":"db5d8951d3f1e6055571caf44137cb14ec513e7991bd079c388deb3319b09e73"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:09:14.771574Z","signature_b64":"nvUwpgYPT9xJtCQrxQ2ADwtzWVbSsWCRgpPNyXcyrZKhuVamHcUQAglWJemtScWap9Y1oyNP4D3x184RmBN5Dg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6cc8eda86c12f41b7e396cc9c8b0d87ee029ad988446fcaa2acd773be94be43b","last_reissued_at":"2026-05-18T01:09:14.771077Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:09:14.771077Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the validity of the linear speed selection mechanism for fronts of the nonlinear diffusion equation","license":"","headline":"","cross_cats":["nlin.PS"],"primary_cat":"patt-sol","authors_text":"Casilla 306, Chile), M. C. Depassier (Facultad de F\\'isica, P. Universidad Cat\\'olica de Chile, R. D. Benguria, Santiago 22","submitted_at":"1994-03-08T18:38:00Z","abstract_excerpt":"We consider the problem of the speed selection mechanism for the one dimensional nonlinear diffusion equation $u_t = u_{xx} + f(u)$. It has been rigorously shown by Aronson and Weinberger that for a wide class of functions $f$, sufficiently localized initial conditions evolve in time into a monotonic front which propagates with speed $c^*$ such that $2 \\sqrt{f'(0)} \\leq c^* < 2 \\sqrt{\\sup(f(u)/u)}$. The lower value $c_L = 2 \\sqrt{f'(0)}$ is that predicted by the linear marginal stability speed selection mechanism. We derive a new lower bound on the the speed of the selected front, this bound d"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"patt-sol/9403001","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"patt-sol/9403001","created_at":"2026-05-18T01:09:14.771181+00:00"},{"alias_kind":"arxiv_version","alias_value":"patt-sol/9403001v1","created_at":"2026-05-18T01:09:14.771181+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.patt-sol/9403001","created_at":"2026-05-18T01:09:14.771181+00:00"},{"alias_kind":"pith_short_12","alias_value":"NTEO3KDMCL2B","created_at":"2026-05-18T12:25:47.102015+00:00"},{"alias_kind":"pith_short_16","alias_value":"NTEO3KDMCL2BW7RZ","created_at":"2026-05-18T12:25:47.102015+00:00"},{"alias_kind":"pith_short_8","alias_value":"NTEO3KDM","created_at":"2026-05-18T12:25:47.102015+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/NTEO3KDMCL2BW7RZNTE4RMGYP3","json":"https://pith.science/pith/NTEO3KDMCL2BW7RZNTE4RMGYP3.json","graph_json":"https://pith.science/api/pith-number/NTEO3KDMCL2BW7RZNTE4RMGYP3/graph.json","events_json":"https://pith.science/api/pith-number/NTEO3KDMCL2BW7RZNTE4RMGYP3/events.json","paper":"https://pith.science/paper/NTEO3KDM"},"agent_actions":{"view_html":"https://pith.science/pith/NTEO3KDMCL2BW7RZNTE4RMGYP3","download_json":"https://pith.science/pith/NTEO3KDMCL2BW7RZNTE4RMGYP3.json","view_paper":"https://pith.science/paper/NTEO3KDM","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=patt-sol/9403001&json=true","fetch_graph":"https://pith.science/api/pith-number/NTEO3KDMCL2BW7RZNTE4RMGYP3/graph.json","fetch_events":"https://pith.science/api/pith-number/NTEO3KDMCL2BW7RZNTE4RMGYP3/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/NTEO3KDMCL2BW7RZNTE4RMGYP3/action/timestamp_anchor","attest_storage":"https://pith.science/pith/NTEO3KDMCL2BW7RZNTE4RMGYP3/action/storage_attestation","attest_author":"https://pith.science/pith/NTEO3KDMCL2BW7RZNTE4RMGYP3/action/author_attestation","sign_citation":"https://pith.science/pith/NTEO3KDMCL2BW7RZNTE4RMGYP3/action/citation_signature","submit_replication":"https://pith.science/pith/NTEO3KDMCL2BW7RZNTE4RMGYP3/action/replication_record"}},"created_at":"2026-05-18T01:09:14.771181+00:00","updated_at":"2026-05-18T01:09:14.771181+00:00"}