{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:UYFOWC7NVMVYBISKQZODVT3D4S","short_pith_number":"pith:UYFOWC7N","schema_version":"1.0","canonical_sha256":"a60aeb0bedab2b80a24a865c3acf63e4810bd92c9aaad51e9cc5ce6f605f66b2","source":{"kind":"arxiv","id":"1009.4092","version":1},"attestation_state":"computed","paper":{"title":"On the energy-minimizing steady states of a thin film equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.AP","authors_text":"Almut Burchard, Benjamin K. Stephens, Marina Chugunova","submitted_at":"2010-09-21T13:41:25Z","abstract_excerpt":"Steady states of the thin film equation $u_t+[u^3 (u_xxx + \\alpha^2 u_x -\\sin(x) )]_x=0$ are considered on the periodic domain $\\Omega = (-\\pi,\\pi)$. The equation defines a generalized gradient flow for an energy functional that controls the $H^1$-norm. The main result establishes that there exists for each given mass a unique nonnegative function of minimal energy. This minimizer is symmetric decreasing about $x=0$. For $\\alpha<1$ there is a critical value for the mass at which the minimizer has a touchdown zero. If the mass exceeds this value, the minimizer is strictly positive. Otherwise, i"},"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":"1009.4092","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-09-21T13:41:25Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"f14cb6a1df3ba25569f9351932490857eedcc2aed017df038bb270644ab22353","abstract_canon_sha256":"5654468b7ab1634b9f16509bb44b4c4efd8d0fd54cdbd83605d518a71d5f97a7"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:40:34.554022Z","signature_b64":"sUyTFwfsxh8KHrC2s8TiAbg2x9PtoUPa+5ii0/8sSEXBzT/AGN7aZYghSBBUFoj84kefcikML1CSA4DPMvyCAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a60aeb0bedab2b80a24a865c3acf63e4810bd92c9aaad51e9cc5ce6f605f66b2","last_reissued_at":"2026-05-18T04:40:34.553561Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:40:34.553561Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the energy-minimizing steady states of a thin film equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.AP","authors_text":"Almut Burchard, Benjamin K. Stephens, Marina Chugunova","submitted_at":"2010-09-21T13:41:25Z","abstract_excerpt":"Steady states of the thin film equation $u_t+[u^3 (u_xxx + \\alpha^2 u_x -\\sin(x) )]_x=0$ are considered on the periodic domain $\\Omega = (-\\pi,\\pi)$. The equation defines a generalized gradient flow for an energy functional that controls the $H^1$-norm. The main result establishes that there exists for each given mass a unique nonnegative function of minimal energy. This minimizer is symmetric decreasing about $x=0$. For $\\alpha<1$ there is a critical value for the mass at which the minimizer has a touchdown zero. If the mass exceeds this value, the minimizer is strictly positive. Otherwise, i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.4092","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":"1009.4092","created_at":"2026-05-18T04:40:34.553635+00:00"},{"alias_kind":"arxiv_version","alias_value":"1009.4092v1","created_at":"2026-05-18T04:40:34.553635+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1009.4092","created_at":"2026-05-18T04:40:34.553635+00:00"},{"alias_kind":"pith_short_12","alias_value":"UYFOWC7NVMVY","created_at":"2026-05-18T12:26:15.391820+00:00"},{"alias_kind":"pith_short_16","alias_value":"UYFOWC7NVMVYBISK","created_at":"2026-05-18T12:26:15.391820+00:00"},{"alias_kind":"pith_short_8","alias_value":"UYFOWC7N","created_at":"2026-05-18T12:26:15.391820+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/UYFOWC7NVMVYBISKQZODVT3D4S","json":"https://pith.science/pith/UYFOWC7NVMVYBISKQZODVT3D4S.json","graph_json":"https://pith.science/api/pith-number/UYFOWC7NVMVYBISKQZODVT3D4S/graph.json","events_json":"https://pith.science/api/pith-number/UYFOWC7NVMVYBISKQZODVT3D4S/events.json","paper":"https://pith.science/paper/UYFOWC7N"},"agent_actions":{"view_html":"https://pith.science/pith/UYFOWC7NVMVYBISKQZODVT3D4S","download_json":"https://pith.science/pith/UYFOWC7NVMVYBISKQZODVT3D4S.json","view_paper":"https://pith.science/paper/UYFOWC7N","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1009.4092&json=true","fetch_graph":"https://pith.science/api/pith-number/UYFOWC7NVMVYBISKQZODVT3D4S/graph.json","fetch_events":"https://pith.science/api/pith-number/UYFOWC7NVMVYBISKQZODVT3D4S/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/UYFOWC7NVMVYBISKQZODVT3D4S/action/timestamp_anchor","attest_storage":"https://pith.science/pith/UYFOWC7NVMVYBISKQZODVT3D4S/action/storage_attestation","attest_author":"https://pith.science/pith/UYFOWC7NVMVYBISKQZODVT3D4S/action/author_attestation","sign_citation":"https://pith.science/pith/UYFOWC7NVMVYBISKQZODVT3D4S/action/citation_signature","submit_replication":"https://pith.science/pith/UYFOWC7NVMVYBISKQZODVT3D4S/action/replication_record"}},"created_at":"2026-05-18T04:40:34.553635+00:00","updated_at":"2026-05-18T04:40:34.553635+00:00"}