{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:JMEJXEFS3S6HRYOW3DSH5MDW2I","short_pith_number":"pith:JMEJXEFS","schema_version":"1.0","canonical_sha256":"4b089b90b2dcbc78e1d6d8e47eb076d209d873acaf2d036998de72ad1ac492d1","source":{"kind":"arxiv","id":"1212.1422","version":4},"attestation_state":"computed","paper":{"title":"Global stability and decay for the classical Stefan problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Mahir Had\\v{z}i\\'c, Steve Shkoller","submitted_at":"2012-12-06T19:16:50Z","abstract_excerpt":"The classical one-phase Stefan problem describes the temperature distribution in a homogeneous medium undergoing a phase transition, such as ice melting to water. This is accomplished by solving the heat equation on a time-dependent domain whose boundary is transported by the normal derivative of the temperature along the evolving and a priori unknown free-boundary. We establish a global-in-time stability result for nearly spherical geometries and small temperatures, using a novel hybrid methodology, which combines energy estimates, decay estimates, and Hopf-type inequalities."},"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":"1212.1422","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-12-06T19:16:50Z","cross_cats_sorted":[],"title_canon_sha256":"31fe719d7eefde0c3dfbb0aaa7bcc3bd545cb8c135d71bff94f614d0f6ccec8f","abstract_canon_sha256":"bba4221e42d1963b6e92cae39f03f35799bb1b6d5bdde27384c83f79e94ce184"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:09:50.650686Z","signature_b64":"r+3xp30odNL3mlhzxug+Q/WqLPPaIuRjwm2vFAdcQvaY52hgVIQdyYZhl8w2xgycS43cwtN0BK6oTq48+y8GBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4b089b90b2dcbc78e1d6d8e47eb076d209d873acaf2d036998de72ad1ac492d1","last_reissued_at":"2026-05-18T03:09:50.646208Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:09:50.646208Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Global stability and decay for the classical Stefan problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Mahir Had\\v{z}i\\'c, Steve Shkoller","submitted_at":"2012-12-06T19:16:50Z","abstract_excerpt":"The classical one-phase Stefan problem describes the temperature distribution in a homogeneous medium undergoing a phase transition, such as ice melting to water. This is accomplished by solving the heat equation on a time-dependent domain whose boundary is transported by the normal derivative of the temperature along the evolving and a priori unknown free-boundary. We establish a global-in-time stability result for nearly spherical geometries and small temperatures, using a novel hybrid methodology, which combines energy estimates, decay estimates, and Hopf-type inequalities."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.1422","kind":"arxiv","version":4},"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":"1212.1422","created_at":"2026-05-18T03:09:50.646334+00:00"},{"alias_kind":"arxiv_version","alias_value":"1212.1422v4","created_at":"2026-05-18T03:09:50.646334+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1212.1422","created_at":"2026-05-18T03:09:50.646334+00:00"},{"alias_kind":"pith_short_12","alias_value":"JMEJXEFS3S6H","created_at":"2026-05-18T12:27:11.947152+00:00"},{"alias_kind":"pith_short_16","alias_value":"JMEJXEFS3S6HRYOW","created_at":"2026-05-18T12:27:11.947152+00:00"},{"alias_kind":"pith_short_8","alias_value":"JMEJXEFS","created_at":"2026-05-18T12:27:11.947152+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/JMEJXEFS3S6HRYOW3DSH5MDW2I","json":"https://pith.science/pith/JMEJXEFS3S6HRYOW3DSH5MDW2I.json","graph_json":"https://pith.science/api/pith-number/JMEJXEFS3S6HRYOW3DSH5MDW2I/graph.json","events_json":"https://pith.science/api/pith-number/JMEJXEFS3S6HRYOW3DSH5MDW2I/events.json","paper":"https://pith.science/paper/JMEJXEFS"},"agent_actions":{"view_html":"https://pith.science/pith/JMEJXEFS3S6HRYOW3DSH5MDW2I","download_json":"https://pith.science/pith/JMEJXEFS3S6HRYOW3DSH5MDW2I.json","view_paper":"https://pith.science/paper/JMEJXEFS","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1212.1422&json=true","fetch_graph":"https://pith.science/api/pith-number/JMEJXEFS3S6HRYOW3DSH5MDW2I/graph.json","fetch_events":"https://pith.science/api/pith-number/JMEJXEFS3S6HRYOW3DSH5MDW2I/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/JMEJXEFS3S6HRYOW3DSH5MDW2I/action/timestamp_anchor","attest_storage":"https://pith.science/pith/JMEJXEFS3S6HRYOW3DSH5MDW2I/action/storage_attestation","attest_author":"https://pith.science/pith/JMEJXEFS3S6HRYOW3DSH5MDW2I/action/author_attestation","sign_citation":"https://pith.science/pith/JMEJXEFS3S6HRYOW3DSH5MDW2I/action/citation_signature","submit_replication":"https://pith.science/pith/JMEJXEFS3S6HRYOW3DSH5MDW2I/action/replication_record"}},"created_at":"2026-05-18T03:09:50.646334+00:00","updated_at":"2026-05-18T03:09:50.646334+00:00"}