{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:ENJELITNEXKUFR4QMZWPYFK7RA","short_pith_number":"pith:ENJELITN","schema_version":"1.0","canonical_sha256":"235245a26d25d542c790666cfc155f8839d2c015142cdb9987410af733fd674c","source":{"kind":"arxiv","id":"1508.02920","version":2},"attestation_state":"computed","paper":{"title":"On melting and freezing for the 2d radial Stefan problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Mahir Hadzic, Pierre Raphael","submitted_at":"2015-08-12T14:00:13Z","abstract_excerpt":"We consider the two dimensional free boundary Stefan problem describing the evolution of a spherically symmetric ice ball $\\{r\\leq \\lambda(t)\\}$. We revisit the pioneering analysis of [20] and prove the existence in the radial class of finite time melting regimes $$ \\lambda(t)=\\left\\{\\begin{array}{ll} (T-t)^{1/2}e^{-\\frac{\\sqrt{2}}{2}\\sqrt{|\\ln(T-t)|}+O(1)}\\\\ (c+o(1))\\frac{(T-t)^{\\frac{k+1}{2}}}{|\\ln (T-t)|^{\\frac{k+1}{2k}}}, \\ \\ k\\in \\Bbb N^*\\end{array}\\right. \\quad\\text{ as } t\\to T $$ which respectively correspond to the fundamental stable melting rate, and a sequence of codimension $k\\in \\"},"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":"1508.02920","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-08-12T14:00:13Z","cross_cats_sorted":[],"title_canon_sha256":"3270750744c652f06a7f992d0a023156d753c58ee1f6af22d752bc11eedd22a6","abstract_canon_sha256":"15aaab55e172b53cc7e98de9520b60ec2aac882e3dff2b0d3b4507dcfdd8e520"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:29:11.082532Z","signature_b64":"jzIa41yAwwcblNMnf281blqvjvSYF7H65TucYIGVajn7V9vjjSxQ+Zj42lWOe3Ac70nsV56s4nSVD+En/3JdBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"235245a26d25d542c790666cfc155f8839d2c015142cdb9987410af733fd674c","last_reissued_at":"2026-05-18T00:29:11.081683Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:29:11.081683Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On melting and freezing for the 2d radial Stefan problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Mahir Hadzic, Pierre Raphael","submitted_at":"2015-08-12T14:00:13Z","abstract_excerpt":"We consider the two dimensional free boundary Stefan problem describing the evolution of a spherically symmetric ice ball $\\{r\\leq \\lambda(t)\\}$. We revisit the pioneering analysis of [20] and prove the existence in the radial class of finite time melting regimes $$ \\lambda(t)=\\left\\{\\begin{array}{ll} (T-t)^{1/2}e^{-\\frac{\\sqrt{2}}{2}\\sqrt{|\\ln(T-t)|}+O(1)}\\\\ (c+o(1))\\frac{(T-t)^{\\frac{k+1}{2}}}{|\\ln (T-t)|^{\\frac{k+1}{2k}}}, \\ \\ k\\in \\Bbb N^*\\end{array}\\right. \\quad\\text{ as } t\\to T $$ which respectively correspond to the fundamental stable melting rate, and a sequence of codimension $k\\in \\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.02920","kind":"arxiv","version":2},"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":"1508.02920","created_at":"2026-05-18T00:29:11.081825+00:00"},{"alias_kind":"arxiv_version","alias_value":"1508.02920v2","created_at":"2026-05-18T00:29:11.081825+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.02920","created_at":"2026-05-18T00:29:11.081825+00:00"},{"alias_kind":"pith_short_12","alias_value":"ENJELITNEXKU","created_at":"2026-05-18T12:29:19.899920+00:00"},{"alias_kind":"pith_short_16","alias_value":"ENJELITNEXKUFR4Q","created_at":"2026-05-18T12:29:19.899920+00:00"},{"alias_kind":"pith_short_8","alias_value":"ENJELITN","created_at":"2026-05-18T12:29:19.899920+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/ENJELITNEXKUFR4QMZWPYFK7RA","json":"https://pith.science/pith/ENJELITNEXKUFR4QMZWPYFK7RA.json","graph_json":"https://pith.science/api/pith-number/ENJELITNEXKUFR4QMZWPYFK7RA/graph.json","events_json":"https://pith.science/api/pith-number/ENJELITNEXKUFR4QMZWPYFK7RA/events.json","paper":"https://pith.science/paper/ENJELITN"},"agent_actions":{"view_html":"https://pith.science/pith/ENJELITNEXKUFR4QMZWPYFK7RA","download_json":"https://pith.science/pith/ENJELITNEXKUFR4QMZWPYFK7RA.json","view_paper":"https://pith.science/paper/ENJELITN","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1508.02920&json=true","fetch_graph":"https://pith.science/api/pith-number/ENJELITNEXKUFR4QMZWPYFK7RA/graph.json","fetch_events":"https://pith.science/api/pith-number/ENJELITNEXKUFR4QMZWPYFK7RA/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ENJELITNEXKUFR4QMZWPYFK7RA/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ENJELITNEXKUFR4QMZWPYFK7RA/action/storage_attestation","attest_author":"https://pith.science/pith/ENJELITNEXKUFR4QMZWPYFK7RA/action/author_attestation","sign_citation":"https://pith.science/pith/ENJELITNEXKUFR4QMZWPYFK7RA/action/citation_signature","submit_replication":"https://pith.science/pith/ENJELITNEXKUFR4QMZWPYFK7RA/action/replication_record"}},"created_at":"2026-05-18T00:29:11.081825+00:00","updated_at":"2026-05-18T00:29:11.081825+00:00"}