{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:HJMNGX33IZRV2XKRQJNGUBTBRB","short_pith_number":"pith:HJMNGX33","schema_version":"1.0","canonical_sha256":"3a58d35f7b46635d5d51825a6a0661885de7097d2d43ab34c6526aad100b24f1","source":{"kind":"arxiv","id":"1807.11100","version":1},"attestation_state":"computed","paper":{"title":"Convergence of Curve Shortening Flow to Translating Soliton","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Beomjun Choi, Kyeongsu Choi, Panagiota Daskalopoulos","submitted_at":"2018-07-29T19:25:58Z","abstract_excerpt":"This paper concerns with the asymptotic behavior of complete non-compact convex curves embedded in $\\mathbb{R}^2$ under the $\\alpha$-curve shortening flow for exponents $\\alpha >\\frac12$. We show that any such curve having in addition its two ends asymptotic to two parallel lines, converges under $\\alpha$-curve shortening flow to the unique translating soliton whose ends are asymptotic to the same parallel lines. This is a new result even in the standard case $\\alpha=1$, and we prove for all exponents up to the critical case $\\alpha>\\frac12$."},"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":"1807.11100","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-07-29T19:25:58Z","cross_cats_sorted":[],"title_canon_sha256":"652bd266de05d929602990eda7ad8b88a29399f2270c983bf1b94add71151300","abstract_canon_sha256":"5f5cb6d784367a7946fa59542c90e622bbddec6b10144e8af7c05406e34d7671"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:09:32.941448Z","signature_b64":"MRMR2YBNV/x5cfd5y2UrSSvypCBCASQqJVRuUN4JMLTOAZXQD2fSSe7v8VYwsON33fhIn22Q75fRbljyz6+6AQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3a58d35f7b46635d5d51825a6a0661885de7097d2d43ab34c6526aad100b24f1","last_reissued_at":"2026-05-18T00:09:32.940772Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:09:32.940772Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Convergence of Curve Shortening Flow to Translating Soliton","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Beomjun Choi, Kyeongsu Choi, Panagiota Daskalopoulos","submitted_at":"2018-07-29T19:25:58Z","abstract_excerpt":"This paper concerns with the asymptotic behavior of complete non-compact convex curves embedded in $\\mathbb{R}^2$ under the $\\alpha$-curve shortening flow for exponents $\\alpha >\\frac12$. We show that any such curve having in addition its two ends asymptotic to two parallel lines, converges under $\\alpha$-curve shortening flow to the unique translating soliton whose ends are asymptotic to the same parallel lines. This is a new result even in the standard case $\\alpha=1$, and we prove for all exponents up to the critical case $\\alpha>\\frac12$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.11100","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":"1807.11100","created_at":"2026-05-18T00:09:32.940879+00:00"},{"alias_kind":"arxiv_version","alias_value":"1807.11100v1","created_at":"2026-05-18T00:09:32.940879+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1807.11100","created_at":"2026-05-18T00:09:32.940879+00:00"},{"alias_kind":"pith_short_12","alias_value":"HJMNGX33IZRV","created_at":"2026-05-18T12:32:28.185984+00:00"},{"alias_kind":"pith_short_16","alias_value":"HJMNGX33IZRV2XKR","created_at":"2026-05-18T12:32:28.185984+00:00"},{"alias_kind":"pith_short_8","alias_value":"HJMNGX33","created_at":"2026-05-18T12:32:28.185984+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/HJMNGX33IZRV2XKRQJNGUBTBRB","json":"https://pith.science/pith/HJMNGX33IZRV2XKRQJNGUBTBRB.json","graph_json":"https://pith.science/api/pith-number/HJMNGX33IZRV2XKRQJNGUBTBRB/graph.json","events_json":"https://pith.science/api/pith-number/HJMNGX33IZRV2XKRQJNGUBTBRB/events.json","paper":"https://pith.science/paper/HJMNGX33"},"agent_actions":{"view_html":"https://pith.science/pith/HJMNGX33IZRV2XKRQJNGUBTBRB","download_json":"https://pith.science/pith/HJMNGX33IZRV2XKRQJNGUBTBRB.json","view_paper":"https://pith.science/paper/HJMNGX33","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1807.11100&json=true","fetch_graph":"https://pith.science/api/pith-number/HJMNGX33IZRV2XKRQJNGUBTBRB/graph.json","fetch_events":"https://pith.science/api/pith-number/HJMNGX33IZRV2XKRQJNGUBTBRB/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/HJMNGX33IZRV2XKRQJNGUBTBRB/action/timestamp_anchor","attest_storage":"https://pith.science/pith/HJMNGX33IZRV2XKRQJNGUBTBRB/action/storage_attestation","attest_author":"https://pith.science/pith/HJMNGX33IZRV2XKRQJNGUBTBRB/action/author_attestation","sign_citation":"https://pith.science/pith/HJMNGX33IZRV2XKRQJNGUBTBRB/action/citation_signature","submit_replication":"https://pith.science/pith/HJMNGX33IZRV2XKRQJNGUBTBRB/action/replication_record"}},"created_at":"2026-05-18T00:09:32.940879+00:00","updated_at":"2026-05-18T00:09:32.940879+00:00"}