{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:VYPBBC5UF6DT2SG3R4S26CSH4Y","short_pith_number":"pith:VYPBBC5U","schema_version":"1.0","canonical_sha256":"ae1e108bb42f873d48db8f25af0a47e623dfe186b05414856dd59a3a3cef5ace","source":{"kind":"arxiv","id":"2608.11011","version":1},"attestation_state":"computed","paper":{"title":"Ancient mean curvature flow asymptotic to Simons cone","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.DG","authors_text":"Junyoung Park","submitted_at":"2026-08-11T14:57:00Z","abstract_excerpt":"In this paper, we prove that a smooth, properly embedded ancient mean curvature flow that is asymptotic to $O(n)\\times O(n)$ symmetric Simons cone for $n \\geq 5$, and lies on one side of the cone has to have a unique asymptotics in the parabolic region. When additionally assuming mean convexity, we upgrade unique asymptotics to full uniqueness, and show that such flow has to be a stationary flow given by one of the leaves of the Hardt-Simon foliation."},"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":"2608.11011","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DG","submitted_at":"2026-08-11T14:57:00Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"2f8d94363414a8d4d76e917f308e107f778346e2cf84e121ff2c5bcc30634e88","abstract_canon_sha256":"a606ea2823c5d7beda761121d9aabfddb47f9259d613ccf0304f1392aa425d30"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-08-12T01:24:00.803854Z","signature_b64":"2UBc9tU5O1U87Kg2qNej8FcofXUQ87YwOaxE8Pj9Lsa/+CZASfkxWPAhGucB4RfN2fNFU7ZVeCjsaoaPDLf2Bw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ae1e108bb42f873d48db8f25af0a47e623dfe186b05414856dd59a3a3cef5ace","last_reissued_at":"2026-08-12T01:24:00.801745Z","signature_status":"signed_v1","first_computed_at":"2026-08-12T01:24:00.801745Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Ancient mean curvature flow asymptotic to Simons cone","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.DG","authors_text":"Junyoung Park","submitted_at":"2026-08-11T14:57:00Z","abstract_excerpt":"In this paper, we prove that a smooth, properly embedded ancient mean curvature flow that is asymptotic to $O(n)\\times O(n)$ symmetric Simons cone for $n \\geq 5$, and lies on one side of the cone has to have a unique asymptotics in the parabolic region. When additionally assuming mean convexity, we upgrade unique asymptotics to full uniqueness, and show that such flow has to be a stationary flow given by one of the leaves of the Hardt-Simon foliation."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.11011","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2608.11011/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2608.11011","created_at":"2026-08-12T01:24:00.805856+00:00"},{"alias_kind":"arxiv_version","alias_value":"2608.11011v1","created_at":"2026-08-12T01:24:00.805856+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2608.11011","created_at":"2026-08-12T01:24:00.805856+00:00"},{"alias_kind":"pith_short_12","alias_value":"VYPBBC5UF6DT","created_at":"2026-08-12T01:24:00.805856+00:00"},{"alias_kind":"pith_short_16","alias_value":"VYPBBC5UF6DT2SG3","created_at":"2026-08-12T01:24:00.805856+00:00"},{"alias_kind":"pith_short_8","alias_value":"VYPBBC5U","created_at":"2026-08-12T01:24:00.805856+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/VYPBBC5UF6DT2SG3R4S26CSH4Y","json":"https://pith.science/pith/VYPBBC5UF6DT2SG3R4S26CSH4Y.json","graph_json":"https://pith.science/api/pith-number/VYPBBC5UF6DT2SG3R4S26CSH4Y/graph.json","events_json":"https://pith.science/api/pith-number/VYPBBC5UF6DT2SG3R4S26CSH4Y/events.json","paper":"https://pith.science/paper/VYPBBC5U"},"agent_actions":{"view_html":"https://pith.science/pith/VYPBBC5UF6DT2SG3R4S26CSH4Y","download_json":"https://pith.science/pith/VYPBBC5UF6DT2SG3R4S26CSH4Y.json","view_paper":"https://pith.science/paper/VYPBBC5U","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2608.11011&json=true","fetch_graph":"https://pith.science/api/pith-number/VYPBBC5UF6DT2SG3R4S26CSH4Y/graph.json","fetch_events":"https://pith.science/api/pith-number/VYPBBC5UF6DT2SG3R4S26CSH4Y/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/VYPBBC5UF6DT2SG3R4S26CSH4Y/action/timestamp_anchor","attest_storage":"https://pith.science/pith/VYPBBC5UF6DT2SG3R4S26CSH4Y/action/storage_attestation","attest_author":"https://pith.science/pith/VYPBBC5UF6DT2SG3R4S26CSH4Y/action/author_attestation","sign_citation":"https://pith.science/pith/VYPBBC5UF6DT2SG3R4S26CSH4Y/action/citation_signature","submit_replication":"https://pith.science/pith/VYPBBC5UF6DT2SG3R4S26CSH4Y/action/replication_record"}},"created_at":"2026-08-12T01:24:00.805856+00:00","updated_at":"2026-08-12T01:24:00.805856+00:00"}