{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:3OMEX4FNYDAMXZKQ6B5CB4AQPK","short_pith_number":"pith:3OMEX4FN","schema_version":"1.0","canonical_sha256":"db984bf0adc0c0cbe550f07a20f0107aa013978cf4f6a8fd7d38f5ba91795254","source":{"kind":"arxiv","id":"1412.4755","version":1},"attestation_state":"computed","paper":{"title":"A maximum principle for self-shrinkers and some consequences","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Antoine Song","submitted_at":"2014-12-15T20:36:45Z","abstract_excerpt":"Using a maximum principle for self-shrinkers of the mean curvature flow, we give new proofs of a rigidity theorem for rotationally symmetric compact self-shrinkers and a result about the asymptotic behavior of self-shrinkers. This comparison argument also implies a linear bound for the second fundamental form of self-shrinking surfaces under natural assumptions. As a consequence, translating solitons can be related to these self-shrinkers."},"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":"1412.4755","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-12-15T20:36:45Z","cross_cats_sorted":[],"title_canon_sha256":"858f667f211f0023f3ed489adaaf1bac08dc3bedae4539277efd76101ab80af7","abstract_canon_sha256":"eab0caed73290e8a72c74b7b812390116ae858be582eecea46160bb113be4463"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:31:18.396373Z","signature_b64":"LuxC5tkaMjIk0ZYqfykQMonK3sa+MWIAOekTWvnkY7qnWI3swvIYIipfuNCHwqI1vBvFdJdIns2t8Bwb0W7tCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"db984bf0adc0c0cbe550f07a20f0107aa013978cf4f6a8fd7d38f5ba91795254","last_reissued_at":"2026-05-18T02:31:18.395841Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:31:18.395841Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A maximum principle for self-shrinkers and some consequences","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Antoine Song","submitted_at":"2014-12-15T20:36:45Z","abstract_excerpt":"Using a maximum principle for self-shrinkers of the mean curvature flow, we give new proofs of a rigidity theorem for rotationally symmetric compact self-shrinkers and a result about the asymptotic behavior of self-shrinkers. This comparison argument also implies a linear bound for the second fundamental form of self-shrinking surfaces under natural assumptions. As a consequence, translating solitons can be related to these self-shrinkers."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.4755","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":"1412.4755","created_at":"2026-05-18T02:31:18.395915+00:00"},{"alias_kind":"arxiv_version","alias_value":"1412.4755v1","created_at":"2026-05-18T02:31:18.395915+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.4755","created_at":"2026-05-18T02:31:18.395915+00:00"},{"alias_kind":"pith_short_12","alias_value":"3OMEX4FNYDAM","created_at":"2026-05-18T12:28:11.866339+00:00"},{"alias_kind":"pith_short_16","alias_value":"3OMEX4FNYDAMXZKQ","created_at":"2026-05-18T12:28:11.866339+00:00"},{"alias_kind":"pith_short_8","alias_value":"3OMEX4FN","created_at":"2026-05-18T12:28:11.866339+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/3OMEX4FNYDAMXZKQ6B5CB4AQPK","json":"https://pith.science/pith/3OMEX4FNYDAMXZKQ6B5CB4AQPK.json","graph_json":"https://pith.science/api/pith-number/3OMEX4FNYDAMXZKQ6B5CB4AQPK/graph.json","events_json":"https://pith.science/api/pith-number/3OMEX4FNYDAMXZKQ6B5CB4AQPK/events.json","paper":"https://pith.science/paper/3OMEX4FN"},"agent_actions":{"view_html":"https://pith.science/pith/3OMEX4FNYDAMXZKQ6B5CB4AQPK","download_json":"https://pith.science/pith/3OMEX4FNYDAMXZKQ6B5CB4AQPK.json","view_paper":"https://pith.science/paper/3OMEX4FN","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1412.4755&json=true","fetch_graph":"https://pith.science/api/pith-number/3OMEX4FNYDAMXZKQ6B5CB4AQPK/graph.json","fetch_events":"https://pith.science/api/pith-number/3OMEX4FNYDAMXZKQ6B5CB4AQPK/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/3OMEX4FNYDAMXZKQ6B5CB4AQPK/action/timestamp_anchor","attest_storage":"https://pith.science/pith/3OMEX4FNYDAMXZKQ6B5CB4AQPK/action/storage_attestation","attest_author":"https://pith.science/pith/3OMEX4FNYDAMXZKQ6B5CB4AQPK/action/author_attestation","sign_citation":"https://pith.science/pith/3OMEX4FNYDAMXZKQ6B5CB4AQPK/action/citation_signature","submit_replication":"https://pith.science/pith/3OMEX4FNYDAMXZKQ6B5CB4AQPK/action/replication_record"}},"created_at":"2026-05-18T02:31:18.395915+00:00","updated_at":"2026-05-18T02:31:18.395915+00:00"}