{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:3EPY6QCEGTCN4RWKMG267W6RYW","short_pith_number":"pith:3EPY6QCE","schema_version":"1.0","canonical_sha256":"d91f8f404434c4de46ca61b5efdbd1c595f84ae8d89e26f6da9d0f7fc0fb741c","source":{"kind":"arxiv","id":"2507.19428","version":2},"attestation_state":"computed","paper":{"title":"Self-expanders of positive genus","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Guanhua Shao, Jiahua Zou","submitted_at":"2025-07-25T16:53:40Z","abstract_excerpt":"For a general class of cones in $\\mathbb{R}^3$, we construct self-expanders of positive genus asymptotic to these cones. As a result, we use these self-expanders to construct a mean curvature flow with genus strictly decreasing but not to zero at the first singular time. We also construct a sequence of self-expanders with unbounded genus which are asymptotic to the same rotationally symmetric cone. Moreover, we characterize the asymptotic behavior of the sequence."},"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":"2507.19428","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2025-07-25T16:53:40Z","cross_cats_sorted":[],"title_canon_sha256":"eb3af116934b0d91d9753fcc99f58f283671539f158ff526a5c14cb568b3850e","abstract_canon_sha256":"f6e0864729c1646ae82578de74839f5384c507f9f72228de85628a6145d9c0b5"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:49:58.279883Z","signature_b64":"O+ov7Fp/raciFu9oPgl1xzg3fR8MrR8SrdTPGoDYfeR99/Xg3doj/bmwAyfVpd31k05WHN7CV64ydonfbm2+Cw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d91f8f404434c4de46ca61b5efdbd1c595f84ae8d89e26f6da9d0f7fc0fb741c","last_reissued_at":"2026-07-05T11:49:58.279403Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:49:58.279403Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Self-expanders of positive genus","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Guanhua Shao, Jiahua Zou","submitted_at":"2025-07-25T16:53:40Z","abstract_excerpt":"For a general class of cones in $\\mathbb{R}^3$, we construct self-expanders of positive genus asymptotic to these cones. As a result, we use these self-expanders to construct a mean curvature flow with genus strictly decreasing but not to zero at the first singular time. We also construct a sequence of self-expanders with unbounded genus which are asymptotic to the same rotationally symmetric cone. Moreover, we characterize the asymptotic behavior of the sequence."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.19428","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2507.19428/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":"2507.19428","created_at":"2026-07-05T11:49:58.279461+00:00"},{"alias_kind":"arxiv_version","alias_value":"2507.19428v2","created_at":"2026-07-05T11:49:58.279461+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2507.19428","created_at":"2026-07-05T11:49:58.279461+00:00"},{"alias_kind":"pith_short_12","alias_value":"3EPY6QCEGTCN","created_at":"2026-07-05T11:49:58.279461+00:00"},{"alias_kind":"pith_short_16","alias_value":"3EPY6QCEGTCN4RWK","created_at":"2026-07-05T11:49:58.279461+00:00"},{"alias_kind":"pith_short_8","alias_value":"3EPY6QCE","created_at":"2026-07-05T11:49:58.279461+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2606.04586","citing_title":"Calibration energy and mean curvature flow","ref_index":73,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/3EPY6QCEGTCN4RWKMG267W6RYW","json":"https://pith.science/pith/3EPY6QCEGTCN4RWKMG267W6RYW.json","graph_json":"https://pith.science/api/pith-number/3EPY6QCEGTCN4RWKMG267W6RYW/graph.json","events_json":"https://pith.science/api/pith-number/3EPY6QCEGTCN4RWKMG267W6RYW/events.json","paper":"https://pith.science/paper/3EPY6QCE"},"agent_actions":{"view_html":"https://pith.science/pith/3EPY6QCEGTCN4RWKMG267W6RYW","download_json":"https://pith.science/pith/3EPY6QCEGTCN4RWKMG267W6RYW.json","view_paper":"https://pith.science/paper/3EPY6QCE","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2507.19428&json=true","fetch_graph":"https://pith.science/api/pith-number/3EPY6QCEGTCN4RWKMG267W6RYW/graph.json","fetch_events":"https://pith.science/api/pith-number/3EPY6QCEGTCN4RWKMG267W6RYW/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/3EPY6QCEGTCN4RWKMG267W6RYW/action/timestamp_anchor","attest_storage":"https://pith.science/pith/3EPY6QCEGTCN4RWKMG267W6RYW/action/storage_attestation","attest_author":"https://pith.science/pith/3EPY6QCEGTCN4RWKMG267W6RYW/action/author_attestation","sign_citation":"https://pith.science/pith/3EPY6QCEGTCN4RWKMG267W6RYW/action/citation_signature","submit_replication":"https://pith.science/pith/3EPY6QCEGTCN4RWKMG267W6RYW/action/replication_record"}},"created_at":"2026-07-05T11:49:58.279461+00:00","updated_at":"2026-07-05T11:49:58.279461+00:00"}