{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:QQKJ37SRF4HWB6B2GURJPLXUSF","short_pith_number":"pith:QQKJ37SR","schema_version":"1.0","canonical_sha256":"84149dfe512f0f60f83a352297aef4917d9d173f375aed3fafd3d7b90576b7cf","source":{"kind":"arxiv","id":"1306.4539","version":1},"attestation_state":"computed","paper":{"title":"Volume-Preserving flow by powers of the mth mean curvature in the hyperbolic space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Chuanxi Wu, Guanghan Li, Shunzi Guo","submitted_at":"2013-06-19T13:26:40Z","abstract_excerpt":"This paper concerns closed hypersurfaces of dimension $n(\\geq 2)$ in the hyperbolic space ${\\mathbb{H}}_{\\kappa}^{n+1}$ of constant sectional curvature $\\kappa$ evolving in direction of its normal vector, where the speed is given by a power $\\beta (\\geq 1/m)$ of the $m$th mean curvature plus a volume preserving term, including the case of powers of the mean curvature and of the $\\mbox{Gau\\ss}$ curvature. The main result is that if the initial hypersurface satisfies that the ratio of the biggest and smallest principal curvature is close enough to 1 everywhere, depending only on $n$, $m$, $\\beta"},"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":"1306.4539","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-06-19T13:26:40Z","cross_cats_sorted":[],"title_canon_sha256":"1da1e9d692841a0aeb3d12996c9655737632a869ce5f2825d1f70acc586d97cf","abstract_canon_sha256":"a104b1c5332fbf6a93d4c2cf22d17295e7cda2f2d063ba0f2b3a89dbf831e3aa"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:20:34.096371Z","signature_b64":"xlD977OWh0WjwztU/P9HkDwEhpDedVkAQseNqO3XBFJYTq+Jr0dGKxm34ROolJOqCsqxpESGA1PYn/iBpslYDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"84149dfe512f0f60f83a352297aef4917d9d173f375aed3fafd3d7b90576b7cf","last_reissued_at":"2026-05-18T03:20:34.095558Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:20:34.095558Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Volume-Preserving flow by powers of the mth mean curvature in the hyperbolic space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Chuanxi Wu, Guanghan Li, Shunzi Guo","submitted_at":"2013-06-19T13:26:40Z","abstract_excerpt":"This paper concerns closed hypersurfaces of dimension $n(\\geq 2)$ in the hyperbolic space ${\\mathbb{H}}_{\\kappa}^{n+1}$ of constant sectional curvature $\\kappa$ evolving in direction of its normal vector, where the speed is given by a power $\\beta (\\geq 1/m)$ of the $m$th mean curvature plus a volume preserving term, including the case of powers of the mean curvature and of the $\\mbox{Gau\\ss}$ curvature. The main result is that if the initial hypersurface satisfies that the ratio of the biggest and smallest principal curvature is close enough to 1 everywhere, depending only on $n$, $m$, $\\beta"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.4539","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":"1306.4539","created_at":"2026-05-18T03:20:34.095678+00:00"},{"alias_kind":"arxiv_version","alias_value":"1306.4539v1","created_at":"2026-05-18T03:20:34.095678+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1306.4539","created_at":"2026-05-18T03:20:34.095678+00:00"},{"alias_kind":"pith_short_12","alias_value":"QQKJ37SRF4HW","created_at":"2026-05-18T12:27:57.521954+00:00"},{"alias_kind":"pith_short_16","alias_value":"QQKJ37SRF4HWB6B2","created_at":"2026-05-18T12:27:57.521954+00:00"},{"alias_kind":"pith_short_8","alias_value":"QQKJ37SR","created_at":"2026-05-18T12:27:57.521954+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/QQKJ37SRF4HWB6B2GURJPLXUSF","json":"https://pith.science/pith/QQKJ37SRF4HWB6B2GURJPLXUSF.json","graph_json":"https://pith.science/api/pith-number/QQKJ37SRF4HWB6B2GURJPLXUSF/graph.json","events_json":"https://pith.science/api/pith-number/QQKJ37SRF4HWB6B2GURJPLXUSF/events.json","paper":"https://pith.science/paper/QQKJ37SR"},"agent_actions":{"view_html":"https://pith.science/pith/QQKJ37SRF4HWB6B2GURJPLXUSF","download_json":"https://pith.science/pith/QQKJ37SRF4HWB6B2GURJPLXUSF.json","view_paper":"https://pith.science/paper/QQKJ37SR","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1306.4539&json=true","fetch_graph":"https://pith.science/api/pith-number/QQKJ37SRF4HWB6B2GURJPLXUSF/graph.json","fetch_events":"https://pith.science/api/pith-number/QQKJ37SRF4HWB6B2GURJPLXUSF/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/QQKJ37SRF4HWB6B2GURJPLXUSF/action/timestamp_anchor","attest_storage":"https://pith.science/pith/QQKJ37SRF4HWB6B2GURJPLXUSF/action/storage_attestation","attest_author":"https://pith.science/pith/QQKJ37SRF4HWB6B2GURJPLXUSF/action/author_attestation","sign_citation":"https://pith.science/pith/QQKJ37SRF4HWB6B2GURJPLXUSF/action/citation_signature","submit_replication":"https://pith.science/pith/QQKJ37SRF4HWB6B2GURJPLXUSF/action/replication_record"}},"created_at":"2026-05-18T03:20:34.095678+00:00","updated_at":"2026-05-18T03:20:34.095678+00:00"}