{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:Z2V5FAS3IFHNZSS4RSWEDWPB6D","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"bc69175624f126555bb9e6663b5f037242fbaf30adeaf71ec5bf18ffaea70969","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2009-11-03T17:38:58Z","title_canon_sha256":"566ad7c79cad81d80f35310e2f82bdadfda756de7d1dbf82fdf5053b9a121164"},"schema_version":"1.0","source":{"id":"0911.0642","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0911.0642","created_at":"2026-05-18T03:26:53Z"},{"alias_kind":"arxiv_version","alias_value":"0911.0642v1","created_at":"2026-05-18T03:26:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0911.0642","created_at":"2026-05-18T03:26:53Z"},{"alias_kind":"pith_short_12","alias_value":"Z2V5FAS3IFHN","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_16","alias_value":"Z2V5FAS3IFHNZSS4","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_8","alias_value":"Z2V5FAS3","created_at":"2026-05-18T12:26:02Z"}],"graph_snapshots":[{"event_id":"sha256:db64712c01272dabedeb6b458b670c7102d4e27dd831211b005982c4139b8dc5","target":"graph","created_at":"2026-05-18T03:26:53Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"Let $K$ be a convex body in $\\bbR^n$ and $\\d>0$. The homothety conjecture asks: Does $K_{\\d}=c K$ imply that $K$ is an ellipsoid? Here $K_{\\d}$ is the (convex) floating body and $c$ is a constant depending on $\\d$ only. In this paper we prove that the homothety conjecture holds true in the class of the convex bodies $B^n_p$, $1\\leq p\\leq \\infty$, the unit balls of $l_p^n$; namely, we show that $(B^n_p)_{\\d} = c B^n_p$ if and only if $p=2$. We also show that the homothety conjecture is true for a general convex body $K$ if $\\d$ is small enough. This improvs earlier results by Sch\\\"utt and Werne","authors_text":"Deping Ye, Elisabeth M. Werner","cross_cats":["math.FA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2009-11-03T17:38:58Z","title":"On the Homothety Conjecture"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0911.0642","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:8d59956db8120d6493c143ffba564211f2455e8d27c3f46e830e53edcfc1e9de","target":"record","created_at":"2026-05-18T03:26:53Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"bc69175624f126555bb9e6663b5f037242fbaf30adeaf71ec5bf18ffaea70969","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2009-11-03T17:38:58Z","title_canon_sha256":"566ad7c79cad81d80f35310e2f82bdadfda756de7d1dbf82fdf5053b9a121164"},"schema_version":"1.0","source":{"id":"0911.0642","kind":"arxiv","version":1}},"canonical_sha256":"ceabd2825b414edcca5c8cac41d9e1f0fc515009dbac14b06e651218c3782bb8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ceabd2825b414edcca5c8cac41d9e1f0fc515009dbac14b06e651218c3782bb8","first_computed_at":"2026-05-18T03:26:53.115956Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:26:53.115956Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"90e8GqHB3n4FWXVmFrp2mJseoig8cnBbMkpcYfmmg4akupiNswbJCoAWbcsllQCACq54is1bw/DAIo7wLLWiDA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:26:53.116460Z","signed_message":"canonical_sha256_bytes"},"source_id":"0911.0642","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8d59956db8120d6493c143ffba564211f2455e8d27c3f46e830e53edcfc1e9de","sha256:db64712c01272dabedeb6b458b670c7102d4e27dd831211b005982c4139b8dc5"],"state_sha256":"36adc3ab622b8b86cd71824b015fda782f896f402f743f2745adfcd1d40a6932"}