{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:Q6ED4XOFM2R4R7AQWLEJYV6T27","short_pith_number":"pith:Q6ED4XOF","schema_version":"1.0","canonical_sha256":"87883e5dc566a3c8fc10b2c89c57d3d7f0c5b9bef6e243eaeac1fda1906a1ad8","source":{"kind":"arxiv","id":"2606.30241","version":1},"attestation_state":"computed","paper":{"title":"On the Perelman-Pukhov quotient of successive radii: better and asymptotically optimal bounds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.MG","authors_text":"Beatriz Mar\\'in Gimeno, Bernardo Gonz\\'alez Merino, Mia Runge","submitted_at":"2026-06-29T12:52:10Z","abstract_excerpt":"Perel'man in 1987 and independently Pukhov in 1979 proved that the quotient between the $(n-i+1)$-th successive outer radius and the $i$-th successive inner radius of a convex body in $n$-dimensions is not larger than $i+1$. Apart from the solved cases by Jung 1901 $(i=1)$ and Steinhagen 1921 $(i=n)$, only Perel'man (1987, $n=3$, $i=2$) and Gonz\\'alez Merino (2017, $n\\geq 4$, $i=2$ and $i=n-1$) provided small improvements that beat this bound.\n  In this paper, we obtain sharper inequalities using relations between these inner and outer measures with the diameter and minimal width. We improve t"},"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":"2606.30241","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2026-06-29T12:52:10Z","cross_cats_sorted":[],"title_canon_sha256":"37cdf65d3332c4c1184b27d264509ffa7c513497e84732ee49987ba4fe5e344c","abstract_canon_sha256":"3a58c1458f27b4f497c38fb7c7eb33904b4763dca56502ac05fe3387dc5d3c7b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-30T02:17:55.740489Z","signature_b64":"rdLKIJ51urqJAMpuNuCxrNg87Z7JyuOxQHzDIP0Fmu5YgfYuCejUg+4E/1pRSjWCT0Gn3NijSwzNQ57J9bNWAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"87883e5dc566a3c8fc10b2c89c57d3d7f0c5b9bef6e243eaeac1fda1906a1ad8","last_reissued_at":"2026-06-30T02:17:55.739586Z","signature_status":"signed_v1","first_computed_at":"2026-06-30T02:17:55.739586Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the Perelman-Pukhov quotient of successive radii: better and asymptotically optimal bounds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.MG","authors_text":"Beatriz Mar\\'in Gimeno, Bernardo Gonz\\'alez Merino, Mia Runge","submitted_at":"2026-06-29T12:52:10Z","abstract_excerpt":"Perel'man in 1987 and independently Pukhov in 1979 proved that the quotient between the $(n-i+1)$-th successive outer radius and the $i$-th successive inner radius of a convex body in $n$-dimensions is not larger than $i+1$. Apart from the solved cases by Jung 1901 $(i=1)$ and Steinhagen 1921 $(i=n)$, only Perel'man (1987, $n=3$, $i=2$) and Gonz\\'alez Merino (2017, $n\\geq 4$, $i=2$ and $i=n-1$) provided small improvements that beat this bound.\n  In this paper, we obtain sharper inequalities using relations between these inner and outer measures with the diameter and minimal width. We improve t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.30241","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/2606.30241/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":"2606.30241","created_at":"2026-06-30T02:17:55.739758+00:00"},{"alias_kind":"arxiv_version","alias_value":"2606.30241v1","created_at":"2026-06-30T02:17:55.739758+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.30241","created_at":"2026-06-30T02:17:55.739758+00:00"},{"alias_kind":"pith_short_12","alias_value":"Q6ED4XOFM2R4","created_at":"2026-06-30T02:17:55.739758+00:00"},{"alias_kind":"pith_short_16","alias_value":"Q6ED4XOFM2R4R7AQ","created_at":"2026-06-30T02:17:55.739758+00:00"},{"alias_kind":"pith_short_8","alias_value":"Q6ED4XOF","created_at":"2026-06-30T02:17:55.739758+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/Q6ED4XOFM2R4R7AQWLEJYV6T27","json":"https://pith.science/pith/Q6ED4XOFM2R4R7AQWLEJYV6T27.json","graph_json":"https://pith.science/api/pith-number/Q6ED4XOFM2R4R7AQWLEJYV6T27/graph.json","events_json":"https://pith.science/api/pith-number/Q6ED4XOFM2R4R7AQWLEJYV6T27/events.json","paper":"https://pith.science/paper/Q6ED4XOF"},"agent_actions":{"view_html":"https://pith.science/pith/Q6ED4XOFM2R4R7AQWLEJYV6T27","download_json":"https://pith.science/pith/Q6ED4XOFM2R4R7AQWLEJYV6T27.json","view_paper":"https://pith.science/paper/Q6ED4XOF","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2606.30241&json=true","fetch_graph":"https://pith.science/api/pith-number/Q6ED4XOFM2R4R7AQWLEJYV6T27/graph.json","fetch_events":"https://pith.science/api/pith-number/Q6ED4XOFM2R4R7AQWLEJYV6T27/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/Q6ED4XOFM2R4R7AQWLEJYV6T27/action/timestamp_anchor","attest_storage":"https://pith.science/pith/Q6ED4XOFM2R4R7AQWLEJYV6T27/action/storage_attestation","attest_author":"https://pith.science/pith/Q6ED4XOFM2R4R7AQWLEJYV6T27/action/author_attestation","sign_citation":"https://pith.science/pith/Q6ED4XOFM2R4R7AQWLEJYV6T27/action/citation_signature","submit_replication":"https://pith.science/pith/Q6ED4XOFM2R4R7AQWLEJYV6T27/action/replication_record"}},"created_at":"2026-06-30T02:17:55.739758+00:00","updated_at":"2026-06-30T02:17:55.739758+00:00"}