{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:Y5LHFFXOWH2IUR24XP2IM5MBPV","short_pith_number":"pith:Y5LHFFXO","schema_version":"1.0","canonical_sha256":"c7567296eeb1f48a475cbbf48675817d42d6833ea7e4735ce3a0b2702a88cf2b","source":{"kind":"arxiv","id":"1708.07914","version":1},"attestation_state":"computed","paper":{"title":"Polytopes of Maximal Volume Product","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.MG","authors_text":"Artem Zvavitch, Matthew Alexander, Matthieu Fradelizi","submitted_at":"2017-08-26T01:33:56Z","abstract_excerpt":"For a convex body $K \\subset {\\mathbb R}^n$, let $K^z = \\{y\\in{\\mathbb R}^n : \\langle y-z, x-z\\rangle\\le 1, \\mbox{\\ for all\\ } x\\in K\\}$ be the polar body of $K$ with respect to the center of polarity $z \\in {\\mathbb R}^n$. The goal of this paper is to study the maximum of the volume product $\\mathcal{P}(K)=\\min_{z\\in {\\rm int}(K)}|K||K^z|$, among convex polytopes $K\\subset {\\mathbb R}^n$ with a number of vertices bounded by some fixed integer $m \\ge n+1$. In particular, we prove that the supremum is reached at a simplicial polytope with exactly $m$ vertices and we provide a new proof of a res"},"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":"1708.07914","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2017-08-26T01:33:56Z","cross_cats_sorted":[],"title_canon_sha256":"793944aa479873b489f7fb68d480c45d2de0392dd528f17c118fbe33df102fa4","abstract_canon_sha256":"a42396a3c16749923ccfadd0b9bcab8fe76c520662defd721beca535fb23cfae"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:36:37.653526Z","signature_b64":"9hRxa1+vJXfhs1WoMrsKZaGrrwHwMe8khz8Vvc8HMANWGc1Ba48aU2fETxzCTR6x05A4RX73dBBFNd1UiZnfCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c7567296eeb1f48a475cbbf48675817d42d6833ea7e4735ce3a0b2702a88cf2b","last_reissued_at":"2026-05-18T00:36:37.652901Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:36:37.652901Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Polytopes of Maximal Volume Product","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.MG","authors_text":"Artem Zvavitch, Matthew Alexander, Matthieu Fradelizi","submitted_at":"2017-08-26T01:33:56Z","abstract_excerpt":"For a convex body $K \\subset {\\mathbb R}^n$, let $K^z = \\{y\\in{\\mathbb R}^n : \\langle y-z, x-z\\rangle\\le 1, \\mbox{\\ for all\\ } x\\in K\\}$ be the polar body of $K$ with respect to the center of polarity $z \\in {\\mathbb R}^n$. The goal of this paper is to study the maximum of the volume product $\\mathcal{P}(K)=\\min_{z\\in {\\rm int}(K)}|K||K^z|$, among convex polytopes $K\\subset {\\mathbb R}^n$ with a number of vertices bounded by some fixed integer $m \\ge n+1$. In particular, we prove that the supremum is reached at a simplicial polytope with exactly $m$ vertices and we provide a new proof of a res"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.07914","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":"1708.07914","created_at":"2026-05-18T00:36:37.652992+00:00"},{"alias_kind":"arxiv_version","alias_value":"1708.07914v1","created_at":"2026-05-18T00:36:37.652992+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1708.07914","created_at":"2026-05-18T00:36:37.652992+00:00"},{"alias_kind":"pith_short_12","alias_value":"Y5LHFFXOWH2I","created_at":"2026-05-18T12:31:56.362134+00:00"},{"alias_kind":"pith_short_16","alias_value":"Y5LHFFXOWH2IUR24","created_at":"2026-05-18T12:31:56.362134+00:00"},{"alias_kind":"pith_short_8","alias_value":"Y5LHFFXO","created_at":"2026-05-18T12:31:56.362134+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/Y5LHFFXOWH2IUR24XP2IM5MBPV","json":"https://pith.science/pith/Y5LHFFXOWH2IUR24XP2IM5MBPV.json","graph_json":"https://pith.science/api/pith-number/Y5LHFFXOWH2IUR24XP2IM5MBPV/graph.json","events_json":"https://pith.science/api/pith-number/Y5LHFFXOWH2IUR24XP2IM5MBPV/events.json","paper":"https://pith.science/paper/Y5LHFFXO"},"agent_actions":{"view_html":"https://pith.science/pith/Y5LHFFXOWH2IUR24XP2IM5MBPV","download_json":"https://pith.science/pith/Y5LHFFXOWH2IUR24XP2IM5MBPV.json","view_paper":"https://pith.science/paper/Y5LHFFXO","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1708.07914&json=true","fetch_graph":"https://pith.science/api/pith-number/Y5LHFFXOWH2IUR24XP2IM5MBPV/graph.json","fetch_events":"https://pith.science/api/pith-number/Y5LHFFXOWH2IUR24XP2IM5MBPV/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/Y5LHFFXOWH2IUR24XP2IM5MBPV/action/timestamp_anchor","attest_storage":"https://pith.science/pith/Y5LHFFXOWH2IUR24XP2IM5MBPV/action/storage_attestation","attest_author":"https://pith.science/pith/Y5LHFFXOWH2IUR24XP2IM5MBPV/action/author_attestation","sign_citation":"https://pith.science/pith/Y5LHFFXOWH2IUR24XP2IM5MBPV/action/citation_signature","submit_replication":"https://pith.science/pith/Y5LHFFXOWH2IUR24XP2IM5MBPV/action/replication_record"}},"created_at":"2026-05-18T00:36:37.652992+00:00","updated_at":"2026-05-18T00:36:37.652992+00:00"}