{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:GZOTGGHO5YJGHAIPTBL6N45H2T","short_pith_number":"pith:GZOTGGHO","schema_version":"1.0","canonical_sha256":"365d3318eeee1263810f9857e6f3a7d4c13e849c51727261e1b4b164e10c1862","source":{"kind":"arxiv","id":"1707.07502","version":3},"attestation_state":"computed","paper":{"title":"The Mahler conjecture in two dimensions via the probabilistic method","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.MG","authors_text":"Matthew Tointon","submitted_at":"2017-07-24T11:55:31Z","abstract_excerpt":"The \"Mahler volume\" is, intuitively speaking, a measure of how \"round\" a centrally symmetric convex body is. In one direction this intuition is given weight by a result of Santalo, who in the 1940s showed that the Mahler volume is maximized, in a given dimension, by the unit sphere and its linear images, and only these. A counterpart to this result in the opposite direction is proposed by a conjecture, formulated by Kurt Mahler in the 1930s and still open in dimensions 4 and greater, asserting that the Mahler volume should be minimized by a cuboid. In this article we present a seemingly new pr"},"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":"1707.07502","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2017-07-24T11:55:31Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"5e736e61fdb2502389fb991b6854a3d4e99d4c5ca04a04a1e224595b3f10973a","abstract_canon_sha256":"2ce4ca04ca9f12e16f0549412879ea5744894b254d075f1c249810d52232b1f9"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:01:30.483793Z","signature_b64":"Lzs9fu9lz/hQVKoLT25Hu1qq/zBxCd7cVk8k4ubMC4gehh+WscnJhMx0d+FgMudYOog+3KuLpJP+4OXrrclLDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"365d3318eeee1263810f9857e6f3a7d4c13e849c51727261e1b4b164e10c1862","last_reissued_at":"2026-05-18T00:01:30.483275Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:01:30.483275Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Mahler conjecture in two dimensions via the probabilistic method","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.MG","authors_text":"Matthew Tointon","submitted_at":"2017-07-24T11:55:31Z","abstract_excerpt":"The \"Mahler volume\" is, intuitively speaking, a measure of how \"round\" a centrally symmetric convex body is. In one direction this intuition is given weight by a result of Santalo, who in the 1940s showed that the Mahler volume is maximized, in a given dimension, by the unit sphere and its linear images, and only these. A counterpart to this result in the opposite direction is proposed by a conjecture, formulated by Kurt Mahler in the 1930s and still open in dimensions 4 and greater, asserting that the Mahler volume should be minimized by a cuboid. In this article we present a seemingly new pr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.07502","kind":"arxiv","version":3},"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":"1707.07502","created_at":"2026-05-18T00:01:30.483374+00:00"},{"alias_kind":"arxiv_version","alias_value":"1707.07502v3","created_at":"2026-05-18T00:01:30.483374+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.07502","created_at":"2026-05-18T00:01:30.483374+00:00"},{"alias_kind":"pith_short_12","alias_value":"GZOTGGHO5YJG","created_at":"2026-05-18T12:31:18.294218+00:00"},{"alias_kind":"pith_short_16","alias_value":"GZOTGGHO5YJGHAIP","created_at":"2026-05-18T12:31:18.294218+00:00"},{"alias_kind":"pith_short_8","alias_value":"GZOTGGHO","created_at":"2026-05-18T12:31:18.294218+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/GZOTGGHO5YJGHAIPTBL6N45H2T","json":"https://pith.science/pith/GZOTGGHO5YJGHAIPTBL6N45H2T.json","graph_json":"https://pith.science/api/pith-number/GZOTGGHO5YJGHAIPTBL6N45H2T/graph.json","events_json":"https://pith.science/api/pith-number/GZOTGGHO5YJGHAIPTBL6N45H2T/events.json","paper":"https://pith.science/paper/GZOTGGHO"},"agent_actions":{"view_html":"https://pith.science/pith/GZOTGGHO5YJGHAIPTBL6N45H2T","download_json":"https://pith.science/pith/GZOTGGHO5YJGHAIPTBL6N45H2T.json","view_paper":"https://pith.science/paper/GZOTGGHO","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1707.07502&json=true","fetch_graph":"https://pith.science/api/pith-number/GZOTGGHO5YJGHAIPTBL6N45H2T/graph.json","fetch_events":"https://pith.science/api/pith-number/GZOTGGHO5YJGHAIPTBL6N45H2T/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/GZOTGGHO5YJGHAIPTBL6N45H2T/action/timestamp_anchor","attest_storage":"https://pith.science/pith/GZOTGGHO5YJGHAIPTBL6N45H2T/action/storage_attestation","attest_author":"https://pith.science/pith/GZOTGGHO5YJGHAIPTBL6N45H2T/action/author_attestation","sign_citation":"https://pith.science/pith/GZOTGGHO5YJGHAIPTBL6N45H2T/action/citation_signature","submit_replication":"https://pith.science/pith/GZOTGGHO5YJGHAIPTBL6N45H2T/action/replication_record"}},"created_at":"2026-05-18T00:01:30.483374+00:00","updated_at":"2026-05-18T00:01:30.483374+00:00"}