{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:GZOTGGHO5YJGHAIPTBL6N45H2T","short_pith_number":"pith:GZOTGGHO","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"},"canonical_sha256":"365d3318eeee1263810f9857e6f3a7d4c13e849c51727261e1b4b164e10c1862","source":{"kind":"arxiv","id":"1707.07502","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1707.07502","created_at":"2026-05-18T00:01:30Z"},{"alias_kind":"arxiv_version","alias_value":"1707.07502v3","created_at":"2026-05-18T00:01:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.07502","created_at":"2026-05-18T00:01:30Z"},{"alias_kind":"pith_short_12","alias_value":"GZOTGGHO5YJG","created_at":"2026-05-18T12:31:18Z"},{"alias_kind":"pith_short_16","alias_value":"GZOTGGHO5YJGHAIP","created_at":"2026-05-18T12:31:18Z"},{"alias_kind":"pith_short_8","alias_value":"GZOTGGHO","created_at":"2026-05-18T12:31:18Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:GZOTGGHO5YJGHAIPTBL6N45H2T","target":"record","payload":{"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"},"canonical_sha256":"365d3318eeee1263810f9857e6f3a7d4c13e849c51727261e1b4b164e10c1862","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"},"source_kind":"arxiv","source_id":"1707.07502","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:01:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"r78UnGWCqaz4z6+mQ4pEtPJebHfiQggIzAW93h9ZdzlGTqZYhts7QnUUS2FHi98tHUDzP7a4Zp3z3WtMQQ9rCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T05:58:02.225020Z"},"content_sha256":"23970673da96a6bc652d2e45d52ce99f73ef791015a0352bfcf9429a5ff56dc5","schema_version":"1.0","event_id":"sha256:23970673da96a6bc652d2e45d52ce99f73ef791015a0352bfcf9429a5ff56dc5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:GZOTGGHO5YJGHAIPTBL6N45H2T","target":"graph","payload":{"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:01:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qReVRRegrP4Fi6z7eLJ8ppmPsrkcaOUOHSzhgtHn0MqnrHKiVlDSoiAj+wXlTh22YvQWs/38SZYFnDdO09y0Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T05:58:02.225374Z"},"content_sha256":"2f0283009b04ffe92a94059b99510fb7ee76c32935844033d67e4a6cec4e76e1","schema_version":"1.0","event_id":"sha256:2f0283009b04ffe92a94059b99510fb7ee76c32935844033d67e4a6cec4e76e1"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GZOTGGHO5YJGHAIPTBL6N45H2T/bundle.json","state_url":"https://pith.science/pith/GZOTGGHO5YJGHAIPTBL6N45H2T/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GZOTGGHO5YJGHAIPTBL6N45H2T/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-24T05:58:02Z","links":{"resolver":"https://pith.science/pith/GZOTGGHO5YJGHAIPTBL6N45H2T","bundle":"https://pith.science/pith/GZOTGGHO5YJGHAIPTBL6N45H2T/bundle.json","state":"https://pith.science/pith/GZOTGGHO5YJGHAIPTBL6N45H2T/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GZOTGGHO5YJGHAIPTBL6N45H2T/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:GZOTGGHO5YJGHAIPTBL6N45H2T","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":"2ce4ca04ca9f12e16f0549412879ea5744894b254d075f1c249810d52232b1f9","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2017-07-24T11:55:31Z","title_canon_sha256":"5e736e61fdb2502389fb991b6854a3d4e99d4c5ca04a04a1e224595b3f10973a"},"schema_version":"1.0","source":{"id":"1707.07502","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1707.07502","created_at":"2026-05-18T00:01:30Z"},{"alias_kind":"arxiv_version","alias_value":"1707.07502v3","created_at":"2026-05-18T00:01:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.07502","created_at":"2026-05-18T00:01:30Z"},{"alias_kind":"pith_short_12","alias_value":"GZOTGGHO5YJG","created_at":"2026-05-18T12:31:18Z"},{"alias_kind":"pith_short_16","alias_value":"GZOTGGHO5YJGHAIP","created_at":"2026-05-18T12:31:18Z"},{"alias_kind":"pith_short_8","alias_value":"GZOTGGHO","created_at":"2026-05-18T12:31:18Z"}],"graph_snapshots":[{"event_id":"sha256:2f0283009b04ffe92a94059b99510fb7ee76c32935844033d67e4a6cec4e76e1","target":"graph","created_at":"2026-05-18T00:01:30Z","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":"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","authors_text":"Matthew Tointon","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2017-07-24T11:55:31Z","title":"The Mahler conjecture in two dimensions via the probabilistic method"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.07502","kind":"arxiv","version":3},"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":"sha256:23970673da96a6bc652d2e45d52ce99f73ef791015a0352bfcf9429a5ff56dc5","target":"record","created_at":"2026-05-18T00:01:30Z","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":"2ce4ca04ca9f12e16f0549412879ea5744894b254d075f1c249810d52232b1f9","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2017-07-24T11:55:31Z","title_canon_sha256":"5e736e61fdb2502389fb991b6854a3d4e99d4c5ca04a04a1e224595b3f10973a"},"schema_version":"1.0","source":{"id":"1707.07502","kind":"arxiv","version":3}},"canonical_sha256":"365d3318eeee1263810f9857e6f3a7d4c13e849c51727261e1b4b164e10c1862","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"365d3318eeee1263810f9857e6f3a7d4c13e849c51727261e1b4b164e10c1862","first_computed_at":"2026-05-18T00:01:30.483275Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:01:30.483275Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Lzs9fu9lz/hQVKoLT25Hu1qq/zBxCd7cVk8k4ubMC4gehh+WscnJhMx0d+FgMudYOog+3KuLpJP+4OXrrclLDA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:01:30.483793Z","signed_message":"canonical_sha256_bytes"},"source_id":"1707.07502","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:23970673da96a6bc652d2e45d52ce99f73ef791015a0352bfcf9429a5ff56dc5","sha256:2f0283009b04ffe92a94059b99510fb7ee76c32935844033d67e4a6cec4e76e1"],"state_sha256":"f8699ade5adfff7b785a10d374441f089d4c443ec77d32fa5895d4196446e8f5"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bQmm51jK/owzi+l19ldhzyaxmPsntrXUjyOyOxKLneS3tLL2LufO0cCeGSV+GHesasxSpZg0asMRF4vb4absDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T05:58:02.227273Z","bundle_sha256":"35ad90991ebd9de18014ec9a22245017c902143b4a0d60d9487e3478f4cedb45"}}