Pith Number

pith:5H3E7PVC

pith:2026:5H3E7PVC42KFFJGD3NMQDZYX54

not attested not anchored not stored refs pending

The non-symmetric Mahler conjecture in dimension three

Dongmeng Xi, Shibing Chen, Yuanyuan Li, Zhefeng Xu

Every convex body in three dimensions has non-symmetric volume product at least 64/9 with respect to its Santaló point.

arxiv:2605.09334 v2 · 2026-05-10 · math.MG

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4 Citations open

5 Replications open

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The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Claims

C1strongest claim

We prove the sharp lower bound P(K) >= 64/9 for every convex body K subset R^3, where P(K) denotes the non-symmetric volume product with respect to the Santaló point.

C2weakest assumption

The claim rests on the existence and uniqueness of the Santaló point for every convex body in R^3 together with the standard definition of the non-symmetric volume product; if either fails for some bodies the bound does not apply.

C3one line summary

The non-symmetric Mahler conjecture holds in dimension three: the volume product P(K) satisfies P(K) >= 64/9 for every convex body K in R^3.

Formal links

2 machine-checked theorem links

Cited by

1 paper in Pith

The Symmetric Mahler Inequality in Dimension Three via Admissible Shadow Systems

Receipt and verification

First computed	2026-05-22T01:03:20.083738Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e9f64fbea2e69452a4c3db5901e717ef3391b987ffda95ea292390de3d53505a

Aliases

arxiv: 2605.09334 · arxiv_version: 2605.09334v2 · doi: 10.48550/arxiv.2605.09334 · pith_short_12: 5H3E7PVC42KF · pith_short_16: 5H3E7PVC42KFFJGD · pith_short_8: 5H3E7PVC

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/5H3E7PVC42KFFJGD3NMQDZYX54 \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: e9f64fbea2e69452a4c3db5901e717ef3391b987ffda95ea292390de3d53505a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5e5b6c913151304ed13d5c858ca0912a8011375e0a30e55b6589954176567de3",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/publicdomain/zero/1.0/",
    "primary_cat": "math.MG",
    "submitted_at": "2026-05-10T05:15:40Z",
    "title_canon_sha256": "5f7929299f12f0048db6ebef9956772f369a5bd7df826bbe74caec5bd3aa00f4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.09334",
    "kind": "arxiv",
    "version": 2
  }
}