Pith Number

pith:BBJZARKZ

pith:2026:BBJZARKZALZEHBQTTCX45IXDUV

not attested not anchored not stored refs pending

Functional perimeter and the dimensional Brunn-Minkowski inequality for log-concave measures

Alexandros Eskenazis, Apostolos Giannopoulos, Natalia Tziotziou

Even log-concave measures satisfy a Brunn-Minkowski inequality for convex sets with exponent at least c over n cubed log n.

arxiv:2605.02747 v2 · 2026-05-04 · math.MG · math.FA

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\usepackage{pith}
\pithnumber{BBJZARKZALZEHBQTTCX45IXDUV}

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Record completeness

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2 Internet Archive

3 Author claim open · sign in to claim

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

For every pair of symmetric convex sets K, L in R^n and every λ in (0,1), μ(λK + (1-λ)L)^{c_n} ≥ λ μ(K)^{c_n} + (1-λ) μ(L)^{c_n} where c_n ≥ c / (n^3 ln n) for some absolute c > 0; the key supporting estimate is ∫ |∇ψ| dμ ≤ C n for isotropic log-concave μ with density e^{-ψ}.

C2weakest assumption

The measures are even and log-concave (so the density is e^{-ψ} with ψ convex), and the gradient integral bound holds for the isotropic case; if this integral bound fails or the evenness is dropped, the claimed exponent on the Brunn-Minkowski inequality need not hold.

C3one line summary

Even log-concave measures satisfy μ(λK + (1-λ)L)^{c_n} ≥ λ μ(K)^{c_n} + (1-λ) μ(L)^{c_n} with c_n ≥ c/(n^3 ln n).

Receipt and verification

First computed	2026-06-04T01:09:50.359540Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

085390455902f243861398afcea2e3a56be968427a8172a943bfc31e2036b0b3

Aliases

arxiv: 2605.02747 · arxiv_version: 2605.02747v2 · doi: 10.48550/arxiv.2605.02747 · pith_short_12: BBJZARKZALZE · pith_short_16: BBJZARKZALZEHBQT · pith_short_8: BBJZARKZ

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Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/BBJZARKZALZEHBQTTCX45IXDUV \
  | 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: 085390455902f243861398afcea2e3a56be968427a8172a943bfc31e2036b0b3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "01423a287a013ec23ab99d946b134b69ba12e1f00c97915264729f352c4e834a",
    "cross_cats_sorted": [
      "math.FA"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.MG",
    "submitted_at": "2026-05-04T15:48:01Z",
    "title_canon_sha256": "4624e96bc1bd2b085866fd0fa18a9186f340476df844142dd7cc4e145ab2a0e2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.02747",
    "kind": "arxiv",
    "version": 2
  }
}