Pith Number

pith:7LOEE2WH

pith:2021:7LOEE2WH7Y54OZLENPW23ZAHP7

not attested not anchored not stored refs pending

A nonabelian Brunn-Minkowski inequality

Chieu-Minh Tran, Ruixiang Zhang, Yifan Jing

arxiv:2101.07782 v3 · 2021-01-19 · math.GR · math.CA · math.CO · math.FA · math.MG

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{7LOEE2WH7Y54OZLENPW23ZAHP7}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

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.

Cited by

1 paper in Pith

Measure doubling in unimodular locally compact groups and quotients

Receipt and verification

First computed	2026-07-05T06:08:01.812884Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

fadc426ac7fe3bc765646bedade4077fefe94dd0457d3c5d26cedf2d8e0cf73b

Aliases

arxiv: 2101.07782 · arxiv_version: 2101.07782v3 · doi: 10.48550/arxiv.2101.07782 · pith_short_12: 7LOEE2WH7Y54 · pith_short_16: 7LOEE2WH7Y54OZLE · pith_short_8: 7LOEE2WH

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/7LOEE2WH7Y54OZLENPW23ZAHP7 \
  | 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: fadc426ac7fe3bc765646bedade4077fefe94dd0457d3c5d26cedf2d8e0cf73b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d6400b0a29e7c00b72711e441f51fd55407fdb9a1004d03b548d7d986231e5ec",
    "cross_cats_sorted": [
      "math.CA",
      "math.CO",
      "math.FA",
      "math.MG"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2021-01-19T18:55:49Z",
    "title_canon_sha256": "2b3850e639012fa4d4ea103736127bd330fc4359997a3b0607276e16c14b4aab"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2101.07782",
    "kind": "arxiv",
    "version": 3
  }
}