Pith Number

pith:4D7WLPB3

pith:2012:4D7WLPB3EAWXSNGSSJZXCYFC4Q

not attested not anchored not stored refs pending

Euclidean balls solve some isoperimetric problems with nonradial weights

Joaquim Serra, Xavier Cabre, Xavier Ros-Oton

arxiv:1210.1788 v2 · 2012-10-05 · math.AP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{4D7WLPB3EAWXSNGSSJZXCYFC4Q}

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.

Receipt and verification

First computed	2026-05-18T03:43:41.692969Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e0ff65bc3b202d7934d292737160a2e42bbe5a8a369d9b6d50456a5c27069ffb

Aliases

arxiv: 1210.1788 · arxiv_version: 1210.1788v2 · doi: 10.48550/arxiv.1210.1788 · pith_short_12: 4D7WLPB3EAWX · pith_short_16: 4D7WLPB3EAWXSNGS · pith_short_8: 4D7WLPB3

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/4D7WLPB3EAWXSNGSSJZXCYFC4Q \
  | 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: e0ff65bc3b202d7934d292737160a2e42bbe5a8a369d9b6d50456a5c27069ffb

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "861901b60c93e904dc7ea0254e93818bc9e579f45b6e7a832a1a30ba7d3a752f",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2012-10-05T15:32:40Z",
    "title_canon_sha256": "6e943f6fcf388869a965d7016450b528bbd890ca12042ee3d82eddd52ee65010"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1210.1788",
    "kind": "arxiv",
    "version": 2
  }
}