Pith Number

pith:3O2OSACD

pith:2012:3O2OSACDRORUEFK7TUYSGPKM75

not attested not anchored not stored refs pending

Isoperimetric profile of radial probability measures on Euclidean spaces

Asuka Takatsu

arxiv:1212.6851 v1 · 2012-12-31 · math.PR · 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{3O2OSACDRORUEFK7TUYSGPKM75}

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	2026-05-18T03:37:30.721482Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

dbb4e900438ba342155f9d31233d4cff6eb32d3d27cc5a80323085c2b1737278

Aliases

arxiv: 1212.6851 · arxiv_version: 1212.6851v1 · doi: 10.48550/arxiv.1212.6851 · pith_short_12: 3O2OSACDRORU · pith_short_16: 3O2OSACDRORUEFK7 · pith_short_8: 3O2OSACD

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/3O2OSACDRORUEFK7TUYSGPKM75 \
  | 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: dbb4e900438ba342155f9d31233d4cff6eb32d3d27cc5a80323085c2b1737278

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "523f6da2c0b23832ca6564dc666b993f8144972a2134d9d7e5243793cf9b909a",
    "cross_cats_sorted": [
      "math.MG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2012-12-31T10:27:26Z",
    "title_canon_sha256": "2c669dae997f649324b93ea2594dfc0d29aa93b5f31eef69bd51ec9718eafb30"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1212.6851",
    "kind": "arxiv",
    "version": 1
  }
}