Pith Number

pith:Y2LW3TRU

pith:2012:Y2LW3TRU6XUIEZDF6SFRHBLOQE

not attested not anchored not stored refs pending

Lift zonoid and barycentric representation on a Banach space with a cylinder measure

Alexei M. Kulik, Taras D. Tymoshkevych

arxiv:1211.2927 v1 · 2012-11-13 · math.PR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{Y2LW3TRU6XUIEZDF6SFRHBLOQE}

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	2026-05-18T03:40:52.331212Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c6976dce34f5e8826465f48b13856e8120252cea38815c4a3cff86ab6d2fb8b0

Aliases

arxiv: 1211.2927 · arxiv_version: 1211.2927v1 · doi: 10.48550/arxiv.1211.2927 · pith_short_12: Y2LW3TRU6XUI · pith_short_16: Y2LW3TRU6XUIEZDF · pith_short_8: Y2LW3TRU

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/Y2LW3TRU6XUIEZDF6SFRHBLOQE \
  | 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: c6976dce34f5e8826465f48b13856e8120252cea38815c4a3cff86ab6d2fb8b0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "cb2d4459bc3f54ce7fe6322a87497a233d5cc722c37dbb40c3f55535a03b9d96",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2012-11-13T09:33:48Z",
    "title_canon_sha256": "79ad4a8793729b365920201359733beb44c7a75d3cc29190991d0939abfc1d35"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1211.2927",
    "kind": "arxiv",
    "version": 1
  }
}