Pith Number

pith:W32KFTPN

pith:2010:W32KFTPNMP2WIHN4C3XG2WU7GM

not attested not anchored not stored refs pending

Equivalent Semigroup Properties for Curvature-Dimension Condition

Feng-Yu Wang

arxiv:1012.5686 v1 · 2010-12-28 · 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{W32KFTPNMP2WIHN4C3XG2WU7GM}

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	2026-05-18T04:32:22.568511Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b6f4a2cded63f5641dbc16ee6d5a9f331807c2d97d653fcec707bac20da4c279

Aliases

arxiv: 1012.5686 · arxiv_version: 1012.5686v1 · doi: 10.48550/arxiv.1012.5686 · pith_short_12: W32KFTPNMP2W · pith_short_16: W32KFTPNMP2WIHN4 · pith_short_8: W32KFTPN

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/W32KFTPNMP2WIHN4C3XG2WU7GM \
  | 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: b6f4a2cded63f5641dbc16ee6d5a9f331807c2d97d653fcec707bac20da4c279

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "39ecc4538b6f65f5b0940304025e511249051e6a5264a21ed4cbbd7c0c6a812e",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2010-12-28T03:09:31Z",
    "title_canon_sha256": "5a05adee1dd9e6fee0cea188132d6813dceb2c693319a79579c077d66c94383e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1012.5686",
    "kind": "arxiv",
    "version": 1
  }
}