Pith Number

pith:4BADJ2U5

pith:2011:4BADJ2U5L53HFSYYITXZELA27V

not attested not anchored not stored refs pending

Local curvature-dimension condition implies measure-contraction property

Fabio Cavalletti, Karl-Theodor Sturm

arxiv:1112.4991 v2 · 2011-12-21 · math.MG · math.FA · 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{4BADJ2U5L53HFSYYITXZELA27V}

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	2026-05-18T03:25:59.642885Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e04034ea9d5f7672cb1844ef922c1afd6d4ece77ac34b719ba139f6a6ece8486

Aliases

arxiv: 1112.4991 · arxiv_version: 1112.4991v2 · doi: 10.48550/arxiv.1112.4991 · pith_short_12: 4BADJ2U5L53H · pith_short_16: 4BADJ2U5L53HFSYY · pith_short_8: 4BADJ2U5

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/4BADJ2U5L53HFSYYITXZELA27V \
  | 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: e04034ea9d5f7672cb1844ef922c1afd6d4ece77ac34b719ba139f6a6ece8486

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b16576125b912f08ad3f62683143c2275c1d0124d5ede26bf889e843228c0713",
    "cross_cats_sorted": [
      "math.FA",
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.MG",
    "submitted_at": "2011-12-21T11:27:46Z",
    "title_canon_sha256": "53ca177726271cf105cdc4295ca8c8674e1b8d2928abd98672fef4d0b07783dd"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1112.4991",
    "kind": "arxiv",
    "version": 2
  }
}