Pith Number

pith:MVGK5P6U

pith:2013:MVGK5P6USHE77ABUHLNLHAQD3Z

not attested not anchored not stored refs pending

On the Equivalence of the Entropic Curvature-Dimension Condition and Bochner's Inequality on Metric Measure Spaces

Karl-Theodor Sturm, Kazumasa Kuwada, Matthias Erbar

arxiv:1303.4382 v2 · 2013-03-18 · math.DG · math.AP · 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{MVGK5P6USHE77ABUHLNLHAQD3Z}

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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	2026-05-18T03:17:24.473574Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

654caebfd491c9ff80343adab38203de5cef8219e7a1f25db8ab513cef744fb0

Aliases

arxiv: 1303.4382 · arxiv_version: 1303.4382v2 · doi: 10.48550/arxiv.1303.4382 · pith_short_12: MVGK5P6USHE7 · pith_short_16: MVGK5P6USHE77ABU · pith_short_8: MVGK5P6U

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/MVGK5P6USHE77ABUHLNLHAQD3Z \
  | 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: 654caebfd491c9ff80343adab38203de5cef8219e7a1f25db8ab513cef744fb0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7c995751dd3b3a02c77918212224d18c4a9ce08b605d57d2df382231590cdbf9",
    "cross_cats_sorted": [
      "math.AP",
      "math.MG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2013-03-18T19:52:39Z",
    "title_canon_sha256": "45d322ce88045b298d6fb9153245cc13a4435a3f87d85021aa59fc3353a96c50"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1303.4382",
    "kind": "arxiv",
    "version": 2
  }
}