Pith Number

pith:KINUE575

pith:2012:KINUE575YMG6RLD3AFCDGQGFLK

not attested not anchored not stored refs pending

Riemannian Ricci curvature lower bounds in metric measure spaces with $\sigma$-finite measure

Andrea Mondino, Luigi Ambrosio, Nicola Gigli, Tapio Rajala

arxiv:1207.4924 v2 · 2012-07-20 · math.DG · 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{KINUE575YMG6RLD3AFCDGQGFLK}

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	2026-05-17T23:46:56.115094Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

521b4277fdc30de8ac7b01443340c55ab63a014a909a9de9bbda15874c41fb9a

Aliases

arxiv: 1207.4924 · arxiv_version: 1207.4924v2 · doi: 10.48550/arxiv.1207.4924 · pith_short_12: KINUE575YMG6 · pith_short_16: KINUE575YMG6RLD3 · pith_short_8: KINUE575

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/KINUE575YMG6RLD3AFCDGQGFLK \
  | 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: 521b4277fdc30de8ac7b01443340c55ab63a014a909a9de9bbda15874c41fb9a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3c1d8269619fb0b7489a29fb5be753305e3f7e0f9252a889e82288d5c5b3807d",
    "cross_cats_sorted": [
      "math.MG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2012-07-20T11:38:50Z",
    "title_canon_sha256": "35fe30bca2e493cfe51c8c1b926c1073f11b30819220100a1f005c9f491fc4fd"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1207.4924",
    "kind": "arxiv",
    "version": 2
  }
}