Pith Number

pith:4FEX7XUS

pith:2013:4FEX7XUSM4QFVVQ3IRPUJ7ZKD2

not attested not anchored not stored refs pending

Ricci curvatures in Carnot groups

Ludovic Rifford

arxiv:1305.6057 v1 · 2013-05-26 · math.OC · 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{4FEX7XUSM4QFVVQ3IRPUJ7ZKD2}

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	2026-05-18T03:24:53.063886Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e1497fde9267205ad61b445f44ff2a1e8289dcc6f44ecec815a5d5bc8fc6d1dd

Aliases

arxiv: 1305.6057 · arxiv_version: 1305.6057v1 · doi: 10.48550/arxiv.1305.6057 · pith_short_12: 4FEX7XUSM4QF · pith_short_16: 4FEX7XUSM4QFVVQ3 · pith_short_8: 4FEX7XUS

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/4FEX7XUSM4QFVVQ3IRPUJ7ZKD2 \
  | 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: e1497fde9267205ad61b445f44ff2a1e8289dcc6f44ecec815a5d5bc8fc6d1dd

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9fd87cccdba724db3aaed1d628e93950406b53898922f54cb468cf2058136e7f",
    "cross_cats_sorted": [
      "math.DG",
      "math.MG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2013-05-26T19:25:20Z",
    "title_canon_sha256": "2ab822c916e36c8b2525f3a02bd655f63b7cb6337e2afecc33a601e70c9c6b26"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1305.6057",
    "kind": "arxiv",
    "version": 1
  }
}