Pith Number

pith:XX3TZNWH

pith:2011:XX3TZNWHK5EUIBVBEY2WDIJX4F

not attested not anchored not stored refs pending

Variational formulas of higher order mean curvatures

Jianquan Ge, Ling Xu

arxiv:1111.2650 v3 · 2011-11-11 · math.DG

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{XX3TZNWHK5EUIBVBEY2WDIJX4F}

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	2026-05-18T01:59:42.182134Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

bdf73cb6c757494406a1263561a137e152939459ab9d1791761d5f3f9f83881f

Aliases

arxiv: 1111.2650 · arxiv_version: 1111.2650v3 · doi: 10.48550/arxiv.1111.2650 · pith_short_12: XX3TZNWHK5EU · pith_short_16: XX3TZNWHK5EUIBVB · pith_short_8: XX3TZNWH

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/XX3TZNWHK5EUIBVBEY2WDIJX4F \
  | 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: bdf73cb6c757494406a1263561a137e152939459ab9d1791761d5f3f9f83881f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1cb146c711af9633c8a75c43c86c522c58bd5495c7576c903b8ac7ab79c3dd28",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2011-11-11T02:47:35Z",
    "title_canon_sha256": "850ae765be75ae2cfa2373f1474d86800a32f4ea5e5c7d3b41bc1d0e5ccc006b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1111.2650",
    "kind": "arxiv",
    "version": 3
  }
}