Pith Number

pith:5GBCKLRB

pith:2013:5GBCKLRBOBCS5SGMVCIZG2Z4UA

not attested not anchored not stored refs pending

Eigenvalues of the Witten-Laplacian on compact Riemannian manifolds

Lingzhong Zeng, Qing-Ming Cheng

arxiv:1304.3212 v2 · 2013-04-11 · 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{5GBCKLRBOBCS5SGMVCIZG2Z4UA}

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	2026-05-18T00:53:19.655458Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e982252e2170452ec8cca891936b3ca01f15e1b0f1c6bfb5f73c88de96dfd1bf

Aliases

arxiv: 1304.3212 · arxiv_version: 1304.3212v2 · doi: 10.48550/arxiv.1304.3212 · pith_short_12: 5GBCKLRBOBCS · pith_short_16: 5GBCKLRBOBCS5SGM · pith_short_8: 5GBCKLRB

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/5GBCKLRBOBCS5SGMVCIZG2Z4UA \
  | 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: e982252e2170452ec8cca891936b3ca01f15e1b0f1c6bfb5f73c88de96dfd1bf

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "10c9be98c1bd11b043b113af5382c47d25c9783e007c6f5e6e10079ca951416d",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by-nc-sa/3.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2013-04-11T06:42:09Z",
    "title_canon_sha256": "1e9c998c7923921d23d20e5025a5d89658ebd4476f8e9f5baff85151411a85d1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1304.3212",
    "kind": "arxiv",
    "version": 2
  }
}