Pith Number

pith:7FRCCQAZ

pith:2011:7FRCCQAZGV7XJGWX3WHG6LXPAI

not attested not anchored not stored refs pending

Estimates for lower bounds of eigenvalues of the poly-Laplacian and quadratic polynomial operator of the Laplacian

Guoxin Wei, He-Jun Sun, Lingzhong Zeng, Qing-Ming Cheng

arxiv:1112.2781 v1 · 2011-12-13 · 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{7FRCCQAZGV7XJGWX3WHG6LXPAI}

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	2026-05-18T04:06:32.484159Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f962214019357f749ad7dd8e6f2eef0217049b494c5ef8b5d2768915c88b8b2c

Aliases

arxiv: 1112.2781 · arxiv_version: 1112.2781v1 · doi: 10.48550/arxiv.1112.2781 · pith_short_12: 7FRCCQAZGV7X · pith_short_16: 7FRCCQAZGV7XJGWX · pith_short_8: 7FRCCQAZ

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/7FRCCQAZGV7XJGWX3WHG6LXPAI \
  | 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: f962214019357f749ad7dd8e6f2eef0217049b494c5ef8b5d2768915c88b8b2c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7caf1e957da9a65da49d3062aa46df571ef9f3ffd62d3c7c8034fdaff6266de0",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2011-12-13T03:19:46Z",
    "title_canon_sha256": "b49f2d7320fca5092951d3dc2727c66c18e0895e9a1fa3bd144afe831376d83c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1112.2781",
    "kind": "arxiv",
    "version": 1
  }
}