Pith Number

pith:W3ZWUQEN

pith:2010:W3ZWUQENEU64BOQZRELGBXBZUG

not attested not anchored not stored refs pending

The sharp estimates for the first eigenvalue of Paneitz operator on 4-dimensional submanifolds

Daguang Chen, Haizhong Li

arxiv:1010.3102 v1 · 2010-10-15 · 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{W3ZWUQENEU64BOQZRELGBXBZUG}

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	2026-05-18T04:39:17.799900Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b6f36a408d253dc0ba19891660dc39a194e622349f4b3aa141b20ed74f32f8cc

Aliases

arxiv: 1010.3102 · arxiv_version: 1010.3102v1 · doi: 10.48550/arxiv.1010.3102 · pith_short_12: W3ZWUQENEU64 · pith_short_16: W3ZWUQENEU64BOQZ · pith_short_8: W3ZWUQEN

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/W3ZWUQENEU64BOQZRELGBXBZUG \
  | 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: b6f36a408d253dc0ba19891660dc39a194e622349f4b3aa141b20ed74f32f8cc

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "513382f40fe12bbf8b59d07d4a8cd0ef0ff60a64e761d3bfc77f572cf37fce15",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2010-10-15T09:15:23Z",
    "title_canon_sha256": "81434356640d114e9dc0a40e5c630e89ca2a0e38ef0e86ac84f16f5a97f8ea5a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1010.3102",
    "kind": "arxiv",
    "version": 1
  }
}