Pith Number

pith:VQ64ZNED

pith:2011:VQ64ZNEDOLKFD7CER5W5TX2C3R

not attested not anchored not stored refs pending

An isoperimetric inequality for eigenvalues of the bi-harmonic operator

G. Feng, Q. Ding, Y. Zhang

arxiv:1101.5224 v1 · 2011-01-27 · math.AP · 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{VQ64ZNEDOLKFD7CER5W5TX2C3R}

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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	2026-05-18T04:30:35.886356Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ac3dccb48372d451fc448f6dd9df42dc75cff831e0cc66334b739b63cb6e5b41

Aliases

arxiv: 1101.5224 · arxiv_version: 1101.5224v1 · doi: 10.48550/arxiv.1101.5224 · pith_short_12: VQ64ZNEDOLKF · pith_short_16: VQ64ZNEDOLKFD7CE · pith_short_8: VQ64ZNED

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/VQ64ZNEDOLKFD7CER5W5TX2C3R \
  | 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: ac3dccb48372d451fc448f6dd9df42dc75cff831e0cc66334b739b63cb6e5b41

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1b4be30c8b200f06dd1c8750daa43e1103d33642e04826ff14e619cc400d93a5",
    "cross_cats_sorted": [
      "math.DG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2011-01-27T08:56:06Z",
    "title_canon_sha256": "3dcb8b4cf4760e46d4d30027e0aad2e14803443990c32104bac9acdec4d2fa07"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1101.5224",
    "kind": "arxiv",
    "version": 1
  }
}