Pith Number

pith:YQNE33KG

pith:2016:YQNE33KG7PWSB7T47VP2TAZFMU

not attested not anchored not stored refs pending

An isoperimetric inequality for the second non-zero eigenvalue of the Laplacian on the projective plane

Alexei V. Penskoi, Nikolai S. Nadirashvili

arxiv:1608.07334 v5 · 2016-08-25 · math.DG · math.SP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{YQNE33KG7PWSB7T47VP2TAZFMU}

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	2026-05-18T00:16:09.597683Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c41a4ded46fbed20fe7cfd5fa983256534c0b667a7b1c059f4f453970b12e3b6

Aliases

arxiv: 1608.07334 · arxiv_version: 1608.07334v5 · doi: 10.48550/arxiv.1608.07334 · pith_short_12: YQNE33KG7PWS · pith_short_16: YQNE33KG7PWSB7T4 · pith_short_8: YQNE33KG

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/YQNE33KG7PWSB7T47VP2TAZFMU \
  | 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: c41a4ded46fbed20fe7cfd5fa983256534c0b667a7b1c059f4f453970b12e3b6

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "11ee00e7bf79f6830c3341aede40918c35cf886ffd53025b0ae77271b8c2ac7f",
    "cross_cats_sorted": [
      "math.SP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2016-08-25T23:15:52Z",
    "title_canon_sha256": "1846222a037bb526c3a042c39c29ac1755cf82718e4bc326efb2c32cbee76030"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1608.07334",
    "kind": "arxiv",
    "version": 5
  }
}