Pith Number

pith:JJTKHZQH

pith:2012:JJTKHZQHL2UZSWR56KF3OHRAGP

not attested not anchored not stored refs pending

Sharp estimate of lower bound for the first eigenvalue in the Laplacian operator on compact Riemannian manifolds

Yue He

arxiv:1210.5685 v1 · 2012-10-21 · math.DG · math.AP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{JJTKHZQHL2UZSWR56KF3OHRAGP}

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	2026-05-18T01:53:45.392891Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4a66a3e6075ea9995a3df28bb71e2033d64236e417fd1a81a9d89a2bde1ce397

Aliases

arxiv: 1210.5685 · arxiv_version: 1210.5685v1 · doi: 10.48550/arxiv.1210.5685 · pith_short_12: JJTKHZQHL2UZ · pith_short_16: JJTKHZQHL2UZSWR5 · pith_short_8: JJTKHZQH

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/JJTKHZQHL2UZSWR56KF3OHRAGP \
  | 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: 4a66a3e6075ea9995a3df28bb71e2033d64236e417fd1a81a9d89a2bde1ce397

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "31fa6ad55869a7aea4a24e12cfb160c932e099f8d5cff4ce57d1b1d2c85c0356",
    "cross_cats_sorted": [
      "math.AP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2012-10-21T04:55:12Z",
    "title_canon_sha256": "e04504794c046bb23cd5301af49141ae3e69d27d8948009c6973db916d015b6b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1210.5685",
    "kind": "arxiv",
    "version": 1
  }
}