Pith Number

pith:ALNJQT7U

pith:2011:ALNJQT7US5ZP3Z7WTVPAZ5EWSH

not attested not anchored not stored refs pending

Bounds for the first eigenvalue of the horizontal Laplacian in positively curved sub-Riemannian manifolds

Robert K. Hladky

arxiv:1111.5004 v1 · 2011-11-21 · 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{ALNJQT7US5ZP3Z7WTVPAZ5EWSH}

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	2026-05-18T04:07:54.550744Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

02da984ff49772fde7f69d5e0cf49691e6301b2800f6d8880bb4d7662a11b980

Aliases

arxiv: 1111.5004 · arxiv_version: 1111.5004v1 · doi: 10.48550/arxiv.1111.5004 · pith_short_12: ALNJQT7US5ZP · pith_short_16: ALNJQT7US5ZP3Z7W · pith_short_8: ALNJQT7U

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/ALNJQT7US5ZP3Z7WTVPAZ5EWSH \
  | 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: 02da984ff49772fde7f69d5e0cf49691e6301b2800f6d8880bb4d7662a11b980

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1164d02590ad22beed51468ed51045629f46b43b33d3ec641fb15b674f05ed63",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2011-11-21T20:56:28Z",
    "title_canon_sha256": "5028fba8e247aba6a282f2ca1217e546887f6d6810b89f49713fa0d8c15a21dd"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1111.5004",
    "kind": "arxiv",
    "version": 1
  }
}