Pith Number

pith:65HNJ3QO

pith:2011:65HNJ3QOZB56SOZMP3RGPNRYS6

not attested not anchored not stored refs pending

Sharpness in the k-nearest neighbours random geometric graph model

Mark Walters, Victor Falgas-Ravry

arxiv:1101.3083 v1 · 2011-01-16 · math.PR · math.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{65HNJ3QOZB56SOZMP3RGPNRYS6}

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	2026-05-18T03:32:45.711937Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f74ed4ee0ec87be93b2c7ee267b638979f86219e72acdd44c50b94d1d975a33a

Aliases

arxiv: 1101.3083 · arxiv_version: 1101.3083v1 · doi: 10.48550/arxiv.1101.3083 · pith_short_12: 65HNJ3QOZB56 · pith_short_16: 65HNJ3QOZB56SOZM · pith_short_8: 65HNJ3QO

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/65HNJ3QOZB56SOZMP3RGPNRYS6 \
  | 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: f74ed4ee0ec87be93b2c7ee267b638979f86219e72acdd44c50b94d1d975a33a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9ca9dd11972f2c1d6fbdea4d1c5494060e075a9974933f7c681540a3f9a73e00",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2011-01-16T17:55:49Z",
    "title_canon_sha256": "f046d87cfbddd651055af97c9ea388b55c0889df8c9460ad967a4b7910579dc0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1101.3083",
    "kind": "arxiv",
    "version": 1
  }
}