Pith Number

pith:CLZNZUTB

pith:2011:CLZNZUTB7GXP3IJZSNPOTQSZWY

not attested not anchored not stored refs pending

Nearest Neighbor Distances on a Circle: Multidimensional Case

Jeffrey D. Shen, Lyndon L. Ji, Pavel M. Bleher, Roland K. W. Roeder, Youkow Homma

arxiv:1107.4134 v2 · 2011-07-20 · math-ph · math.DS · math.MP · math.NT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{CLZNZUTB7GXP3IJZSNPOTQSZWY}

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	2026-05-18T02:01:13.910776Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

12f2dcd261f9aefda139935ee9c259b631671200a7effd6c175093dbfcdbf551

Aliases

arxiv: 1107.4134 · arxiv_version: 1107.4134v2 · doi: 10.48550/arxiv.1107.4134 · pith_short_12: CLZNZUTB7GXP · pith_short_16: CLZNZUTB7GXP3IJZ · pith_short_8: CLZNZUTB

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/CLZNZUTB7GXP3IJZSNPOTQSZWY \
  | 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: 12f2dcd261f9aefda139935ee9c259b631671200a7effd6c175093dbfcdbf551

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f5dce4ab9bdbcb17128e1dc252e05b918cc33663dadcfffb5061691e0016daa0",
    "cross_cats_sorted": [
      "math.DS",
      "math.MP",
      "math.NT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2011-07-20T22:37:05Z",
    "title_canon_sha256": "8b6e366f17e28d1de5df190c7564721f71a913dd66a760942c49013a035a3243"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1107.4134",
    "kind": "arxiv",
    "version": 2
  }
}