Pith Number

pith:A6KDOM3E

pith:2012:A6KDOM3EA2LL2CH6JCQNCLBFGA

not attested not anchored not stored refs pending

On the length of a random minimum spanning tree

Alan Frieze, Colin Cooper, Joel Spencer, Nate Ince, Svante Janson

arxiv:1208.5170 v2 · 2012-08-25 · 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{A6KDOM3EA2LL2CH6JCQNCLBFGA}

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	2026-05-17T23:53:18.513926Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

07943733640696bd08fe48a0d12c2530132c71b52a5d7ad8fbe28a9214cc6dd4

Aliases

arxiv: 1208.5170 · arxiv_version: 1208.5170v2 · doi: 10.48550/arxiv.1208.5170 · pith_short_12: A6KDOM3EA2LL · pith_short_16: A6KDOM3EA2LL2CH6 · pith_short_8: A6KDOM3E

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/A6KDOM3EA2LL2CH6JCQNCLBFGA \
  | 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: 07943733640696bd08fe48a0d12c2530132c71b52a5d7ad8fbe28a9214cc6dd4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "fb72e7fe61d21298389f154ef7ebd59082467eccc1dd3921611f3f0b55a00bf0",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2012-08-25T20:42:59Z",
    "title_canon_sha256": "2b9a263d5707ce7f98081d3770c5faa8fdda984852ba6e08b88f87c92eb6907f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1208.5170",
    "kind": "arxiv",
    "version": 2
  }
}