Pith Number

pith:OPIIEZI7

pith:2011:OPIIEZI7HDJZFGLTPO2HMS6JKO

not attested not anchored not stored refs pending

The Length of a Minimal Tree With a Given Topology: generalization of Maxwell Formula

A.A.Tuzhilin, A.O.Ivanov

arxiv:1101.2117 v1 · 2011-01-11 · math.MG · 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{OPIIEZI7HDJZFGLTPO2HMS6JKO}

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	2026-05-18T04:31:50.819699Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

73d082651f38d39299737bb4764bc95385e46c7e0263b67b72ffb2f4eca3fd64

Aliases

arxiv: 1101.2117 · arxiv_version: 1101.2117v1 · doi: 10.48550/arxiv.1101.2117 · pith_short_12: OPIIEZI7HDJZ · pith_short_16: OPIIEZI7HDJZFGLT · pith_short_8: OPIIEZI7

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/OPIIEZI7HDJZFGLTPO2HMS6JKO \
  | 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: 73d082651f38d39299737bb4764bc95385e46c7e0263b67b72ffb2f4eca3fd64

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "df6ae566bd5df899af275ff8cd203087f292baad6e7e143e8c660f2c15e20d94",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.MG",
    "submitted_at": "2011-01-11T12:52:32Z",
    "title_canon_sha256": "0e9287eb299ca0428923e55ae087cd670374f1a7efd1d18a7b7fa44f9af4aa62"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1101.2117",
    "kind": "arxiv",
    "version": 1
  }
}