Pith Number

pith:A4IYWBQD

pith:2017:A4IYWBQD7DEHGIVWZR4FFUMZQE

not attested not anchored not stored refs pending

A universal tree-based network with the minimum number of reticulations

Charles Semple, Magnus Bordewich

arxiv:1707.08274 v2 · 2017-07-26 · 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{A4IYWBQD7DEHGIVWZR4FFUMZQE}

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	2026-05-18T00:27:27.942287Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

07118b0603f8c87322b6cc7852d199813fdbcbdbcc70b7ba9a2c9b42562ed276

Aliases

arxiv: 1707.08274 · arxiv_version: 1707.08274v2 · doi: 10.48550/arxiv.1707.08274 · pith_short_12: A4IYWBQD7DEH · pith_short_16: A4IYWBQD7DEHGIVW · pith_short_8: A4IYWBQD

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/A4IYWBQD7DEHGIVWZR4FFUMZQE \
  | 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: 07118b0603f8c87322b6cc7852d199813fdbcbdbcc70b7ba9a2c9b42562ed276

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "cc9989b86c91d6de6359bd2de5a05616acd0dc2920d4898f2bcb88c10d715b2d",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2017-07-26T02:17:01Z",
    "title_canon_sha256": "a94d06e13234391fff61964a93556a602990290b0d9cd9681f17c190b26cac43"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1707.08274",
    "kind": "arxiv",
    "version": 2
  }
}