Pith Number

pith:2Q5ZCMO4

pith:2023:2Q5ZCMO46SL4FK3AYA3D54VOUP

not attested not anchored not stored refs pending

Acyclic graphs with at least $2\ell+1$ vertices are $\ell$-recognizable

Alexandr V. Kostochka, Dara Zirlin, Douglas B. West, Mina Nahvi

arxiv:2308.04509 v1 · 2023-08-08 · 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{2Q5ZCMO46SL4FK3AYA3D54VOUP}

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	2026-07-05T06:39:38.857240Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d43b9131dcf497c2ab60c0363ef2aea3df827813abdb99ba5ea961d513c70718

Aliases

arxiv: 2308.04509 · arxiv_version: 2308.04509v1 · doi: 10.48550/arxiv.2308.04509 · pith_short_12: 2Q5ZCMO46SL4 · pith_short_16: 2Q5ZCMO46SL4FK3A · pith_short_8: 2Q5ZCMO4

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/2Q5ZCMO46SL4FK3AYA3D54VOUP \
  | 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: d43b9131dcf497c2ab60c0363ef2aea3df827813abdb99ba5ea961d513c70718

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1778db85d8853f61210667ebab78f87e03bde741bd46c1c8d1978f30459c5131",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2023-08-08T18:17:49Z",
    "title_canon_sha256": "43c2e730119a449954d22ae8e0f42ab7fc09b36a20e8d801376a161a7f525d3d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2308.04509",
    "kind": "arxiv",
    "version": 1
  }
}