Pith Number

pith:A4YNCYAR

pith:2026:A4YNCYAR3NUN5K2AUJFYHKHUMZ

not attested not anchored not stored refs pending

Counting triangles in graphs with no wheels of order at least five

Bo Ning, Chunyang Dou, Xing Peng

arxiv:2606.19717 v1 · 2026-06-18 · 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{A4YNCYAR3NUN5K2AUJFYHKHUMZ}

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	2026-06-19T16:12:33.170423Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0730d16011db68deab40a24b83a8f46648cd5d591c6c6f0775cd1f57687c5765

Aliases

arxiv: 2606.19717 · arxiv_version: 2606.19717v1 · doi: 10.48550/arxiv.2606.19717 · pith_short_12: A4YNCYAR3NUN · pith_short_16: A4YNCYAR3NUN5K2A · pith_short_8: A4YNCYAR

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/A4YNCYAR3NUN5K2AUJFYHKHUMZ \
  | 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: 0730d16011db68deab40a24b83a8f46648cd5d591c6c6f0775cd1f57687c5765

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a23dffdf7b311f5aa1a436add8521bf559c7e18853d011d4a759fc268ee78adb",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2026-06-18T02:33:02Z",
    "title_canon_sha256": "4d9b009b6490eb9bd187ee0f812094871ea046a41cec787651c9d027685856a9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.19717",
    "kind": "arxiv",
    "version": 1
  }
}