Pith Number

pith:KZTU2CJJ

pith:2026:KZTU2CJJ57M2FO5X2FIPBRSVQ4

not attested not anchored not stored refs pending

2-cell embeddings of cubic graphs I. The unstable dual

Bojan Mohar, MacKenzie Carr

arxiv:2606.06768 v1 · 2026-06-04 · 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{KZTU2CJJ57M2FO5X2FIPBRSVQ4}

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	2026-06-08T01:04:27.360378Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

56674d0929efd9a2bbb7d150f0c655871c197537f4cc9fb5600d3e32e59dd485

Aliases

arxiv: 2606.06768 · arxiv_version: 2606.06768v1 · doi: 10.48550/arxiv.2606.06768 · pith_short_12: KZTU2CJJ57M2 · pith_short_16: KZTU2CJJ57M2FO5X · pith_short_8: KZTU2CJJ

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/KZTU2CJJ57M2FO5X2FIPBRSVQ4 \
  | 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: 56674d0929efd9a2bbb7d150f0c655871c197537f4cc9fb5600d3e32e59dd485

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d1cc5850bf57aaba18161a204b70d18e8b8a1f1da892802b9f8be94b9e11a26d",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2026-06-04T23:14:19Z",
    "title_canon_sha256": "a334bcd74d7401d020675be304bc174a1d63f8b0740000a18fe8446f29c1bb26"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.06768",
    "kind": "arxiv",
    "version": 1
  }
}