Pith Number

pith:VGM6ENMT

pith:2026:VGM6ENMT6LRYEOME3UNSF6XVFC

not attested not anchored not stored refs pending

On the automorphism group of direct product of digraphs

Binzhou Xia, Guang Rao, Yu Wang

arxiv:2606.22947 v1 · 2026-06-22 · math.CO · math.GR

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{VGM6ENMT6LRYEOME3UNSF6XVFC}

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	2026-06-23T03:14:04.982707Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a999e23593f2e3823984dd1b22faf528bb1a3a383d2a856fc9e005648e6fde9d

Aliases

arxiv: 2606.22947 · arxiv_version: 2606.22947v1 · doi: 10.48550/arxiv.2606.22947 · pith_short_12: VGM6ENMT6LRY · pith_short_16: VGM6ENMT6LRYEOME · pith_short_8: VGM6ENMT

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/VGM6ENMT6LRYEOME3UNSF6XVFC \
  | 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: a999e23593f2e3823984dd1b22faf528bb1a3a383d2a856fc9e005648e6fde9d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "18ca655f8f2dfd0a6517bb0e9e203b6da1fcdf1fbaafd53270072fac8f6217f5",
    "cross_cats_sorted": [
      "math.GR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2026-06-22T07:25:14Z",
    "title_canon_sha256": "b32351273ea97a55393999640c909e3984322ff97abc1bea108cefebb0e23d01"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.22947",
    "kind": "arxiv",
    "version": 1
  }
}