Pith Number

pith:NXX3UEQW

pith:2018:NXX3UEQWLWY2TLZKGA5TGAR3BZ

not attested not anchored not stored refs pending

The Hall--Paige conjecture, and synchronization for affine and diagonal groups

Hua Zhang, John N. Bray, Pablo Spiga, Peter J. Cameron, Qi Cai

arxiv:1811.12671 v2 · 2018-11-30 · math.GR · 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{NXX3UEQWLWY2TLZKGA5TGAR3BZ}

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	2026-05-17T23:44:42.803326Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6defba12165db1a9af2a303b33023b0e5b65049d1f8b5ef9bf8a7588a21a76fa

Aliases

arxiv: 1811.12671 · arxiv_version: 1811.12671v2 · doi: 10.48550/arxiv.1811.12671 · pith_short_12: NXX3UEQWLWY2 · pith_short_16: NXX3UEQWLWY2TLZK · pith_short_8: NXX3UEQW

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/NXX3UEQWLWY2TLZKGA5TGAR3BZ \
  | 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: 6defba12165db1a9af2a303b33023b0e5b65049d1f8b5ef9bf8a7588a21a76fa

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "87f58b59592ef832405b18e05fc2af515434345c3501c99a0393fc23017d43a9",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2018-11-30T08:50:11Z",
    "title_canon_sha256": "673f1f01c221faae0bf9189a5c88734f29ec664638bb29a85d129d1226884ad3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1811.12671",
    "kind": "arxiv",
    "version": 2
  }
}