Pith Number

pith:3M3C5N4X

pith:2011:3M3C5N4X3CVM3ILZCMVQXT7ORN

not attested not anchored not stored refs pending

Cayley automatic groups are not Cayley biautomatic

Alexei Miasnikov, Zoran Sunic

arxiv:1108.2759 v1 · 2011-08-13 · 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{3M3C5N4X3CVM3ILZCMVQXT7ORN}

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	2026-05-18T04:15:35.656710Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

db362eb797d8aacda179132b0bcfee8b6caf16a64c422c7808f74f7f9259178c

Aliases

arxiv: 1108.2759 · arxiv_version: 1108.2759v1 · doi: 10.48550/arxiv.1108.2759 · pith_short_12: 3M3C5N4X3CVM · pith_short_16: 3M3C5N4X3CVM3ILZ · pith_short_8: 3M3C5N4X

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/3M3C5N4X3CVM3ILZCMVQXT7ORN \
  | 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: db362eb797d8aacda179132b0bcfee8b6caf16a64c422c7808f74f7f9259178c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "dc1ce31f9294e7f135cb67c1d9a834bba18d36648154732f11d9ebf8f3455916",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2011-08-13T05:21:05Z",
    "title_canon_sha256": "96883d563c3d32bb4520d55d53ecc85d45f111fa7af797afbcdf822e2bd8691e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1108.2759",
    "kind": "arxiv",
    "version": 1
  }
}