Pith Number

pith:5VFXWLUG

pith:2010:5VFXWLUGMQY7AI6CR5RO5VERA6

not attested not anchored not stored refs pending

Characterising planar Cayley graphs and Cayley complexes in terms of group presentations

Agelos Georgakopoulos

arxiv:1011.4255 v3 · 2010-11-18 · 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{5VFXWLUGMQY7AI6CR5RO5VERA6}

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	2026-05-18T02:23:36.277202Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ed4b7b2e866431f023c28f62eed491078ea2107e9d778cd3857d1cc74f98c28c

Aliases

arxiv: 1011.4255 · arxiv_version: 1011.4255v3 · doi: 10.48550/arxiv.1011.4255 · pith_short_12: 5VFXWLUGMQY7 · pith_short_16: 5VFXWLUGMQY7AI6C · pith_short_8: 5VFXWLUG

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/5VFXWLUGMQY7AI6CR5RO5VERA6 \
  | 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: ed4b7b2e866431f023c28f62eed491078ea2107e9d778cd3857d1cc74f98c28c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4460d7c1b514995837aeb7451ffbeb168118aec6a73523aea8d654e8f52994ca",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2010-11-18T18:51:08Z",
    "title_canon_sha256": "9b92b00bcc08e5bedb171ef06b0dbb63db4c450a0325675753bd25d5b8de12ae"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1011.4255",
    "kind": "arxiv",
    "version": 3
  }
}