Pith Number

pith:5VTZCGCK

pith:2012:5VTZCGCKTD2GDGUGC35276Y2AF

not attested not anchored not stored refs pending

Fixed points of endomorphisms of graph groups

Emanuele Rodaro, Mihalis Sykiotis, Pedro V. Silva

arxiv:1210.4094 v1 · 2012-10-15 · 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{5VTZCGCKTD2GDGUGC35276Y2AF}

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	2026-05-18T03:08:47.539832Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ed6791184a98f4619a8616fbaffb1a0142078162075a7c7e11c6636cc41e8c0d

Aliases

arxiv: 1210.4094 · arxiv_version: 1210.4094v1 · doi: 10.48550/arxiv.1210.4094 · pith_short_12: 5VTZCGCKTD2G · pith_short_16: 5VTZCGCKTD2GDGUG · pith_short_8: 5VTZCGCK

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/5VTZCGCKTD2GDGUGC35276Y2AF \
  | 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: ed6791184a98f4619a8616fbaffb1a0142078162075a7c7e11c6636cc41e8c0d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "096c41784c94f6403662d89dd184ae2a9c31b94169a75cd48cc9abc13fa74720",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2012-10-15T16:28:36Z",
    "title_canon_sha256": "2bbdb3d05fe04a68a691e5579d4718b4b4587ca50af5165fa38b6182dac66e74"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1210.4094",
    "kind": "arxiv",
    "version": 1
  }
}