Pith Number

pith:6T663VXF

pith:2012:6T663VXFTNV7JMLDMPL3ZOG6P7

not attested not anchored not stored refs pending

Monoids of O-type, subword reversing, and ordered groups

Patrick Dehornoy (LMNO)

arxiv:1204.3211 v3 · 2012-04-14 · 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{6T663VXFTNV7JMLDMPL3ZOG6P7}

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	2026-05-18T03:56:09.139077Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f4fdedd6e59b6bf4b16363d7bcb8de7fdbe217fb7dd08b3077fa7452595e5cba

Aliases

arxiv: 1204.3211 · arxiv_version: 1204.3211v3 · doi: 10.48550/arxiv.1204.3211 · pith_short_12: 6T663VXFTNV7 · pith_short_16: 6T663VXFTNV7JMLD · pith_short_8: 6T663VXF

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/6T663VXFTNV7JMLDMPL3ZOG6P7 \
  | 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: f4fdedd6e59b6bf4b16363d7bcb8de7fdbe217fb7dd08b3077fa7452595e5cba

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "bc475a790912ea8ff0c6c3da4b338ca442328ca139dc1f2d66bd2156d75bd2b4",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2012-04-14T20:28:02Z",
    "title_canon_sha256": "ea66621c59315b8ed219bd20d21e063d73e50e35c929749a97e236ee6c098e87"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1204.3211",
    "kind": "arxiv",
    "version": 3
  }
}