Pith Number

pith:GPX3OMYI

pith:2012:GPX3OMYIBS4N4UE4ZTWEXIC3WT

not attested not anchored not stored refs pending

Simplicity of some twin tree automorphism groups with trivial commutation relations

Bertrand R\'emy, Jun Morita

arxiv:1211.4373 v1 · 2012-11-19 · 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{GPX3OMYIBS4N4UE4ZTWEXIC3WT}

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	2026-05-18T03:40:27.176803Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

33efb733080cb8de509cccec4ba05bb4d881e38df51ddcdf28e9fbc36d643e68

Aliases

arxiv: 1211.4373 · arxiv_version: 1211.4373v1 · doi: 10.48550/arxiv.1211.4373 · pith_short_12: GPX3OMYIBS4N · pith_short_16: GPX3OMYIBS4N4UE4 · pith_short_8: GPX3OMYI

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/GPX3OMYIBS4N4UE4ZTWEXIC3WT \
  | 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: 33efb733080cb8de509cccec4ba05bb4d881e38df51ddcdf28e9fbc36d643e68

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "52c3ccf3b4557f415752de1d71eea465045beab900d27e78ffa95b339644181d",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2012-11-19T11:54:55Z",
    "title_canon_sha256": "b265cdf05a615915a2acba0ce1c14fd889b8d2b4a4c83604d8f10910410ce32f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1211.4373",
    "kind": "arxiv",
    "version": 1
  }
}