Pith Number

pith:PU3GFURX

pith:2009:PU3GFURXHF6KKAJYOLSCF7WSFH

not attested not anchored not stored refs pending

The congruence subgroup problem for branch groups

Laurent Bartholdi, Olivier Siegenthaler, Pavel Zalesskii

arxiv:0902.3220 v1 · 2009-02-18 · 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{PU3GFURXHF6KKAJYOLSCF7WSFH}

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	2026-05-18T03:58:37.084888Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7d3662d237397ca5013872e422fed229d79cae700d81e8f872dea4cdb576bfa1

Aliases

arxiv: 0902.3220 · arxiv_version: 0902.3220v1 · doi: 10.48550/arxiv.0902.3220 · pith_short_12: PU3GFURXHF6K · pith_short_16: PU3GFURXHF6KKAJY · pith_short_8: PU3GFURX

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/PU3GFURXHF6KKAJYOLSCF7WSFH \
  | 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: 7d3662d237397ca5013872e422fed229d79cae700d81e8f872dea4cdb576bfa1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "40d0282a6fedd0d67213e8713b96f1942919338df4171aa5f0ebebca9066f942",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2009-02-18T20:51:35Z",
    "title_canon_sha256": "590aedf05a90956b1168f9bc61fb0aadf9798e114d95b7be69acf17d6a2b6d82"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0902.3220",
    "kind": "arxiv",
    "version": 1
  }
}