Pith Number

pith:GJ4RVJH2

pith:2009:GJ4RVJH2LF2JNW2QIFHW24NB5N

not attested not anchored not stored refs pending

Computing equations for residually free groups

Gilbert Levitt, Vincent Guirardel

arxiv:0902.2119 v2 · 2009-02-12 · math.GR · math.GT

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{GJ4RVJH2LF2JNW2QIFHW24NB5N}

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	2026-05-17T23:44:05.069258Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

32791aa4fa597496db50414f6d71a1eb65dae1157699ce691093616243372705

Aliases

arxiv: 0902.2119 · arxiv_version: 0902.2119v2 · doi: 10.48550/arxiv.0902.2119 · pith_short_12: GJ4RVJH2LF2J · pith_short_16: GJ4RVJH2LF2JNW2Q · pith_short_8: GJ4RVJH2

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/GJ4RVJH2LF2JNW2QIFHW24NB5N \
  | 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: 32791aa4fa597496db50414f6d71a1eb65dae1157699ce691093616243372705

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "feafbc06c1cb3dc58ded9fef1dfacea5c8637b7561b1af58cdea620211e97f4d",
    "cross_cats_sorted": [
      "math.GT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2009-02-12T14:33:23Z",
    "title_canon_sha256": "ed24474719265be2c88f067a3ef19187abb4635a25cfaac2c20cc38863ca56fc"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0902.2119",
    "kind": "arxiv",
    "version": 2
  }
}