Pith Number

pith:VEFQ43M4

pith:2011:VEFQ43M4RSI6DAF3KZ672Y24EG

not attested not anchored not stored refs pending

Every finitely generated group is weakly exact

Piotr W. Nowak, Ronald G. Douglas

arxiv:1109.0313 v1 · 2011-09-01 · math.FA · math.GR · math.OA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{VEFQ43M4RSI6DAF3KZ672Y24EG}

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	2026-05-18T04:14:16.047198Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a90b0e6d9c8c91e180bb567dfd635c21a70f7c9580026adcf27a95a58943b736

Aliases

arxiv: 1109.0313 · arxiv_version: 1109.0313v1 · doi: 10.48550/arxiv.1109.0313 · pith_short_12: VEFQ43M4RSI6 · pith_short_16: VEFQ43M4RSI6DAF3 · pith_short_8: VEFQ43M4

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/VEFQ43M4RSI6DAF3KZ672Y24EG \
  | 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: a90b0e6d9c8c91e180bb567dfd635c21a70f7c9580026adcf27a95a58943b736

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e61b7b1f32b1f351d8c2e35f6b35a26afe26b30e670491d3426cf92ab38d8980",
    "cross_cats_sorted": [
      "math.GR",
      "math.OA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2011-09-01T21:58:11Z",
    "title_canon_sha256": "4e6fdfc654aff9e7cd407edaf2e1516f7b714f70eb4e277dd99a60bfbfeb21df"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1109.0313",
    "kind": "arxiv",
    "version": 1
  }
}