Pith Number

pith:E6BMKACL

pith:2008:E6BMKACLYA46JHBKXL4MP5FZ62

not attested not anchored not stored refs pending

Large scale geometry of commutator subgroups

Danny Calegari, Dongping Zhuang

arxiv:0807.4704 v2 · 2008-07-29 · 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{E6BMKACLYA46JHBKXL4MP5FZ62}

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	2026-05-18T02:41:51.557114Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2782c5004bc039e49c2abaf8c7f4b9f6b23f2450f5ba21df2506bf4f2bebdf54

Aliases

arxiv: 0807.4704 · arxiv_version: 0807.4704v2 · doi: 10.48550/arxiv.0807.4704 · pith_short_12: E6BMKACLYA46 · pith_short_16: E6BMKACLYA46JHBK · pith_short_8: E6BMKACL

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/E6BMKACLYA46JHBKXL4MP5FZ62 \
  | 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: 2782c5004bc039e49c2abaf8c7f4b9f6b23f2450f5ba21df2506bf4f2bebdf54

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "334c427c59aa94e93b61d033e3f01d23508c9b86f31052a6f4490f701d4e79d3",
    "cross_cats_sorted": [
      "math.GT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2008-07-29T16:45:33Z",
    "title_canon_sha256": "1b529f2086ec077bb526a73a3f189fa47678da989e0a495f3304870439fcc435"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0807.4704",
    "kind": "arxiv",
    "version": 2
  }
}