Pith Number

pith:IQ3E3VLE

pith:2002:IQ3E3VLE3NXS2DXM2TV4JMVKZZ

not attested not anchored not stored refs pending

Engulfing in word-hyperbolic groups

B. T. Williams, G. A. Niblo

arxiv:math/0209185 v1 · 2002-09-15 · 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{IQ3E3VLE3NXS2DXM2TV4JMVKZZ}

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	2026-05-18T02:41:32.864285Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

44364dd564db6f2d0eecd4ebc4b2aace4904523d80618d247e74f80bdbe638be

Aliases

arxiv: math/0209185 · arxiv_version: math/0209185v1 · doi: 10.48550/arxiv.math/0209185 · pith_short_12: IQ3E3VLE3NXS · pith_short_16: IQ3E3VLE3NXS2DXM · pith_short_8: IQ3E3VLE

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/IQ3E3VLE3NXS2DXM2TV4JMVKZZ \
  | 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: 44364dd564db6f2d0eecd4ebc4b2aace4904523d80618d247e74f80bdbe638be

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "06dd9c80681e66a15c1890fd87b7fe506667e7bf3220bd6f0a23642cdebf94a3",
    "cross_cats_sorted": [
      "math.GT"
    ],
    "license": "",
    "primary_cat": "math.GR",
    "submitted_at": "2002-09-15T21:39:44Z",
    "title_canon_sha256": "c3815b1b3c56a95e4c4f6b52c2793b58ab2da44fa8a37a99519b480d24d46cfe"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0209185",
    "kind": "arxiv",
    "version": 1
  }
}