Pith Number

pith:Q4J5OBN2

pith:2010:Q4J5OBN2GQVP7EYSAQNIWD64SN

not attested not anchored not stored refs pending

Simple closed curves, word length, and nilpotent quotients of free groups

Asaf Hadari, Khalid Bou Rabee

arxiv:1009.0332 v1 · 2010-09-02 · math.GT · 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{Q4J5OBN2GQVP7EYSAQNIWD64SN}

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	2026-05-18T03:40:25.901967Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8713d705ba342aff9312041a8b0fdc93492fb9ecfd13b240deb244b427dd8ee7

Aliases

arxiv: 1009.0332 · arxiv_version: 1009.0332v1 · doi: 10.48550/arxiv.1009.0332 · pith_short_12: Q4J5OBN2GQVP · pith_short_16: Q4J5OBN2GQVP7EYS · pith_short_8: Q4J5OBN2

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/Q4J5OBN2GQVP7EYSAQNIWD64SN \
  | 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: 8713d705ba342aff9312041a8b0fdc93492fb9ecfd13b240deb244b427dd8ee7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "36b967aac7649ba09a8e99e153e05f6903876d654e9e6dd5dfdf0a241ba9d8b3",
    "cross_cats_sorted": [
      "math.GR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2010-09-02T05:50:24Z",
    "title_canon_sha256": "a7d378fd9fc38eed354a1e5cbbde4fc4dfba510f05595544874a379d3ef8d7ad"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1009.0332",
    "kind": "arxiv",
    "version": 1
  }
}