Pith Number

pith:KNUI7UDX

pith:2010:KNUI7UDXTHKRDHSOOC5DISNAT4

not attested not anchored not stored refs pending

Growth of small generating sets in SL_n(Z/pZ)

Harald Andres Helfgott, Nick Gill

arxiv:1002.1605 v2 · 2010-02-08 · math.GR · math.CO · math.NT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{KNUI7UDXTHKRDHSOOC5DISNAT4}

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	2026-05-18T04:41:05.918440Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

53688fd07799d5119e4e70ba3449a09f24211ee47b9097b875f70a27c4d941a5

Aliases

arxiv: 1002.1605 · arxiv_version: 1002.1605v2 · doi: 10.48550/arxiv.1002.1605 · pith_short_12: KNUI7UDXTHKR · pith_short_16: KNUI7UDXTHKRDHSO · pith_short_8: KNUI7UDX

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/KNUI7UDXTHKRDHSOOC5DISNAT4 \
  | 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: 53688fd07799d5119e4e70ba3449a09f24211ee47b9097b875f70a27c4d941a5

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "87843fffedb993259d670ac0a2751f8d2ae3fa907ea46ac0d2389cb3d40d5585",
    "cross_cats_sorted": [
      "math.CO",
      "math.NT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2010-02-08T15:48:28Z",
    "title_canon_sha256": "0db69f00b4a929cc98c18d3be661044006486e6846d3e6d9646f5f4804489c52"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1002.1605",
    "kind": "arxiv",
    "version": 2
  }
}