Pith Number

pith:XZ73GW5V

pith:2010:XZ73GW5VZ6GVGHDOYT27HGLHST

not attested not anchored not stored refs pending

Growth in solvable subgroups of GL_r(Z/pZ)

Harald Andres Helfgott, Nick Gill

arxiv:1008.5264 v3 · 2010-08-31 · math.GR · math.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{XZ73GW5VZ6GVGHDOYT27HGLHST}

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	2026-05-18T03:13:46.650199Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

be7fb35bb5cf8d531c6ec4f5f3996794fa95683891e7ac4d9080b3c429a06119

Aliases

arxiv: 1008.5264 · arxiv_version: 1008.5264v3 · doi: 10.48550/arxiv.1008.5264 · pith_short_12: XZ73GW5VZ6GV · pith_short_16: XZ73GW5VZ6GVGHDO · pith_short_8: XZ73GW5V

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/XZ73GW5VZ6GVGHDOYT27HGLHST \
  | 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: be7fb35bb5cf8d531c6ec4f5f3996794fa95683891e7ac4d9080b3c429a06119

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "66f59226f46fdc2acc755393545fee751602cb886c4791b3cc8e815a4e09818d",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2010-08-31T09:27:41Z",
    "title_canon_sha256": "30aa79bc1ed46e1ea00929733a92eb841f4bcd8db2b3f08da7dde113db2c85cf"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1008.5264",
    "kind": "arxiv",
    "version": 3
  }
}