Pith Number

pith:T4ZW52N2

pith:2013:T4ZW52N22QLWHUA572TY6ZBOZ6

not attested not anchored not stored refs pending

On groups with slow intersection growth

Francesco Matucci, Martin Kassabov

arxiv:1309.7903 v1 · 2013-09-30 · 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{T4ZW52N22QLWHUA572TY6ZBOZ6}

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	2026-05-18T03:11:47.867608Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9f336ee9bad41763d01dfea78f642ecf8f506f3521c6230c7e85217b2d988144

Aliases

arxiv: 1309.7903 · arxiv_version: 1309.7903v1 · doi: 10.48550/arxiv.1309.7903 · pith_short_12: T4ZW52N22QLW · pith_short_16: T4ZW52N22QLWHUA5 · pith_short_8: T4ZW52N2

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/T4ZW52N22QLWHUA572TY6ZBOZ6 \
  | 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: 9f336ee9bad41763d01dfea78f642ecf8f506f3521c6230c7e85217b2d988144

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "746541a34f3d5b681f6c45f891f1718de5c72820a0775d41befbf3b702cf0d0b",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2013-09-30T16:04:51Z",
    "title_canon_sha256": "f1cf8409fcff820c1bebb8ade5162133138bf33f03539eb0a61e4696d03ddc0f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1309.7903",
    "kind": "arxiv",
    "version": 1
  }
}