Pith Number

pith:WOJ62W6R

pith:2013:WOJ62W6RDKI7HJVRAQS2PAQ3PR

not attested not anchored not stored refs pending

Intersection growth in groups

Francesco Matucci, Ian Biringer, Khalid Bou-Rabee, Martin Kassabov

arxiv:1309.7993 v2 · 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{WOJ62W6RDKI7HJVRAQS2PAQ3PR}

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	2026-05-18T03:05:27.882388Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b393ed5bd11a91f3a6b10425a7821b7c70596a304dd6fbcba9e42bc70290b442

Aliases

arxiv: 1309.7993 · arxiv_version: 1309.7993v2 · doi: 10.48550/arxiv.1309.7993 · pith_short_12: WOJ62W6RDKI7 · pith_short_16: WOJ62W6RDKI7HJVR · pith_short_8: WOJ62W6R

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/WOJ62W6RDKI7HJVRAQS2PAQ3PR \
  | 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: b393ed5bd11a91f3a6b10425a7821b7c70596a304dd6fbcba9e42bc70290b442

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8d72cc0f05a5ca2d4c3fc3e2c3b4c6ff509bb337f799b2d5e63ed0f583178bc1",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2013-09-30T19:55:59Z",
    "title_canon_sha256": "d98940bbd492ffb771543f0e6d117d2bae044fdf956def699bbbfa9913318a5b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1309.7993",
    "kind": "arxiv",
    "version": 2
  }
}