Pith Number

pith:FODW2WIU

pith:2016:FODW2WIUJ3F46MCZZ45YFGHCCZ

not attested not anchored not stored refs pending

Bounds on the number of conjugacy classes of the symmetric and alternating groups

Bret Benesh, Cong Tuan Son Van

arxiv:1607.06456 v1 · 2016-07-21 · 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{FODW2WIUJ3F46MCZZ45YFGHCCZ}

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	2026-05-18T01:10:41.677144Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2b876d59144ecbcf3059cf3b8298e2164ae062cc0a13c233fa686edc5ae268e5

Aliases

arxiv: 1607.06456 · arxiv_version: 1607.06456v1 · doi: 10.48550/arxiv.1607.06456 · pith_short_12: FODW2WIUJ3F4 · pith_short_16: FODW2WIUJ3F46MCZ · pith_short_8: FODW2WIU

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/FODW2WIUJ3F46MCZZ45YFGHCCZ \
  | 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: 2b876d59144ecbcf3059cf3b8298e2164ae062cc0a13c233fa686edc5ae268e5

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ff092434d523dbcc7d1b002f0b7f9e5e91365b179b5fc9995bb283d61d3adb35",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2016-07-21T18:18:43Z",
    "title_canon_sha256": "2dd89f516382405d5f05bf2fba8dcbe5d2943128a2a8339c5d37bd2e07daf38c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1607.06456",
    "kind": "arxiv",
    "version": 1
  }
}