Pith Number

pith:YZ2VIS4Q

pith:2015:YZ2VIS4QMRQG72OEMXI23H2YHT

not attested not anchored not stored refs pending

Divisibility of binomial coefficients and generation of alternating groups

John Shareshian, Russ Woodroofe

arxiv:1505.05143 v3 · 2015-05-19 · math.CO · math.GR · 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{YZ2VIS4QMRQG72OEMXI23H2YHT}

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	2026-05-18T00:32:21.722904Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c675544b9064606fe9c465d1ad9f583cf78a51dedfbe5d2a4530b2f4d34875f1

Aliases

arxiv: 1505.05143 · arxiv_version: 1505.05143v3 · doi: 10.48550/arxiv.1505.05143 · pith_short_12: YZ2VIS4QMRQG · pith_short_16: YZ2VIS4QMRQG72OE · pith_short_8: YZ2VIS4Q

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/YZ2VIS4QMRQG72OEMXI23H2YHT \
  | 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: c675544b9064606fe9c465d1ad9f583cf78a51dedfbe5d2a4530b2f4d34875f1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8d4aaedad037d5399487c1924fb2f268ac866c207f59798ec2d9429e2828332a",
    "cross_cats_sorted": [
      "math.GR",
      "math.NT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2015-05-19T20:00:26Z",
    "title_canon_sha256": "be855c84972914a2ddb1ea23afce1ff7a09d3d9684e765d8d4042119e014644c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1505.05143",
    "kind": "arxiv",
    "version": 3
  }
}