Pith Number

pith:M3UWGDBW

pith:2011:M3UWGDBWHNDZXEUDWE3ZVJNMI6

not attested not anchored not stored refs pending

Formulae for the number of partitions of n into at most m parts (using the quasi-polynomial ansatz)

Andrew V. Sills, Doron Zeilberger

arxiv:1108.4391 v2 · 2011-08-22 · math.CO · 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{M3UWGDBWHNDZXEUDWE3ZVJNMI6}

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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	2026-05-17T23:59:18.392622Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

66e9630c363b479b9283b1379aa5ac47929339d82a0c00088fd2abcaa5f7be7a

Aliases

arxiv: 1108.4391 · arxiv_version: 1108.4391v2 · doi: 10.48550/arxiv.1108.4391 · pith_short_12: M3UWGDBWHNDZ · pith_short_16: M3UWGDBWHNDZXEUD · pith_short_8: M3UWGDBW

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/M3UWGDBWHNDZXEUDWE3ZVJNMI6 \
  | 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: 66e9630c363b479b9283b1379aa5ac47929339d82a0c00088fd2abcaa5f7be7a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b22e2aa6bdc7ea9e112bac87c67c5b20e0ed05c2cabb7fac4b4b9c4b0009122b",
    "cross_cats_sorted": [
      "math.NT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2011-08-22T17:57:43Z",
    "title_canon_sha256": "697cea33ad16461107079a406de288e258d8508be1dca51b80b86691771b7226"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1108.4391",
    "kind": "arxiv",
    "version": 2
  }
}