Pith Number

pith:E4GPOIXC

pith:2021:E4GPOIXCJVURZQRQRNEOZDKOYN

not attested not anchored not stored refs pending

Infinite families of crank functions, Stanton-type conjectures, and unimodality

Kathrin Bringmann, Kevin Gomez, Larry Rolen, Zack Tripp

arxiv:2108.12979 v2 · 2021-08-30 · math.NT · math.CO

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{E4GPOIXCJVURZQRQRNEOZDKOYN}

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	2026-07-05T04:07:05.184054Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

270cf722e24d691cc2308b48ec8d4ec361a11f84881603d01244311860cbb905

Aliases

arxiv: 2108.12979 · arxiv_version: 2108.12979v2 · doi: 10.48550/arxiv.2108.12979 · pith_short_12: E4GPOIXCJVUR · pith_short_16: E4GPOIXCJVURZQRQ · pith_short_8: E4GPOIXC

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/E4GPOIXCJVURZQRQRNEOZDKOYN \
  | 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: 270cf722e24d691cc2308b48ec8d4ec361a11f84881603d01244311860cbb905

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4b4599c26699222444f8eae8b16da7a442a2f561a6ab7fae7cc8333f37f51b88",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2021-08-30T03:38:20Z",
    "title_canon_sha256": "4486f0ebaf54380056a01595251b3d5c789aa39e31c99464cc6e1dea96920107"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2108.12979",
    "kind": "arxiv",
    "version": 2
  }
}