Pith Number

pith:KGNMZ3MH

pith:2009:KGNMZ3MHBSQM67XKLZR2HAVNPY

not attested not anchored not stored refs pending

Asymptotics for rank and crank moments

K. Bringmann, K. Mahlburg, R. Rhoades

arxiv:0903.1297 v1 · 2009-03-06 · 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{KGNMZ3MHBSQM67XKLZR2HAVNPY}

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	2026-05-18T02:58:03.419338Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

519acced870ca0cf7eea5e63a382ad7e07360189264d6589628172378d80beed

Aliases

arxiv: 0903.1297 · arxiv_version: 0903.1297v1 · doi: 10.48550/arxiv.0903.1297 · pith_short_12: KGNMZ3MHBSQM · pith_short_16: KGNMZ3MHBSQM67XK · pith_short_8: KGNMZ3MH

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/KGNMZ3MHBSQM67XKLZR2HAVNPY \
  | 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: 519acced870ca0cf7eea5e63a382ad7e07360189264d6589628172378d80beed

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "142cf151b33c88e9bb132c1d2969bbbf565307eb8f0f6afccb07c5391c11aaf1",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2009-03-06T21:28:46Z",
    "title_canon_sha256": "c412cb754ed1d40958a4dfa853518724ced33fcb28d35183063c70551c73bd31"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0903.1297",
    "kind": "arxiv",
    "version": 1
  }
}