Pith Number

pith:ZWU33YYJ

pith:2012:ZWU33YYJQOUEQPWJMCVU6W2YRN

not attested not anchored not stored refs pending

Asymptotic inequalities for positive crank and rank moments

Karl Mahlburg, Kathrin Bringmann

arxiv:1205.2155 v1 · 2012-05-10 · 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{ZWU33YYJQOUEQPWJMCVU6W2YRN}

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	2026-05-18T03:55:56.909860Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cda9bde30983a8483ec960ab4f5b588b7e0c89b6c683500c49278e11c55d0ee5

Aliases

arxiv: 1205.2155 · arxiv_version: 1205.2155v1 · doi: 10.48550/arxiv.1205.2155 · pith_short_12: ZWU33YYJQOUE · pith_short_16: ZWU33YYJQOUEQPWJ · pith_short_8: ZWU33YYJ

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/ZWU33YYJQOUEQPWJMCVU6W2YRN \
  | 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: cda9bde30983a8483ec960ab4f5b588b7e0c89b6c683500c49278e11c55d0ee5

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9019323910535600d8de8ba7bd0ca8af213612cdf90dc224141a4b9745f2c3ae",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2012-05-10T04:11:09Z",
    "title_canon_sha256": "a3cb943ec3f6f406832bd1e83242ead43fe1cb4b4dd24d3007279223366fd00a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1205.2155",
    "kind": "arxiv",
    "version": 1
  }
}