Pith Number

pith:W5YTA554

pith:2011:W5YTA554H5YMWHDMNEOSKVY2V6

not attested not anchored not stored refs pending

On a problem of Chen and Liu concerning the prime power factorization of $n!$

Johannes F. Morgenbesser, T. Stoll

arxiv:1110.4814 v1 · 2011-10-21 · 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{W5YTA554H5YMWHDMNEOSKVY2V6}

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	2026-05-18T04:10:34.961062Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b7713077bc3f70cb1c6c691d25571aafba4f90dfab65a438e84415b203124877

Aliases

arxiv: 1110.4814 · arxiv_version: 1110.4814v1 · doi: 10.48550/arxiv.1110.4814 · pith_short_12: W5YTA554H5YM · pith_short_16: W5YTA554H5YMWHDM · pith_short_8: W5YTA554

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/W5YTA554H5YMWHDMNEOSKVY2V6 \
  | 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: b7713077bc3f70cb1c6c691d25571aafba4f90dfab65a438e84415b203124877

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c2cf67148e961858254505aa9e8ed8572994fa9cfcf68040c116ddcc5ac1214e",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2011-10-21T15:03:45Z",
    "title_canon_sha256": "cb7cde700d5b246a8149944df5f087539a6709fe69bc54a476ade78560125b5a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1110.4814",
    "kind": "arxiv",
    "version": 1
  }
}