Pith Number

pith:L5I4NULE

pith:2005:L5I4NULEJIQHA4ATT37K3UPWAX

not attested not anchored not stored refs pending

Sieving by large integers and covering systems of congruences

Carl Pomerance, Gang Yu, Kevin Ford, Michael Filaseta, Sergei Konyagin

arxiv:math/0507374 v3 · 2005-07-18 · 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{L5I4NULEJIQHA4ATT37K3UPWAX}

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	2026-07-04T14:59:20.336770Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5f51c6d1644a207070139efeadd1f605ee365397f5c0d099140e59327c983f3d

Aliases

arxiv: math/0507374 · arxiv_version: math/0507374v3 · doi: 10.48550/arxiv.math/0507374 · pith_short_12: L5I4NULEJIQH · pith_short_16: L5I4NULEJIQHA4AT · pith_short_8: L5I4NULE

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/L5I4NULEJIQHA4ATT37K3UPWAX \
  | 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: 5f51c6d1644a207070139efeadd1f605ee365397f5c0d099140e59327c983f3d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "022306ea86c2c61bac1a15ac47a7a199de936db9dcc1083a329fe9dae92469f0",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.NT",
    "submitted_at": "2005-07-18T22:09:34Z",
    "title_canon_sha256": "2fb3ed95e71d3144432983c5ee3fb841618d5f01609c0b2f1650ac86fb6ee249"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0507374",
    "kind": "arxiv",
    "version": 3
  }
}