Pith Number

pith:ZU57SR4Y

pith:2002:ZU57SR4YK42AZWPJEQFDSTNK7P

not attested not anchored not stored refs pending

On the distribution of the order and index of g(mod p) over residue classes

Pieter Moree

arxiv:math/0211259 v3 · 2002-11-17 · 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{ZU57SR4YK42AZWPJEQFDSTNK7P}

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	2026-05-18T01:05:29.240386Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cd3bf9479857340cd9e9240a394daafbfddd98826e53d8ab499f22de08082716

Aliases

arxiv: math/0211259 · arxiv_version: math/0211259v3 · doi: 10.48550/arxiv.math/0211259 · pith_short_12: ZU57SR4YK42A · pith_short_16: ZU57SR4YK42AZWPJ · pith_short_8: ZU57SR4Y

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/ZU57SR4YK42AZWPJEQFDSTNK7P \
  | 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: cd3bf9479857340cd9e9240a394daafbfddd98826e53d8ab499f22de08082716

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8391d78a208ab89cd14289f19cb34fd518fd587c10225c600e09922642b48250",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.NT",
    "submitted_at": "2002-11-17T15:25:10Z",
    "title_canon_sha256": "0ba52989874d37668babe85944c4b35713c38f71da5c8a9f489dd54c0841d2be"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0211259",
    "kind": "arxiv",
    "version": 3
  }
}