Pith Number

pith:N5IS2ZEW

pith:2010:N5IS2ZEW5WHFBCWF2ZHCXAT2GG

not attested not anchored not stored refs pending

An O(M(n) log n) algorithm for the Jacobi symbol

Paul Zimmermann, Richard P. Brent

arxiv:1004.2091 v2 · 2010-04-13 · cs.DS · 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{N5IS2ZEW5WHFBCWF2ZHCXAT2GG}

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	2026-05-18T04:34:46.096171Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6f512d6496ed8e508ac5d64e2b827a31972260a7dd3db2099d2227d14b4b050a

Aliases

arxiv: 1004.2091 · arxiv_version: 1004.2091v2 · doi: 10.48550/arxiv.1004.2091 · pith_short_12: N5IS2ZEW5WHF · pith_short_16: N5IS2ZEW5WHFBCWF · pith_short_8: N5IS2ZEW

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/N5IS2ZEW5WHFBCWF2ZHCXAT2GG \
  | 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: 6f512d6496ed8e508ac5d64e2b827a31972260a7dd3db2099d2227d14b4b050a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "27d90764c85d94648af4cc1f0cdc46417b69eff62585fd08530b1fd10eacd800",
    "cross_cats_sorted": [
      "math.NT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.DS",
    "submitted_at": "2010-04-13T02:15:09Z",
    "title_canon_sha256": "be9830a4beec14b8a52680e75027a1a17074b65d21c2301115f2509901e7014e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1004.2091",
    "kind": "arxiv",
    "version": 2
  }
}