Pith Number

pith:4XOLAUTR

pith:2012:4XOLAUTRKQIS55A334NQKNKPKB

not attested not anchored not stored refs pending

On Newton-Raphson iteration for multiplicative inverses modulo prime powers

Jean-Guillaume Dumas (CASYS)

arxiv:1209.6626 v5 · 2012-09-28 · cs.SC · cs.MS

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{4XOLAUTRKQIS55A334NQKNKPKB}

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	2026-05-17T23:48:12.544852Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e5dcb0527154112ef41bdf1b05354f5058fce1a24aebcce30340c6ab47140ad9

Aliases

arxiv: 1209.6626 · arxiv_version: 1209.6626v5 · doi: 10.48550/arxiv.1209.6626 · pith_short_12: 4XOLAUTRKQIS · pith_short_16: 4XOLAUTRKQIS55A3 · pith_short_8: 4XOLAUTR

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/4XOLAUTRKQIS55A334NQKNKPKB \
  | 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: e5dcb0527154112ef41bdf1b05354f5058fce1a24aebcce30340c6ab47140ad9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8650ffd221a80eb3864593aeba2503a28c8cddefebccec40da25fd238993ebc6",
    "cross_cats_sorted": [
      "cs.MS"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.SC",
    "submitted_at": "2012-09-28T19:52:06Z",
    "title_canon_sha256": "def752a8727025676f67e6c40dc45061804a2758b973030c245ece076c296f2e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1209.6626",
    "kind": "arxiv",
    "version": 5
  }
}