Pith Number

pith:LL6OBZN5

pith:2018:LL6OBZN55CXKDNJXCWCSRDYODK

not attested not anchored not stored refs pending

Primes $p \equiv 1 \bmod{d}$ and $a^{(p-1)/d} \equiv 1 \bmod{p}$}

Liangyi Zhao, Peng Gao

arxiv:1807.09410 v3 · 2018-07-25 · 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{LL6OBZN55CXKDNJXCWCSRDYODK}

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	2026-05-17T23:43:56.590141Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5afce0e5bde8aea1b5371585288f0e1a98e3b8791a0153f527be3f0f8010111c

Aliases

arxiv: 1807.09410 · arxiv_version: 1807.09410v3 · doi: 10.48550/arxiv.1807.09410 · pith_short_12: LL6OBZN55CXK · pith_short_16: LL6OBZN55CXKDNJX · pith_short_8: LL6OBZN5

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/LL6OBZN55CXKDNJXCWCSRDYODK \
  | 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: 5afce0e5bde8aea1b5371585288f0e1a98e3b8791a0153f527be3f0f8010111c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9fa6104dd4d2a16e348bc154380471b3db097ed1ffb46e4c1b0bc23fb9dfbf28",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2018-07-25T01:46:23Z",
    "title_canon_sha256": "7c215d95fb5d23fb4ca28c7e81e0f3c0ab0b09435843b588a43f0f16530dee65"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1807.09410",
    "kind": "arxiv",
    "version": 3
  }
}