Pith Number

pith:JXIR4EZH

pith:2012:JXIR4EZHBVRMRYAOCDGJM3D25F

not attested not anchored not stored refs pending

Infinitely Many Carmichael Numbers in Arithmetic Progressions

Thomas Wright

arxiv:1212.5850 v1 · 2012-12-24 · 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{JXIR4EZHBVRMRYAOCDGJM3D25F}

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	2026-05-18T02:57:53.128539Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4dd11e13270d62c8e00e10cc966c7ae94e89b044ab48f9b2bfb1088ed5f0d302

Aliases

arxiv: 1212.5850 · arxiv_version: 1212.5850v1 · doi: 10.48550/arxiv.1212.5850 · pith_short_12: JXIR4EZHBVRM · pith_short_16: JXIR4EZHBVRMRYAO · pith_short_8: JXIR4EZH

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/JXIR4EZHBVRMRYAOCDGJM3D25F \
  | 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: 4dd11e13270d62c8e00e10cc966c7ae94e89b044ab48f9b2bfb1088ed5f0d302

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "cb9c93753939f87a8fa7f0d1e89e20ac9e1643ff209de1ea2bfe31694943bd70",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2012-12-24T01:05:36Z",
    "title_canon_sha256": "b5add9e119e7c42042c90b57e6d2e44fb4bcc54770992efa247506776cbf8855"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1212.5850",
    "kind": "arxiv",
    "version": 1
  }
}