Pith Number

pith:VOINM5QW

pith:2012:VOINM5QWSGSDJWQYRINXKHLD6B

not attested not anchored not stored refs pending

Constructing Carmichael numbers through improved subset-product algorithms

Andrew Shallue, Jon Grantham, Steven Hayman, W.R. Alford

arxiv:1203.6664 v2 · 2012-03-29 · 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{VOINM5QWSGSDJWQYRINXKHLD6B}

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	2026-05-17T23:51:35.099020Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ab90d6761691a434da188a1b751d63f06c5093da4d7ea4f195da3d283ff293e1

Aliases

arxiv: 1203.6664 · arxiv_version: 1203.6664v2 · doi: 10.48550/arxiv.1203.6664 · pith_short_12: VOINM5QWSGSD · pith_short_16: VOINM5QWSGSDJWQY · pith_short_8: VOINM5QW

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/VOINM5QWSGSDJWQYRINXKHLD6B \
  | 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: ab90d6761691a434da188a1b751d63f06c5093da4d7ea4f195da3d283ff293e1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6cee570500f5f08b134c34fbe6812582fee91a7c61d304c2f520d4b65d04a190",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2012-03-29T20:38:28Z",
    "title_canon_sha256": "c60f99fc0ac0ff57752c5f2d275a02424ebbcbc9d104c26cb2d76aa472f7b22c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1203.6664",
    "kind": "arxiv",
    "version": 2
  }
}