Pith Number

pith:BWGMIPLM

pith:2012:BWGMIPLM6QTP6QKB27CNR4EMWU

not attested not anchored not stored refs pending

ABC implies primitive prime divisors in arithmetic dynamic

Chad Gratton, Khoa Nguyen, Thomas J. Tucker

arxiv:1208.2989 v1 · 2012-08-14 · 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{BWGMIPLM6QTP6QKB27CNR4EMWU}

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	2026-05-18T02:57:53.317017Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0d8cc43d6cf426ff4141d7c4d8f08cb5196a1b6872ac7ea91c8b55eb9f7cea60

Aliases

arxiv: 1208.2989 · arxiv_version: 1208.2989v1 · doi: 10.48550/arxiv.1208.2989 · pith_short_12: BWGMIPLM6QTP · pith_short_16: BWGMIPLM6QTP6QKB · pith_short_8: BWGMIPLM

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/BWGMIPLM6QTP6QKB27CNR4EMWU \
  | 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: 0d8cc43d6cf426ff4141d7c4d8f08cb5196a1b6872ac7ea91c8b55eb9f7cea60

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b59e19616e532e9f5c2da3dd55c2ece1b58e070f8021ed5a157b4b54e4b6b4ba",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2012-08-14T22:53:16Z",
    "title_canon_sha256": "e79037b5d8115d2ced74db57f3d3b8eade7758124bb40800338a755786282255"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1208.2989",
    "kind": "arxiv",
    "version": 1
  }
}