Pith Number

pith:TOVGUDEI

pith:2012:TOVGUDEIT3RVSMFY663UXMZRPO

not attested not anchored not stored refs pending

Supercongruences and Complex Multiplication

Benjamin Sheller, Hao Yuan, Jonas Kibelbek, Kevin Moss, Ling Long

arxiv:1210.4489 v3 · 2012-10-16 · 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{TOVGUDEIT3RVSMFY663UXMZRPO}

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	2026-05-18T03:40:25.197424Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9baa6a0c889ee35930b8f7b74bb3317b8abe25a9c7adf27fc4e6e9115bcfc78b

Aliases

arxiv: 1210.4489 · arxiv_version: 1210.4489v3 · doi: 10.48550/arxiv.1210.4489 · pith_short_12: TOVGUDEIT3RV · pith_short_16: TOVGUDEIT3RVSMFY · pith_short_8: TOVGUDEI

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/TOVGUDEIT3RVSMFY663UXMZRPO \
  | 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: 9baa6a0c889ee35930b8f7b74bb3317b8abe25a9c7adf27fc4e6e9115bcfc78b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "119c6d9885e27d0dcdad8021a85685a3cf9e4d4a11b6777628e038a4e0b0246d",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2012-10-16T16:57:33Z",
    "title_canon_sha256": "f98b8f55fbc830d39be7ed1622e1f2a395ba4fc57f1e5fb563450427c4d16413"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1210.4489",
    "kind": "arxiv",
    "version": 3
  }
}