Pith Number

pith:QQJNKOKD

pith:2010:QQJNKOKDUWZZELHLZXX2TASLBE

not attested not anchored not stored refs pending

The first non-vanishing quadratic twist of an automorphic L-series

Alex Kontorovich, Jeff Hoffstein

arxiv:1008.0839 v1 · 2010-08-04 · 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{QQJNKOKDUWZZELHLZXX2TASLBE}

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	2026-05-18T04:42:35.523680Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8412d53943a5b3922cebcdefa9824b092fdd5a13221c727f4969b8fbec103620

Aliases

arxiv: 1008.0839 · arxiv_version: 1008.0839v1 · doi: 10.48550/arxiv.1008.0839 · pith_short_12: QQJNKOKDUWZZ · pith_short_16: QQJNKOKDUWZZELHL · pith_short_8: QQJNKOKD

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/QQJNKOKDUWZZELHLZXX2TASLBE \
  | 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: 8412d53943a5b3922cebcdefa9824b092fdd5a13221c727f4969b8fbec103620

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a6151a1182c939e1b4ae9870980fe8a859723343f1b3e359fee8fc4b14630803",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2010-08-04T18:37:45Z",
    "title_canon_sha256": "b79545b3d68b86262214be3fc5db9a55812592b7f0d32adec93e18a4c63bab12"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1008.0839",
    "kind": "arxiv",
    "version": 1
  }
}