Pith Number

pith:QNNQRSGU

pith:2026:QNNQRSGUG3G4YF6ISVTLRXKYIL

not attested not anchored not stored refs pending

Extreme values of quadratic Dirichlet $L$-functions with prime-related moduli

Hao Zhang, Shengbo Zhao, Weijia Wang, Zikang Dong

arxiv:2607.25403 v1 · 2026-07-28 · 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{QNNQRSGUG3G4YF6ISVTLRXKYIL}

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	2026-07-29T01:25:13.853294Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

835b08c8d436cdcc17c89566b8dd5842ec10b7b663793cb29ba4f416eddda678

Aliases

arxiv: 2607.25403 · arxiv_version: 2607.25403v1 · doi: 10.48550/arxiv.2607.25403 · pith_short_12: QNNQRSGUG3G4 · pith_short_16: QNNQRSGUG3G4YF6I · pith_short_8: QNNQRSGU

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/QNNQRSGUG3G4YF6ISVTLRXKYIL \
  | 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: 835b08c8d436cdcc17c89566b8dd5842ec10b7b663793cb29ba4f416eddda678

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "43c8aa715bc6786a2fcc6c1d349cc22fd84f83488d15ce840eb5d81544ab9c3a",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2026-07-28T08:01:54Z",
    "title_canon_sha256": "6687ef03fcbc1d4509a77b693489fa53dcf6fe51f74b5a3a721a2cfdfa4af61d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.25403",
    "kind": "arxiv",
    "version": 1
  }
}