Pith Number

pith:7XG4RG4I

pith:1999:7XG4RG4IY2NXYZEDSRD2TNZHIC

not attested not anchored not stored refs pending

Nonvanishing of quadratic Dirichlet L-functions at s=1/2

K. Soundararajan

arxiv:math/9902163 v2 · 1999-02-23 · 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{7XG4RG4IY2NXYZEDSRD2TNZHIC}

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	2026-07-04T15:51:32.907395Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

fdcdc89b88c69b7c64839447a9b7274089da9978bdb8ae35144f95df69c79bcb

Aliases

arxiv: math/9902163 · arxiv_version: math/9902163v2 · doi: 10.48550/arxiv.math/9902163 · pith_short_12: 7XG4RG4IY2NX · pith_short_16: 7XG4RG4IY2NXYZED · pith_short_8: 7XG4RG4I

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/7XG4RG4IY2NXYZEDSRD2TNZHIC \
  | 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: fdcdc89b88c69b7c64839447a9b7274089da9978bdb8ae35144f95df69c79bcb

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "dbc720740d975f2afe2c5d4e89b350746d1096c4f5dd0a6bbe9fb0e8bcfcc9ec",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.NT",
    "submitted_at": "1999-02-23T00:00:00Z",
    "title_canon_sha256": "dc73a10bec77154097cee69c13395b88f3c095dc8be5846c48ddb3ea26b16730"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/9902163",
    "kind": "arxiv",
    "version": 2
  }
}