Pith Number

pith:AZNIMSQ5

pith:2022:AZNIMSQ5UUF5VBR5PL7JNCMD2Z

not attested not anchored not stored refs pending

Averages of long Dirichlet polynomials with modular coefficients

Alessandro Fazzari, Brian Conrey

arxiv:2207.12989 v2 · 2022-07-26 · 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{AZNIMSQ5UUF5VBR5PL7JNCMD2Z}

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	2026-07-05T06:25:37.761480Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

065a864a1da50bda863d7afe968983d67c4dbf450bf6ce623317ce5455e0f4aa

Aliases

arxiv: 2207.12989 · arxiv_version: 2207.12989v2 · doi: 10.48550/arxiv.2207.12989 · pith_short_12: AZNIMSQ5UUF5 · pith_short_16: AZNIMSQ5UUF5VBR5 · pith_short_8: AZNIMSQ5

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/AZNIMSQ5UUF5VBR5PL7JNCMD2Z \
  | 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: 065a864a1da50bda863d7afe968983d67c4dbf450bf6ce623317ce5455e0f4aa

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b03ba97f5d01ebbfb866863d23069a65c447ed9af893b3bafb474b9bf8523b21",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2022-07-26T15:49:22Z",
    "title_canon_sha256": "e961dec2a4c7f39b6617d96b170fc9a6f0d4f0f504c8a47d01c48ea0fdd23093"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2207.12989",
    "kind": "arxiv",
    "version": 2
  }
}