Pith Number

pith:HT6Z7VJT

pith:2009:HT6Z7VJTCPV34AOPL2KBIDWQDT

not attested not anchored not stored refs pending

One level density of low-lying zeros of families of $L$-functions

Liangyi Zhao, Peng Gao

arxiv:0910.5063 v3 · 2009-10-27 · 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{HT6Z7VJTCPV34AOPL2KBIDWQDT}

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	2026-05-17T23:53:19.869409Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3cfd9fd53313ebbe01cf5e94140ed01ce218d25e77bd338f4c1d09fc73fa68bf

Aliases

arxiv: 0910.5063 · arxiv_version: 0910.5063v3 · doi: 10.48550/arxiv.0910.5063 · pith_short_12: HT6Z7VJTCPV3 · pith_short_16: HT6Z7VJTCPV34AOP · pith_short_8: HT6Z7VJT

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/HT6Z7VJTCPV34AOPL2KBIDWQDT \
  | 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: 3cfd9fd53313ebbe01cf5e94140ed01ce218d25e77bd338f4c1d09fc73fa68bf

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d8b6a91aca7612f94bcc21705e9438ea1b7ef4c59d5c51d8e69a8049d9bd0114",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2009-10-27T08:59:45Z",
    "title_canon_sha256": "f01ab41b7ea1a7294acd887a8cbde654952365dd4ff07d5f46f1c38fd87c909f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0910.5063",
    "kind": "arxiv",
    "version": 3
  }
}