Pith Number

pith:3QPKJOB5

pith:2013:3QPKJOB5PIIGVS4QWXBDGX4AAV

not attested not anchored not stored refs pending

A log-free zero-density estimate and small gaps in coefficients of $L$-functions

Amir Akbary, Timothy S. Trudgian

arxiv:1312.5820 v2 · 2013-12-20 · 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{3QPKJOB5PIIGVS4QWXBDGX4AAV}

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	2026-05-18T02:54:46.620560Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

dc1ea4b83d7a106acb90b5c2335f80057f2404046769064cdce615f1a77bd2c8

Aliases

arxiv: 1312.5820 · arxiv_version: 1312.5820v2 · doi: 10.48550/arxiv.1312.5820 · pith_short_12: 3QPKJOB5PIIG · pith_short_16: 3QPKJOB5PIIGVS4Q · pith_short_8: 3QPKJOB5

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/3QPKJOB5PIIGVS4QWXBDGX4AAV \
  | 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: dc1ea4b83d7a106acb90b5c2335f80057f2404046769064cdce615f1a77bd2c8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a58414768ed15657d51d212f6dc06d49e896f878f4b048201fe14250a09b5a00",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2013-12-20T06:25:45Z",
    "title_canon_sha256": "9419a9e6475073bc864830b53be61bbe4035b12f63bf0a5443bfbe2cfe4254d0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1312.5820",
    "kind": "arxiv",
    "version": 2
  }
}