Pith Number

pith:YZ7ZWTXQ

pith:2011:YZ7ZWTXQK2UHHRIXTRKFDNR43D

not attested not anchored not stored refs pending

Primes in Tuples IV: Density of small gaps between consecutive primes

C. Y. Yildirim, D. A. Goldston, J. Pintz

arxiv:1103.5886 v1 · 2011-03-30 · 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{YZ7ZWTXQK2UHHRIXTRKFDNR43D}

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	2026-05-18T04:25:27.307117Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c67f9b4ef056a873c5179c5451b63cd8f9132d3d22fe5bca0a93b6232387888c

Aliases

arxiv: 1103.5886 · arxiv_version: 1103.5886v1 · doi: 10.48550/arxiv.1103.5886 · pith_short_12: YZ7ZWTXQK2UH · pith_short_16: YZ7ZWTXQK2UHHRIX · pith_short_8: YZ7ZWTXQ

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/YZ7ZWTXQK2UHHRIXTRKFDNR43D \
  | 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: c67f9b4ef056a873c5179c5451b63cd8f9132d3d22fe5bca0a93b6232387888c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4a4601e43a1bfd23f5b19fa9db06a8201b533ef755001856fb30b868dc926737",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2011-03-30T11:53:24Z",
    "title_canon_sha256": "aab7fde69cdca0247ce1ec46c8d1db4a9401414ebcc1d6e9b453a9885a7938f4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1103.5886",
    "kind": "arxiv",
    "version": 1
  }
}