Pith Number

pith:CLUFQRSP

pith:2014:CLUFQRSPBEA2E5YM3WOUJO5IVW

not attested not anchored not stored refs pending

Best possible densities of Dickson m-tuples, as a consequence of Zhang-Maynard-Tao

Andrew Granville, Daniel M. Kane, Dimitris Koukoulopoulos, Robert J. Lemke Oliver

arxiv:1410.8198 v2 · 2014-10-29 · math.NT · math.CO

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{CLUFQRSPBEA2E5YM3WOUJO5IVW}

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	2026-05-18T00:42:44.661423Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

12e858464f0901a2770cdd9d44bba8adbc5e46555380fbe620b861f201402dc6

Aliases

arxiv: 1410.8198 · arxiv_version: 1410.8198v2 · doi: 10.48550/arxiv.1410.8198 · pith_short_12: CLUFQRSPBEA2 · pith_short_16: CLUFQRSPBEA2E5YM · pith_short_8: CLUFQRSP

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/CLUFQRSPBEA2E5YM3WOUJO5IVW \
  | 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: 12e858464f0901a2770cdd9d44bba8adbc5e46555380fbe620b861f201402dc6

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "cc1f0eeb64022f94956855217fa728d886a436392414b21d82c6f000454e0c9d",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2014-10-29T23:36:14Z",
    "title_canon_sha256": "9d86e2497043f88b8adae9f052f534f9cc5ffd9959f92ede8a9b642d5dfbcf73"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1410.8198",
    "kind": "arxiv",
    "version": 2
  }
}