Pith Number

pith:PXWWKC4U

pith:2010:PXWWKC4U5CW2YNCP7BWEIWU6LX

not attested not anchored not stored refs pending

The shifted primes and the multidimensional Szemeredi and polynomial van der Waerden theorems

Alexander Leibman, Tamar Ziegler, Vitaly Bergelson

arxiv:1007.1839 v2 · 2010-07-12 · math.DS · 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{PXWWKC4U5CW2YNCP7BWEIWU6LX}

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	2026-05-18T04:05:27.845993Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7ded650b94e8adac344ff86c445a9e5deca8fe6d4775e855796a6d2b67cbc022

Aliases

arxiv: 1007.1839 · arxiv_version: 1007.1839v2 · doi: 10.48550/arxiv.1007.1839 · pith_short_12: PXWWKC4U5CW2 · pith_short_16: PXWWKC4U5CW2YNCP · pith_short_8: PXWWKC4U

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/PXWWKC4U5CW2YNCP7BWEIWU6LX \
  | 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: 7ded650b94e8adac344ff86c445a9e5deca8fe6d4775e855796a6d2b67cbc022

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a413290bb5b3fa71b4fe433e3cf1628509035df8649ae0e2fe55dc10cb535710",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2010-07-12T08:03:55Z",
    "title_canon_sha256": "9d7e5479ae335b34b015a487dbc0c36f204f47f9f6fa0ecb90310738d6723ece"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1007.1839",
    "kind": "arxiv",
    "version": 2
  }
}