Pith Number

pith:54JMWZWP

pith:2010:54JMWZWPLHAWTR2DEOPHX5TMQK

not attested not anchored not stored refs pending

The polynomial multidimensional Szemer\'edi Theorem along shifted primes

Bernard Host, Bryna Kra, Nikos Frantzikinakis

arxiv:1009.1484 v2 · 2010-09-08 · math.DS · math.CO · 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{54JMWZWPLHAWTR2DEOPHX5TMQK}

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	2026-05-18T04:15:16.800970Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ef12cb66cf59c169c743239e7bf66c828c26ab5972b49e8803c7a521e4b442b1

Aliases

arxiv: 1009.1484 · arxiv_version: 1009.1484v2 · doi: 10.48550/arxiv.1009.1484 · pith_short_12: 54JMWZWPLHAW · pith_short_16: 54JMWZWPLHAWTR2D · pith_short_8: 54JMWZWP

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/54JMWZWPLHAWTR2DEOPHX5TMQK \
  | 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: ef12cb66cf59c169c743239e7bf66c828c26ab5972b49e8803c7a521e4b442b1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8a841d51d09c1925981fd39de171053a283079cdd44a01e8b578f61687613de2",
    "cross_cats_sorted": [
      "math.CO",
      "math.NT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2010-09-08T09:12:55Z",
    "title_canon_sha256": "6d7ac771807d5273d7ad188ba6f920e756f3c72451770072f07c2088d72efbb4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1009.1484",
    "kind": "arxiv",
    "version": 2
  }
}