Pith Number

pith:K3UMD6CF

pith:2004:K3UMD6CFBVVYJJCPJ3KIF3YQE6

not attested not anchored not stored refs pending

The primes contain arbitrarily long arithmetic progressions

Ben Green, Terence Tao

arxiv:math/0404188 v6 · 2004-04-08 · math.NT · math.DS

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{K3UMD6CFBVVYJJCPJ3KIF3YQE6}

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.

Cited by

1 paper in Pith

Computational relative entropy

Receipt and verification

First computed	2026-07-04T15:04:24.542794Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

56e8c1f8450d6b84a44f4ed482ef1027b44789af35009b9ce128cbb458c23244

Aliases

arxiv: math/0404188 · arxiv_version: math/0404188v6 · doi: 10.48550/arxiv.math/0404188 · pith_short_12: K3UMD6CFBVVY · pith_short_16: K3UMD6CFBVVYJJCP · pith_short_8: K3UMD6CF

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/K3UMD6CFBVVYJJCPJ3KIF3YQE6 \
  | 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: 56e8c1f8450d6b84a44f4ed482ef1027b44789af35009b9ce128cbb458c23244

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0da9014dd3d274c64f60124d81436a0608201bba17db8c97426b8852b101f943",
    "cross_cats_sorted": [
      "math.DS"
    ],
    "license": "",
    "primary_cat": "math.NT",
    "submitted_at": "2004-04-08T16:48:41Z",
    "title_canon_sha256": "fd67bb7a2c70cc61e99d9cbccfd32e4efc849c0a2552226eeef6f2e92ef470d0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0404188",
    "kind": "arxiv",
    "version": 6
  }
}