Pith Number

pith:FOUNN7K7

pith:2005:FOUNN7K7BL5CK7U3FCPK5J4W4N

not attested not anchored not stored refs pending

New bounds for Szemeredi's Theorem, I: Progressions of length 4 in finite field geometries

Ben Green, Terence Tao

arxiv:math/0509560 v3 · 2005-09-23 · 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{FOUNN7K7BL5CK7U3FCPK5J4W4N}

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	2026-05-18T02:57:51.053655Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2ba8d6fd5f0afa257e9b289eaea796e36d5ad64599f16cf5e36707331b2bb61c

Aliases

arxiv: math/0509560 · arxiv_version: math/0509560v3 · doi: 10.48550/arxiv.math/0509560 · pith_short_12: FOUNN7K7BL5C · pith_short_16: FOUNN7K7BL5CK7U3 · pith_short_8: FOUNN7K7

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/FOUNN7K7BL5CK7U3FCPK5J4W4N \
  | 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: 2ba8d6fd5f0afa257e9b289eaea796e36d5ad64599f16cf5e36707331b2bb61c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "128e9021955b094e108879df986a71a84340bee2bf6dcf333852bb9025fcef2f",
    "cross_cats_sorted": [
      "math.NT"
    ],
    "license": "",
    "primary_cat": "math.CO",
    "submitted_at": "2005-09-23T14:59:44Z",
    "title_canon_sha256": "8933eb4377a9e7fc0b4a7721d6ee3ebed9e8936aa6798e8be6c2a7d14ebb24aa"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0509560",
    "kind": "arxiv",
    "version": 3
  }
}