Pith Number

pith:S4HKEY7I

pith:2009:S4HKEY7IRNINXNVAOSIJG7AHPI

not attested not anchored not stored refs pending

An inverse theorem for the Gowers U^4 norm

Ben Green, Tamar Ziegler, Terence Tao

arxiv:0911.5681 v3 · 2009-11-30 · 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{S4HKEY7IRNINXNVAOSIJG7AHPI}

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	2026-05-18T04:05:28.011687Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

970ea263e88b50dbb6a07490937c077a377fc25f265c3a717fb27dd269c0f9cc

Aliases

arxiv: 0911.5681 · arxiv_version: 0911.5681v3 · doi: 10.48550/arxiv.0911.5681 · pith_short_12: S4HKEY7IRNIN · pith_short_16: S4HKEY7IRNINXNVA · pith_short_8: S4HKEY7I

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/S4HKEY7IRNINXNVAOSIJG7AHPI \
  | 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: 970ea263e88b50dbb6a07490937c077a377fc25f265c3a717fb27dd269c0f9cc

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1ec8a33a3c48894dbce306921da8ea47a1a41d0acdc8f3424fd1355e2e3d5ea2",
    "cross_cats_sorted": [
      "math.DS"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2009-11-30T16:12:59Z",
    "title_canon_sha256": "550c6beeca2a282e5669dbf742680f7691496cf6c4bbe081b788165a35cd6df7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0911.5681",
    "kind": "arxiv",
    "version": 3
  }
}