Pith Number

pith:WMXUB645

pith:2010:WMXUB645YYYKCC3NPE3KAAKS2I

not attested not anchored not stored refs pending

A point of view on Gowers uniformity norms

Bernard Host, Bryna Kra

arxiv:1010.0414 v2 · 2010-10-03 · math.CO · 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{WMXUB645YYYKCC3NPE3KAAKS2I}

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	2026-05-18T02:23:47.624960Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b32f40fb9dc630a10b6d7936a00152d22c5cef5177dd90bdfb9fe4007a1d7ccb

Aliases

arxiv: 1010.0414 · arxiv_version: 1010.0414v2 · doi: 10.48550/arxiv.1010.0414 · pith_short_12: WMXUB645YYYK · pith_short_16: WMXUB645YYYKCC3N · pith_short_8: WMXUB645

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/WMXUB645YYYKCC3NPE3KAAKS2I \
  | 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: b32f40fb9dc630a10b6d7936a00152d22c5cef5177dd90bdfb9fe4007a1d7ccb

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "08967c1b5603c0ca1a3244c9344ca580b70a8e40b0fe826c99769fbd817ff346",
    "cross_cats_sorted": [
      "math.DS"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2010-10-03T15:17:40Z",
    "title_canon_sha256": "ccd8902b22e3126cb1fe9f70cb6248453366d2b78f207f5b252eb3d3857a7155"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1010.0414",
    "kind": "arxiv",
    "version": 2
  }
}