Pith Number

pith:WQ34WBCG

pith:2010:WQ34WBCGZBIXZE3GORL7476IB5

not attested not anchored not stored refs pending

Sum-product estimates for rational functions

Boris Bukh, Jacob Tsimerman

arxiv:1002.2554 v2 · 2010-02-12 · math.CO · math.AG · 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{WQ34WBCGZBIXZE3GORL7476IB5}

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	2026-05-18T02:58:02.384496Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b437cb0446c8517c93667457fe7fc80f7a917b33117a17436eb222cd5fc11d14

Aliases

arxiv: 1002.2554 · arxiv_version: 1002.2554v2 · doi: 10.48550/arxiv.1002.2554 · pith_short_12: WQ34WBCGZBIX · pith_short_16: WQ34WBCGZBIXZE3G · pith_short_8: WQ34WBCG

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/WQ34WBCGZBIXZE3GORL7476IB5 \
  | 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: b437cb0446c8517c93667457fe7fc80f7a917b33117a17436eb222cd5fc11d14

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8ca8858588a21a249a0b2a1484bcba29fe6e1d7c86c37984fc88d0c95b0873ca",
    "cross_cats_sorted": [
      "math.AG",
      "math.NT"
    ],
    "license": "http://creativecommons.org/licenses/by/3.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2010-02-12T14:13:20Z",
    "title_canon_sha256": "211e2d78c98d7eb6e848829a85a27bf95fe7fe212b6b1f398dece7559aedd822"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1002.2554",
    "kind": "arxiv",
    "version": 2
  }
}