Pith Number

pith:EXCDU456

pith:2010:EXCDU456BZYUI7V4WQO2PFQKBV

not attested not anchored not stored refs pending

An improved sum-product inequality in fields of prime order

Misha Rudnev

arxiv:1011.2738 v2 · 2010-11-11 · math.CO · math.GR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{EXCDU456BZYUI7V4WQO2PFQKBV}

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	2026-05-18T04:23:47.856586Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

25c43a73be0e71447ebcb41da7960a0d404c773566510277f67206352f986244

Aliases

arxiv: 1011.2738 · arxiv_version: 1011.2738v2 · doi: 10.48550/arxiv.1011.2738 · pith_short_12: EXCDU456BZYU · pith_short_16: EXCDU456BZYUI7V4 · pith_short_8: EXCDU456

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/EXCDU456BZYUI7V4WQO2PFQKBV \
  | 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: 25c43a73be0e71447ebcb41da7960a0d404c773566510277f67206352f986244

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9ac84a8220e89f78647907ed97ccf963a503d052b0d8639daab9c4d3f8dc5a6b",
    "cross_cats_sorted": [
      "math.GR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2010-11-11T19:01:30Z",
    "title_canon_sha256": "c151f8994455820ff62fbc0be663b8d5d30af0e5b34e444faa281e9ab6ba31bb"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1011.2738",
    "kind": "arxiv",
    "version": 2
  }
}