Pith Number

pith:IH2BQ33U

pith:2009:IH2BQ33UDXHEHJOGSOW2A3NECN

not attested not anchored not stored refs pending

Slightly improved sum-product estimates in fields of prime order

Liangpan Li

arxiv:0907.2051 v1 · 2009-07-12 · math.NT · math.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{IH2BQ33UDXHEHJOGSOW2A3NECN}

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	2026-07-04T15:46:06.367242Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

41f4186f741dce43a5c693ada06da413735e79e110e6ecfc0be1b494603a4fa2

Aliases

arxiv: 0907.2051 · arxiv_version: 0907.2051v1 · doi: 10.48550/arxiv.0907.2051 · pith_short_12: IH2BQ33UDXHE · pith_short_16: IH2BQ33UDXHEHJOG · pith_short_8: IH2BQ33U

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/IH2BQ33UDXHEHJOGSOW2A3NECN \
  | 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: 41f4186f741dce43a5c693ada06da413735e79e110e6ecfc0be1b494603a4fa2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7641161f0c7fb1e5155e14010e8e1bd731e556ec048e69c24981db32d50b6af0",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2009-07-12T19:28:58Z",
    "title_canon_sha256": "51a793c3261cc79a1b14be89e0a94103238486b24ee2827756343dad844bd390"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0907.2051",
    "kind": "arxiv",
    "version": 1
  }
}