Pith Number

pith:IWQ2ZFO4

pith:2021:IWQ2ZFO4TG7VEOMA4Z2KZROKVR

not attested not anchored not stored refs pending

The Sharp Erd\H{o}s-Tur\'an Inequality

Jiuya Wang, Ruiwen Shu

arxiv:2109.11006 v2 · 2021-09-22 · math.CA · 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{IWQ2ZFO4TG7VEOMA4Z2KZROKVR}

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.

Cited by

1 paper in Pith

Data Generation without Function Estimation

Receipt and verification

First computed	2026-07-05T03:23:14.399752Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

45a1ac95dc99bf523980e674acc5caac5032ef543dc8ff0183544d935167e5a3

Aliases

arxiv: 2109.11006 · arxiv_version: 2109.11006v2 · doi: 10.48550/arxiv.2109.11006 · pith_short_12: IWQ2ZFO4TG7V · pith_short_16: IWQ2ZFO4TG7VEOMA · pith_short_8: IWQ2ZFO4

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/IWQ2ZFO4TG7VEOMA4Z2KZROKVR \
  | 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: 45a1ac95dc99bf523980e674acc5caac5032ef543dc8ff0183544d935167e5a3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "05e5b5f86a16434c236b065ceb8dd7fbc358e595333c1fb7f08c32fd24465016",
    "cross_cats_sorted": [
      "math.NT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2021-09-22T19:55:08Z",
    "title_canon_sha256": "04ebbe03ed5d920872bd713f5787582da02b98789ef664288b85fa50148e2e8d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2109.11006",
    "kind": "arxiv",
    "version": 2
  }
}