Pith Number

pith:CF7YAI2B

pith:2017:CF7YAI2BC2RC2ZDSV63NW7DGFJ

not attested not anchored not stored refs pending

Bourgain-Chang's proof of the weak Erd\H{o}s-Szemer\'edi conjecture

Dmitrii Zhelezov

arxiv:1710.09316 v1 · 2017-10-25 · 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{CF7YAI2BC2RC2ZDSV63NW7DGFJ}

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	2026-05-18T00:31:59.815384Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

117f80234116a22d6472afb6db7c662a509bf7aba7da1dc200768c9eae42092c

Aliases

arxiv: 1710.09316 · arxiv_version: 1710.09316v1 · doi: 10.48550/arxiv.1710.09316 · pith_short_12: CF7YAI2BC2RC · pith_short_16: CF7YAI2BC2RC2ZDS · pith_short_8: CF7YAI2B

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/CF7YAI2BC2RC2ZDSV63NW7DGFJ \
  | 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: 117f80234116a22d6472afb6db7c662a509bf7aba7da1dc200768c9eae42092c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2d22f95fa2a8132102907437bbeb8875b106f237fbe897faa6084915c532e361",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2017-10-25T15:54:52Z",
    "title_canon_sha256": "da7773bbb71660e12ae6ffdc22f34623ae76d7b61e7fd91557ed72a56674e926"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1710.09316",
    "kind": "arxiv",
    "version": 1
  }
}