Pith Number

pith:ZPYZGG6F

pith:2026:ZPYZGG6FWBMV3NUHMVESPFJ3ZP

not attested not anchored not stored refs pending

Three-color van der Waerden numbers grow super-exponentially

Jacob Fox, Zach Hunter

arxiv:2606.02541 v1 · 2026-06-01 · math.CO · 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{ZPYZGG6FWBMV3NUHMVESPFJ3ZP}

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	2026-06-02T03:05:09.013906Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cbf1931bc5b0595db687654927953bcbe1376f381f9c31b64c19beabe038e260

Aliases

arxiv: 2606.02541 · arxiv_version: 2606.02541v1 · doi: 10.48550/arxiv.2606.02541 · pith_short_12: ZPYZGG6FWBMV · pith_short_16: ZPYZGG6FWBMV3NUH · pith_short_8: ZPYZGG6F

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/ZPYZGG6FWBMV3NUHMVESPFJ3ZP \
  | 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: cbf1931bc5b0595db687654927953bcbe1376f381f9c31b64c19beabe038e260

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "14d833b41b73c04bbb56afec97a7be2971946ca6aa0ff28ca1090db8c812bd60",
    "cross_cats_sorted": [
      "math.NT"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2026-06-01T17:45:49Z",
    "title_canon_sha256": "bef6b5c8b386c925391c653c43f6c3fb8a7184bf6e6aa483b011845064c7a7eb"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.02541",
    "kind": "arxiv",
    "version": 1
  }
}