Pith Number

pith:GLRWDEIF

pith:2010:GLRWDEIFFQKAPP5W6RJ32HD7X2

not attested not anchored not stored refs pending

Lower Bounds on the van der Waerden Numbers: Randomized- and Deterministic-Constructive

Bernhard Haeupler, William Gasarch

arxiv:1005.3749 v2 · 2010-05-20 · 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{GLRWDEIFFQKAPP5W6RJ32HD7X2}

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	2026-05-18T04:24:53.109565Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

32e36191052c1407bfb6f453bd1c7fbea7b91cb14b6992df9b6a8da5b7351531

Aliases

arxiv: 1005.3749 · arxiv_version: 1005.3749v2 · doi: 10.48550/arxiv.1005.3749 · pith_short_12: GLRWDEIFFQKA · pith_short_16: GLRWDEIFFQKAPP5W · pith_short_8: GLRWDEIF

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/GLRWDEIFFQKAPP5W6RJ32HD7X2 \
  | 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: 32e36191052c1407bfb6f453bd1c7fbea7b91cb14b6992df9b6a8da5b7351531

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "18cbc1612069858d01c247d3a93791871cceb428876248d7c2c798f1656c23f9",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2010-05-20T16:07:04Z",
    "title_canon_sha256": "52e0dbfc470f28bf41b4f4688e7f4a40256032be0e2c863d27868478cb619625"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1005.3749",
    "kind": "arxiv",
    "version": 2
  }
}