Pith Number

pith:KJY37BQP

pith:2010:KJY37BQPWDZAXAO6YNPH5ADZAY

not attested not anchored not stored refs pending

Exact Ramsey Theory: Green-Tao numbers and SAT

Oliver Kullmann

arxiv:1004.0653 v2 · 2010-04-05 · cs.DM · cs.DS

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{KJY37BQPWDZAXAO6YNPH5ADZAY}

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	2026-05-18T04:19:22.320331Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5271bf860fb0f20b81dec35e7e8079061f8f2c18387dfb5fe1b8ba9fdcc8ae7f

Aliases

arxiv: 1004.0653 · arxiv_version: 1004.0653v2 · doi: 10.48550/arxiv.1004.0653 · pith_short_12: KJY37BQPWDZA · pith_short_16: KJY37BQPWDZAXAO6 · pith_short_8: KJY37BQP

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/KJY37BQPWDZAXAO6YNPH5ADZAY \
  | 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: 5271bf860fb0f20b81dec35e7e8079061f8f2c18387dfb5fe1b8ba9fdcc8ae7f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2b9012d0e1a286c3965b133b28d3be11fdb3a9b9a655fa6c0aa7043332bfdf3c",
    "cross_cats_sorted": [
      "cs.DS"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.DM",
    "submitted_at": "2010-04-05T16:14:31Z",
    "title_canon_sha256": "8a41799bd9543731915e84e40776f69a5cef479ca144ae21429adae421a2ffd2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1004.0653",
    "kind": "arxiv",
    "version": 2
  }
}