Pith Number

pith:CAGDC2AF

pith:2009:CAGDC2AFPYSRFKJAZTUOMARRKA

not attested not anchored not stored refs pending

On a non-abelian Balog-Szemeredi-type lemma

Tom Sanders

arxiv:0912.0306 v2 · 2009-12-02 · 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{CAGDC2AFPYSRFKJAZTUOMARRKA}

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	2026-05-18T04:39:19.599424Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

100c3168057e2512a920cce8e602315027dad05e563b133210ad3c4bc50f949e

Aliases

arxiv: 0912.0306 · arxiv_version: 0912.0306v2 · doi: 10.48550/arxiv.0912.0306 · pith_short_12: CAGDC2AFPYSR · pith_short_16: CAGDC2AFPYSRFKJA · pith_short_8: CAGDC2AF

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/CAGDC2AFPYSRFKJAZTUOMARRKA \
  | 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: 100c3168057e2512a920cce8e602315027dad05e563b133210ad3c4bc50f949e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "254ca45679335ecf1d57a447953ee76cacddf193fb2bf23448860e26a6143662",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2009-12-02T00:15:48Z",
    "title_canon_sha256": "8a8b0a2c2bcb2239476bd0eed47d2f3fba195c4a7efdb28ac3d0d4c3cd283deb"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0912.0306",
    "kind": "arxiv",
    "version": 2
  }
}