Pith Number

pith:YO3PMJJR

pith:2010:YO3PMJJRSSH7XDROK6XCKQ2RPS

not attested not anchored not stored refs pending

Maker Can Construct a Sparse Graph on a Small Board

Heidi Gebauer

arxiv:1011.2178 v2 · 2010-11-09 · math.CO · cs.DM

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{YO3PMJJRSSH7XDROK6XCKQ2RPS}

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	2026-05-18T04:19:54.711979Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c3b6f62531948ffb8e2e57ae2543517c8ca88a0f64585b332afece68c5881d85

Aliases

arxiv: 1011.2178 · arxiv_version: 1011.2178v2 · doi: 10.48550/arxiv.1011.2178 · pith_short_12: YO3PMJJRSSH7 · pith_short_16: YO3PMJJRSSH7XDRO · pith_short_8: YO3PMJJR

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/YO3PMJJRSSH7XDROK6XCKQ2RPS \
  | 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: c3b6f62531948ffb8e2e57ae2543517c8ca88a0f64585b332afece68c5881d85

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2b1a24b51a0f473bff1f4b6c9b53a1148d0ef6067c15d86c9fd641ef47cbadc3",
    "cross_cats_sorted": [
      "cs.DM"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2010-11-09T19:32:10Z",
    "title_canon_sha256": "766b53ba13fd3d4a16686e020d7e8c26aa63151734ccf98d02940940d03322dc"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1011.2178",
    "kind": "arxiv",
    "version": 2
  }
}