Pith Number

pith:CB2L63E7

pith:2011:CB2L63E7M44OTQ7MEF2HYDEE6Q

not attested not anchored not stored refs pending

Classes of graphs with small rank decompositions are chi-bounded

Daniel Kral, Zdenek Dvorak

arxiv:1107.2161 v1 · 2011-07-11 · 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{CB2L63E7M44OTQ7MEF2HYDEE6Q}

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	2026-05-18T04:18:32.779185Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1074bf6c9f6738e9c3ec21747c0c84f401fb0add8a6aaa5ea1cde9a3d0e2d47e

Aliases

arxiv: 1107.2161 · arxiv_version: 1107.2161v1 · doi: 10.48550/arxiv.1107.2161 · pith_short_12: CB2L63E7M44O · pith_short_16: CB2L63E7M44OTQ7M · pith_short_8: CB2L63E7

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/CB2L63E7M44OTQ7MEF2HYDEE6Q \
  | 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: 1074bf6c9f6738e9c3ec21747c0c84f401fb0add8a6aaa5ea1cde9a3d0e2d47e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f91779a0a7a5810cc7b98b6ed23beb6fcac32f664d9a1008349e52a747be9c6e",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2011-07-11T22:35:14Z",
    "title_canon_sha256": "5b8ae8b1c1c940b8f70beb55d3736994c27cc3eb4f6ed77f5d3c4ea42d3ae63e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1107.2161",
    "kind": "arxiv",
    "version": 1
  }
}