Pith Number

pith:XZFJ2BSI

pith:2012:XZFJ2BSISCNNMHW5DIRWZLRDUN

not attested not anchored not stored refs pending

Counting independent sets of a fixed size in graphs with a given minimum degree

David Galvin, John Engbers

arxiv:1204.3060 v1 · 2012-04-13 · 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{XZFJ2BSISCNNMHW5DIRWZLRDUN}

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	2026-05-18T03:57:54.026510Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

be4a9d0648909ad61edd1a236cae23a34c48b9e593980287bbb54c68d6be9fbc

Aliases

arxiv: 1204.3060 · arxiv_version: 1204.3060v1 · doi: 10.48550/arxiv.1204.3060 · pith_short_12: XZFJ2BSISCNN · pith_short_16: XZFJ2BSISCNNMHW5 · pith_short_8: XZFJ2BSI

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/XZFJ2BSISCNNMHW5DIRWZLRDUN \
  | 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: be4a9d0648909ad61edd1a236cae23a34c48b9e593980287bbb54c68d6be9fbc

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "bb11fc53a5091603440e93d28033e471776054086006e2b26a158b162eae1e78",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2012-04-13T17:41:05Z",
    "title_canon_sha256": "801afec93cee58b3326b19e674bcb449ad7e14cda3257119c41001c57dc71706"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1204.3060",
    "kind": "arxiv",
    "version": 1
  }
}