Pith Number

pith:KHO4I3IB

pith:2016:KHO4I3IBOQNAR52HQHXDZAQQRE

not attested not anchored not stored refs pending

$k$-protected vertices in unlabeled rooted plane trees

Keith Copenhaver

arxiv:1606.00083 v3 · 2016-06-01 · 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{KHO4I3IBOQNAR52HQHXDZAQQRE}

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.

Cited by

1 paper in Pith

Nonleaf Patterns in Trees: Protected Nodes and Fine Numbers

Receipt and verification

First computed	2026-05-18T01:11:43.447481Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

51ddc46d01741a08f74781ee3c8210892647169530d5fd85026b7a9902996ccd

Aliases

arxiv: 1606.00083 · arxiv_version: 1606.00083v3 · doi: 10.48550/arxiv.1606.00083 · pith_short_12: KHO4I3IBOQNA · pith_short_16: KHO4I3IBOQNAR52H · pith_short_8: KHO4I3IB

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/KHO4I3IBOQNAR52HQHXDZAQQRE \
  | 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: 51ddc46d01741a08f74781ee3c8210892647169530d5fd85026b7a9902996ccd

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ba4933513872011d587914afc7e0ef1dffc2ef7c4aab7ddd06dae9c16d743e14",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2016-06-01T00:50:32Z",
    "title_canon_sha256": "3b06d9710e49511587fdeb84087fff7a32d2143898bbc45fb6144e9e411e0cce"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1606.00083",
    "kind": "arxiv",
    "version": 3
  }
}