Pith Number

pith:X4BBXKFX

pith:2015:X4BBXKFXPMTU6QLVBXWPLHKEOX

not attested not anchored not stored refs pending

The height of multiple edge plane trees

Clemens Heuberger, Helmut Prodinger, Stephan Wagner

arxiv:1503.04749 v1 · 2015-03-16 · 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{X4BBXKFXPMTU6QLVBXWPLHKEOX}

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	2026-05-18T01:14:45.489467Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

bf021ba8b77b274f41750decf59d4475fb4af4d4b29775809fdf7cb492dff2a5

Aliases

arxiv: 1503.04749 · arxiv_version: 1503.04749v1 · doi: 10.48550/arxiv.1503.04749 · pith_short_12: X4BBXKFXPMTU · pith_short_16: X4BBXKFXPMTU6QLV · pith_short_8: X4BBXKFX

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/X4BBXKFXPMTU6QLVBXWPLHKEOX \
  | 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: bf021ba8b77b274f41750decf59d4475fb4af4d4b29775809fdf7cb492dff2a5

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2b4981f3ff39ce5554a6af1dc652f333815bfa07303d184a58f4d9ea1ec64cc2",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2015-03-16T17:52:41Z",
    "title_canon_sha256": "7e7c91570176c302494bcfc6aecb41c3ddbabe599fd4ec48de39963a3a8280db"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1503.04749",
    "kind": "arxiv",
    "version": 1
  }
}