Pith Number

pith:I3X6EY2A

pith:2011:I3X6EY2AMT2QYOHZDXYOWAUQ2M

not attested not anchored not stored refs pending

On the enumeration of labelled hypertrees and of labelled bipartite trees

Roland Bacher (IF)

arxiv:1102.2708 v1 · 2011-02-14 · 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{I3X6EY2AMT2QYOHZDXYOWAUQ2M}

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	2026-05-18T04:28:46.667679Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

46efe2634064f50c38f91df0eb0290d32108a4ba7e58a56d21d8a6e2176285f2

Aliases

arxiv: 1102.2708 · arxiv_version: 1102.2708v1 · doi: 10.48550/arxiv.1102.2708 · pith_short_12: I3X6EY2AMT2Q · pith_short_16: I3X6EY2AMT2QYOHZ · pith_short_8: I3X6EY2A

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/I3X6EY2AMT2QYOHZDXYOWAUQ2M \
  | 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: 46efe2634064f50c38f91df0eb0290d32108a4ba7e58a56d21d8a6e2176285f2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3ab45655e2400d14504d3e7f99b420bb7c5893457e7b95c43424a584798cfaa1",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2011-02-14T09:26:58Z",
    "title_canon_sha256": "f35f254ae8db575e322373bbf577eb9a055f6a1254271a908fddf5548a71b94b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1102.2708",
    "kind": "arxiv",
    "version": 1
  }
}