Pith Number

pith:WU27RB4I

pith:2007:WU27RB4IVK2CN53W46RWYHSCZA

not attested not anchored not stored refs pending

A combinatorial basis for the free Lie algebra of the labelled rooted trees

Muriel Livernet (LAGA), Nantel Bergeron

arxiv:0707.4460 v1 · 2007-07-30 · math.RA · 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{WU27RB4IVK2CN53W46RWYHSCZA}

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	2026-05-18T04:39:59.894729Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b535f88788aab426f776e7a36c1e42c8191510efff4d23442ce35571e6afbf41

Aliases

arxiv: 0707.4460 · arxiv_version: 0707.4460v1 · doi: 10.48550/arxiv.0707.4460 · pith_short_12: WU27RB4IVK2C · pith_short_16: WU27RB4IVK2CN53W · pith_short_8: WU27RB4I

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/WU27RB4IVK2CN53W46RWYHSCZA \
  | 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: b535f88788aab426f776e7a36c1e42c8191510efff4d23442ce35571e6afbf41

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "de2bd86077957462e2bf68d873cdd68cbac85942eafb4f5ecb736b4cf925aefd",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "",
    "primary_cat": "math.RA",
    "submitted_at": "2007-07-30T18:58:03Z",
    "title_canon_sha256": "1064d66c37baa54c34a617191837603673437541994097e19052f05b47f29ed4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0707.4460",
    "kind": "arxiv",
    "version": 1
  }
}