Pith Number

pith:7BJ7OAOJ

pith:2010:7BJ7OAOJ77AXCNSNGRZD53W6GX

not attested not anchored not stored refs pending

Ranking and unranking trees with a given number or a given set of leaves

Jeffrey B. Remmel, S. Gill Williamson

arxiv:1009.2060 v1 · 2010-09-10 · 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{7BJ7OAOJ77AXCNSNGRZD53W6GX}

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	2026-05-18T04:41:05.517129Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f853f701c9ffc171364d34723eeede35c4f140eb99811ebc917cf3e8e3591edf

Aliases

arxiv: 1009.2060 · arxiv_version: 1009.2060v1 · doi: 10.48550/arxiv.1009.2060 · pith_short_12: 7BJ7OAOJ77AX · pith_short_16: 7BJ7OAOJ77AXCNSN · pith_short_8: 7BJ7OAOJ

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/7BJ7OAOJ77AXCNSNGRZD53W6GX \
  | 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: f853f701c9ffc171364d34723eeede35c4f140eb99811ebc917cf3e8e3591edf

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "741bf44bb66402e8e3904ab3b08b74909e15d636e96f3c651f6a17a6af25294a",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2010-09-10T17:16:11Z",
    "title_canon_sha256": "3385681766058c1464a617aab57ddc0227049db34443cfb8d68cbb90a619947a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1009.2060",
    "kind": "arxiv",
    "version": 1
  }
}