Pith Number

pith:UGROGXTQ

pith:2012:UGROGXTQ7KX7OX42SZEI3LQIJ5

not attested not anchored not stored refs pending

Counting smaller trees in the Tamari order

Gregory Chatel, Viviane Pons

arxiv:1212.0751 v1 · 2012-12-04 · 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{UGROGXTQ7KX7OX42SZEI3LQIJ5}

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	2026-05-18T03:39:15.332044Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a1a2e35e70faaff75f9a96488dae084f5e82087e5fb27d7e0be1aa2b08a2b784

Aliases

arxiv: 1212.0751 · arxiv_version: 1212.0751v1 · doi: 10.48550/arxiv.1212.0751 · pith_short_12: UGROGXTQ7KX7 · pith_short_16: UGROGXTQ7KX7OX42 · pith_short_8: UGROGXTQ

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/UGROGXTQ7KX7OX42SZEI3LQIJ5 \
  | 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: a1a2e35e70faaff75f9a96488dae084f5e82087e5fb27d7e0be1aa2b08a2b784

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "23e20ef8a2266975b966f9ef57da85c07629e67c68238b6966a65db3516d7285",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2012-12-04T15:09:14Z",
    "title_canon_sha256": "9525a43f9dda6514cf3f4ba6a31e1c8a585eed404191825e66c68b7b8efe8933"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1212.0751",
    "kind": "arxiv",
    "version": 1
  }
}