Pith Number

pith:Z6XTVWG6

pith:2001:Z6XTVWG6OGJRWEUEH7NNWRUAY5

not attested not anchored not stored refs pending

Order structure on the algebra of permutations and of planar binary trees

Jean-Louis Loday, Maria O. Ronco

arxiv:math/0102066 v1 · 2001-02-08 · math.CO · math.QA

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{Z6XTVWG6OGJRWEUEH7NNWRUAY5}

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	2026-05-18T01:05:37.950079Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cfaf3ad8de71931b12843fdadb4680c74b76628a5658dbc124a217dde6193d62

Aliases

arxiv: math/0102066 · arxiv_version: math/0102066v1 · doi: 10.48550/arxiv.math/0102066 · pith_short_12: Z6XTVWG6OGJR · pith_short_16: Z6XTVWG6OGJRWEUE · pith_short_8: Z6XTVWG6

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/Z6XTVWG6OGJRWEUEH7NNWRUAY5 \
  | 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: cfaf3ad8de71931b12843fdadb4680c74b76628a5658dbc124a217dde6193d62

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "793a5efd8c58330b45ed2206c3bbdbfdc2e9113e75dc7b72f26b658cd19dd526",
    "cross_cats_sorted": [
      "math.QA"
    ],
    "license": "",
    "primary_cat": "math.CO",
    "submitted_at": "2001-02-08T10:20:19Z",
    "title_canon_sha256": "3ff40010aa4a3e8d91ae3fc7c181556093da172001640047a8be73d7a58ad0a2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0102066",
    "kind": "arxiv",
    "version": 1
  }
}