Pith Number

pith:ODYNM4KY

pith:2020:ODYNM4KYDYYL6RD26MD4BBI3RM

not attested not anchored not stored refs pending

The birational Lalanne-Kreweras involution

Michael Joseph, Sam Hopkins

arxiv:2012.15795 v2 · 2020-12-31 · 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{ODYNM4KYDYYL6RD26MD4BBI3RM}

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	2026-07-05T04:27:41.646198Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

70f0d671581e30bf447af307c0851b8b0d6ce958b62b749e8f82055a07f713c0

Aliases

arxiv: 2012.15795 · arxiv_version: 2012.15795v2 · doi: 10.48550/arxiv.2012.15795 · pith_short_12: ODYNM4KYDYYL · pith_short_16: ODYNM4KYDYYL6RD2 · pith_short_8: ODYNM4KY

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/ODYNM4KYDYYL6RD26MD4BBI3RM \
  | 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: 70f0d671581e30bf447af307c0851b8b0d6ce958b62b749e8f82055a07f713c0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "cb3e556bf954d033fc9aace1d01a2d91431d7271f44b8bebe6b9bb446ec6c990",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2020-12-31T18:18:31Z",
    "title_canon_sha256": "364b0802694490d174e3c35ba9b97db15d47e02b0408874531549cd3ecf9e36c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2012.15795",
    "kind": "arxiv",
    "version": 2
  }
}