Pith Number

pith:T36WM5DG

pith:2017:T36WM5DG4XGLQTKIWT4PHZGPDT

not attested not anchored not stored refs pending

An involution on Dyck paths that preserves the rise composition and interchanges the number of returns and the position of the first double fall

Martin Rubey

arxiv:1701.07009 v1 · 2017-01-24 · 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{T36WM5DG4XGLQTKIWT4PHZGPDT}

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	2026-05-18T00:52:09.894125Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9efd667466e5ccb84d48b4f8f3e4cf1cda00b25727635891ff38023dd9bd5153

Aliases

arxiv: 1701.07009 · arxiv_version: 1701.07009v1 · doi: 10.48550/arxiv.1701.07009 · pith_short_12: T36WM5DG4XGL · pith_short_16: T36WM5DG4XGLQTKI · pith_short_8: T36WM5DG

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/T36WM5DG4XGLQTKIWT4PHZGPDT \
  | 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: 9efd667466e5ccb84d48b4f8f3e4cf1cda00b25727635891ff38023dd9bd5153

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c1a4d99968c2b3d5152e47b68656d0363ed30f5cef32c7ceddf5886c573b31f4",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2017-01-24T18:47:32Z",
    "title_canon_sha256": "ca042e44875df542cc068f9e01abbbe69d8a27992a45df2fc9897dcb8b18a45e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1701.07009",
    "kind": "arxiv",
    "version": 1
  }
}