Pith Number

pith:TUQLURYF

pith:2025:TUQLURYFPZ23J4YRCG2RVRRZGS

not attested not anchored not stored refs pending

Lattice paths and the Geode

Ira M. Gessel

arxiv:2507.09405 v2 · 2025-07-12 · 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{TUQLURYFPZ23J4YRCG2RVRRZGS}

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.

Cited by

1 paper in Pith

Ordered trees and the Geode

Receipt and verification

First computed	2026-07-05T11:39:13.468563Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9d20ba47057e75b4f31111b51ac639349d235d2895e704e7967ad6cade00f001

Aliases

arxiv: 2507.09405 · arxiv_version: 2507.09405v2 · doi: 10.48550/arxiv.2507.09405 · pith_short_12: TUQLURYFPZ23 · pith_short_16: TUQLURYFPZ23J4YR · pith_short_8: TUQLURYF

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/TUQLURYFPZ23J4YRCG2RVRRZGS \
  | 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: 9d20ba47057e75b4f31111b51ac639349d235d2895e704e7967ad6cade00f001

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0e5ec30f85ab71760d7a9a24554821f4091d5b16584c6987375553b6476d2633",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2025-07-12T21:16:49Z",
    "title_canon_sha256": "22d26e6e191d7ed1813b3c3e6553eae52dac6789179a73d110671d280f75ba51"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2507.09405",
    "kind": "arxiv",
    "version": 2
  }
}