Pith Number

pith:TWSUYTUR

pith:2019:TWSUYTURTE4FNJMSY4QAIQGZK3

not attested not anchored not stored refs pending

Hook-length formula and applications to alternating permutations

Lucas Randazzo

arxiv:1904.08374 v1 · 2019-04-17 · 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{TWSUYTURTE4FNJMSY4QAIQGZK3}

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	2026-05-17T23:48:17.888477Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9da54c4e91993856a592c7200440d956e13479bc60c0d789f4644ba2179d52de

Aliases

arxiv: 1904.08374 · arxiv_version: 1904.08374v1 · doi: 10.48550/arxiv.1904.08374 · pith_short_12: TWSUYTURTE4F · pith_short_16: TWSUYTURTE4FNJMS · pith_short_8: TWSUYTUR

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/TWSUYTURTE4FNJMSY4QAIQGZK3 \
  | 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: 9da54c4e91993856a592c7200440d956e13479bc60c0d789f4644ba2179d52de

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0652027beb483cd2368c214ef4f467f78938b5a36338da3f71df03e81530b563",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2019-04-17T17:18:53Z",
    "title_canon_sha256": "f683327853edccf74ff21b5716488d5dc44941bea9a62dcae942926871a3e709"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1904.08374",
    "kind": "arxiv",
    "version": 1
  }
}