Pith Number

pith:4WHEZZLV

pith:2016:4WHEZZLVDNYQ6GOUDVEPRKPBE4

not attested not anchored not stored refs pending

Combinatorial differential operators in: Fa\`a di Bruno formula, enumeration of ballot paths, enriched rooted trees and increasing rooted trees

Miguel A. Mendez

arxiv:1610.03602 v1 · 2016-10-12 · 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{4WHEZZLVDNYQ6GOUDVEPRKPBE4}

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	2026-05-18T01:02:29.810668Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e58e4ce5751b710f19d41d48f8a9e1273b939101cb05723641529855aa847f6b

Aliases

arxiv: 1610.03602 · arxiv_version: 1610.03602v1 · doi: 10.48550/arxiv.1610.03602 · pith_short_12: 4WHEZZLVDNYQ · pith_short_16: 4WHEZZLVDNYQ6GOU · pith_short_8: 4WHEZZLV

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/4WHEZZLVDNYQ6GOUDVEPRKPBE4 \
  | 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: e58e4ce5751b710f19d41d48f8a9e1273b939101cb05723641529855aa847f6b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3759aff0c52ffb74ed08aa12406b3b50cf20e1b6b3e2a9b2f320317f1c39bd4f",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2016-10-12T05:21:31Z",
    "title_canon_sha256": "250ef1bb366200b245fa75a45ae02af65da0692baba5c8ca4ce0ff0ee43c29b4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1610.03602",
    "kind": "arxiv",
    "version": 1
  }
}