Pith Number

pith:KALM5ECF

pith:2012:KALM5ECFDJGWMRBFMMKDWGTECW

not attested not anchored not stored refs pending

Implicit Divided Differences, Little Schr\"oder Numbers, and Catalan Numbers

Georg Muntingh

arxiv:1204.2709 v2 · 2012-04-12 · math.CO · math.NA

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{KALM5ECFDJGWMRBFMMKDWGTECW}

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	2026-05-18T02:28:13.635499Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5016ce90451a4d66442563143b1a6415bc875a93f7b8487eebf5136c38bc4521

Aliases

arxiv: 1204.2709 · arxiv_version: 1204.2709v2 · doi: 10.48550/arxiv.1204.2709 · pith_short_12: KALM5ECFDJGW · pith_short_16: KALM5ECFDJGWMRBF · pith_short_8: KALM5ECF

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/KALM5ECFDJGWMRBFMMKDWGTECW \
  | 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: 5016ce90451a4d66442563143b1a6415bc875a93f7b8487eebf5136c38bc4521

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7728dd4577bb954e5df140ac18ee6c90fb7bd60c899c93466cee4919b43c4da9",
    "cross_cats_sorted": [
      "math.NA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2012-04-12T13:06:38Z",
    "title_canon_sha256": "23c7f0c8708810fd85a07db826c73ccb358fdd3f9cfed237817cd9d3b04b17d6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1204.2709",
    "kind": "arxiv",
    "version": 2
  }
}