Pith Number

pith:W7K4DU5X

pith:2010:W7K4DU5XUQCGEGD5LX65D4RCCY

not attested not anchored not stored refs pending

On Delannoy numbers and Schr\"oder numbers

Zhi-Wei Sun

arxiv:1009.2486 v4 · 2010-09-13 · math.NT · 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{W7K4DU5XUQCGEGD5LX65D4RCCY}

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	2026-05-18T04:15:04.373061Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b7d5c1d3b7a40462187d5dfdd1f222162a2d86b40f727b5bc7a94241105f652c

Aliases

arxiv: 1009.2486 · arxiv_version: 1009.2486v4 · doi: 10.48550/arxiv.1009.2486 · pith_short_12: W7K4DU5XUQCG · pith_short_16: W7K4DU5XUQCGEGD5 · pith_short_8: W7K4DU5X

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/W7K4DU5XUQCGEGD5LX65D4RCCY \
  | 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: b7d5c1d3b7a40462187d5dfdd1f222162a2d86b40f727b5bc7a94241105f652c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ec0abf01884c77c4297b150cb5bbd30580a7568eb0761984fe70da8dfe272539",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2010-09-13T19:36:16Z",
    "title_canon_sha256": "3643d143ca9b67bdbb43869b34e97e9ffb11120d20c5a2ba8158785d694fa89a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1009.2486",
    "kind": "arxiv",
    "version": 4
  }
}