Pith Number

pith:2E2ITMWV

pith:2009:2E2ITMWVZY4HHP2DJPSKDXIKMM

not attested not anchored not stored refs pending

Factors of binomial sums from the Catalan triangle

Jiang Zeng, Victor J. W. Guo

arxiv:0909.0307 v2 · 2009-09-02 · 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{2E2ITMWVZY4HHP2DJPSKDXIKMM}

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	2026-05-18T04:26:01.543277Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d13489b2d5ce3873bf434be4a1dd0a633fa0f98a253607bdd3c9505205e30d9a

Aliases

arxiv: 0909.0307 · arxiv_version: 0909.0307v2 · doi: 10.48550/arxiv.0909.0307 · pith_short_12: 2E2ITMWVZY4H · pith_short_16: 2E2ITMWVZY4HHP2D · pith_short_8: 2E2ITMWV

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/2E2ITMWVZY4HHP2DJPSKDXIKMM \
  | 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: d13489b2d5ce3873bf434be4a1dd0a633fa0f98a253607bdd3c9505205e30d9a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b6a7c3fcd31e1ee09c5eb9698734aa9e8a750add127c4b98efcaface41e52338",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2009-09-02T02:23:13Z",
    "title_canon_sha256": "b6aca401ef47350a020e376e685ffb12287e1d2a5632e7d63202b070502ac81e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0909.0307",
    "kind": "arxiv",
    "version": 2
  }
}