Pith Number

pith:D7PCW4FT

pith:2011:D7PCW4FT3GKWOBTTKJ56GXKFR6

not attested not anchored not stored refs pending

On sums related to central binomial and trinomial coefficients

Zhi-Wei Sun

arxiv:1101.0600 v25 · 2011-01-03 · math.NT · math.CA · 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{D7PCW4FT3GKWOBTTKJ56GXKFR6}

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	2026-05-18T02:39:38.479470Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1fde2b70b3d995670673527be35d458fb0e6aa7761211902ce465731726c7248

Aliases

arxiv: 1101.0600 · arxiv_version: 1101.0600v25 · doi: 10.48550/arxiv.1101.0600 · pith_short_12: D7PCW4FT3GKW · pith_short_16: D7PCW4FT3GKWOBTT · pith_short_8: D7PCW4FT

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/D7PCW4FT3GKWOBTTKJ56GXKFR6 \
  | 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: 1fde2b70b3d995670673527be35d458fb0e6aa7761211902ce465731726c7248

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c12f37bc5dbd98f8d607510fdb4728a69af2e0ae9911fbc4111f73e82d6d4053",
    "cross_cats_sorted": [
      "math.CA",
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2011-01-03T20:56:03Z",
    "title_canon_sha256": "0781a4fb7089b7eb3f2ee1230d422f0f31555f5a3318cbb48028ba68ca35e38f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1101.0600",
    "kind": "arxiv",
    "version": 25
  }
}