Pith Number

pith:IQH47UYV

pith:2009:IQH47UYVPGI4M34PIAG4L2FLCH

not attested not anchored not stored refs pending

On congruences related to central binomial coefficients

Zhi-Wei Sun

arxiv:0911.2415 v16 · 2009-11-12 · 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{IQH47UYVPGI4M34PIAG4L2FLCH}

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	2026-05-18T04:16:30.944208Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

440fcfd3157991c66f8f400dc5e8ab11fe1b000fd59bce64fa3ef7ff028693a9

Aliases

arxiv: 0911.2415 · arxiv_version: 0911.2415v16 · doi: 10.48550/arxiv.0911.2415 · pith_short_12: IQH47UYVPGI4 · pith_short_16: IQH47UYVPGI4M34P · pith_short_8: IQH47UYV

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/IQH47UYVPGI4M34PIAG4L2FLCH \
  | 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: 440fcfd3157991c66f8f400dc5e8ab11fe1b000fd59bce64fa3ef7ff028693a9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "250e99b5e142bfc9f4add04c388a230d48913229a02f4d4a40a13312102eaa60",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2009-11-12T19:15:58Z",
    "title_canon_sha256": "8e3778115d41665cc2c44bf0d353329615bb7a6ef8fdff376f20d5dbed5b4f74"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0911.2415",
    "kind": "arxiv",
    "version": 16
  }
}