Pith Number

pith:HA3LUJOJ

pith:2004:HA3LUJOJUMKF3QNEPIKIJXUSXV

not attested not anchored not stored refs pending

On sums of binomial coefficients and their applications

Zhi-Wei Sun

arxiv:math/0404385 v3 · 2004-04-21 · 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{HA3LUJOJUMKF3QNEPIKIJXUSXV}

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	2026-07-04T15:12:50.913019Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3836ba25c9a3145dc1a47a1484de92bd53ccfc6ce14459935aad33f565ee87da

Aliases

arxiv: math/0404385 · arxiv_version: math/0404385v3 · doi: 10.48550/arxiv.math/0404385 · pith_short_12: HA3LUJOJUMKF · pith_short_16: HA3LUJOJUMKF3QNE · pith_short_8: HA3LUJOJ

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/HA3LUJOJUMKF3QNEPIKIJXUSXV \
  | 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: 3836ba25c9a3145dc1a47a1484de92bd53ccfc6ce14459935aad33f565ee87da

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2ffffa1b654a93ecd6add6959be2a139ca616b0a418fc24d8edb63a81594d2a6",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2004-04-21T14:24:55Z",
    "title_canon_sha256": "84acbea8f60ec8a0b4192fa8f60d287d9fd153684c5cfb136a624cdc908a2cc1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0404385",
    "kind": "arxiv",
    "version": 3
  }
}