Pith Number

pith:CARWF66U

pith:2010:CARWF66UFQOJAY7FQ2PC2SAHBS

not attested not anchored not stored refs pending

Factors of sums and alternating sums involving binomial coefficients and powers of integers

Jiang Zeng, Victor J. W. Guo

arxiv:1008.3316 v2 · 2010-08-19 · 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{CARWF66UFQOJAY7FQ2PC2SAHBS}

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	2026-05-18T03:58:24.932753Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

102362fbd42c1c9063e5869e2d48070caccde2c81582a9d85136d701b84c52e4

Aliases

arxiv: 1008.3316 · arxiv_version: 1008.3316v2 · doi: 10.48550/arxiv.1008.3316 · pith_short_12: CARWF66UFQOJ · pith_short_16: CARWF66UFQOJAY7F · pith_short_8: CARWF66U

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/CARWF66UFQOJAY7FQ2PC2SAHBS \
  | 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: 102362fbd42c1c9063e5869e2d48070caccde2c81582a9d85136d701b84c52e4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b63c9fed3a78dffb379c40dd8468324990859f258e94d54cbff8dc91fbc8271b",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2010-08-19T14:53:25Z",
    "title_canon_sha256": "29b3eb68f4e64dd147d8a943dbed59d3622e533a7c2abbcf30f7c4d661edd987"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1008.3316",
    "kind": "arxiv",
    "version": 2
  }
}