Pith Number

pith:IGUZVMLQ

pith:2018:IGUZVMLQCQ5KPNI4TDUN6L5ZI2

not attested not anchored not stored refs pending

Divisibility of some binomial sums

Hao Pan, He-Xia Ni

arxiv:1808.03213 v1 · 2018-08-09 · 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{IGUZVMLQCQ5KPNI4TDUN6L5ZI2}

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	2026-05-18T00:08:29.888345Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

41a99ab170143aa7b51c98e8df2fb946949e8d5e7ffb5ab3e17d1034f62c6618

Aliases

arxiv: 1808.03213 · arxiv_version: 1808.03213v1 · doi: 10.48550/arxiv.1808.03213 · pith_short_12: IGUZVMLQCQ5K · pith_short_16: IGUZVMLQCQ5KPNI4 · pith_short_8: IGUZVMLQ

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/IGUZVMLQCQ5KPNI4TDUN6L5ZI2 \
  | 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: 41a99ab170143aa7b51c98e8df2fb946949e8d5e7ffb5ab3e17d1034f62c6618

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "65fbb1b97d3d38ec3ed1f07b0e7972342ab21b2a72a1fd3666679c642584a772",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2018-08-09T15:59:17Z",
    "title_canon_sha256": "58b94c328938e0ae8553ec51266edd6ee88736e412661162c2aff88c3e13fb32"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1808.03213",
    "kind": "arxiv",
    "version": 1
  }
}