Pith Number

pith:2KGBUBAY

pith:2012:2KGBUBAYIOK37OHI537GKW53QL

not attested not anchored not stored refs pending

Some 3-adic congruences for binomial sums

Hao Pan, Yong Zhang

arxiv:1203.2823 v1 · 2012-03-13 · 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{2KGBUBAYIOK37OHI537GKW53QL}

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	2026-05-18T04:00:14.463501Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d28c1a04184395bfb8e8eefe655bbb82fba1914dc11715533bd271b70d4aafcd

Aliases

arxiv: 1203.2823 · arxiv_version: 1203.2823v1 · doi: 10.48550/arxiv.1203.2823 · pith_short_12: 2KGBUBAYIOK3 · pith_short_16: 2KGBUBAYIOK37OHI · pith_short_8: 2KGBUBAY

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/2KGBUBAYIOK37OHI537GKW53QL \
  | 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: d28c1a04184395bfb8e8eefe655bbb82fba1914dc11715533bd271b70d4aafcd

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d685bec7e074888cef9f846b9045d1b2a0b7929ad36d5b7d3bbeba52e9186a58",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2012-03-13T14:31:14Z",
    "title_canon_sha256": "f4c3b79d875ccb719d7db2575546c802d78f12a793a90f549cf6e7c2c4a48092"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1203.2823",
    "kind": "arxiv",
    "version": 1
  }
}