Pith Number

pith:XFQGUALI

pith:2011:XFQGUALIJ44NIBRBVM3BAOH6EG

not attested not anchored not stored refs pending

Proof of some conjectures of Z.-W. Sun on congruences for Apery polynomials

Jiang Zeng, Victor J. W. Guo

arxiv:1101.0983 v2 · 2011-01-05 · 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{XFQGUALIJ44NIBRBVM3BAOH6EG}

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	2026-05-18T03:56:34.154149Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b9606a01684f38d40621ab361038fe2182ecc495ced6c904ece1d2d3e44f5b80

Aliases

arxiv: 1101.0983 · arxiv_version: 1101.0983v2 · doi: 10.48550/arxiv.1101.0983 · pith_short_12: XFQGUALIJ44N · pith_short_16: XFQGUALIJ44NIBRB · pith_short_8: XFQGUALI

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/XFQGUALIJ44NIBRBVM3BAOH6EG \
  | 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: b9606a01684f38d40621ab361038fe2182ecc495ced6c904ece1d2d3e44f5b80

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9c700d259a096a9c6d1cf22b7890d4ee6d7697eee2f3e120a40c0528894927e7",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2011-01-05T14:14:32Z",
    "title_canon_sha256": "bf65b2cc7e83a931cb5573546c7b15cb8f2b94eeec8825e00deb51edab0eb59b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1101.0983",
    "kind": "arxiv",
    "version": 2
  }
}