Pith Number

pith:LHJ2KZWE

pith:2011:LHJ2KZWEKQZPOF5BAIXBZH7D3Q

not attested not anchored not stored refs pending

Conjectures and results on $x^2$ mod $p^2$ with $4p=x^2+dy^2$

Zhi-Wei Sun

arxiv:1103.4325 v11 · 2011-03-22 · 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{LHJ2KZWEKQZPOF5BAIXBZH7D3Q}

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	2026-05-18T02:58:32.996976Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

59d3a566c45432f717a1022e1c9fe3dc0b5aaedc2588946bb2b2d09b5b97804b

Aliases

arxiv: 1103.4325 · arxiv_version: 1103.4325v11 · doi: 10.48550/arxiv.1103.4325 · pith_short_12: LHJ2KZWEKQZP · pith_short_16: LHJ2KZWEKQZPOF5B · pith_short_8: LHJ2KZWE

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/LHJ2KZWEKQZPOF5BAIXBZH7D3Q \
  | 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: 59d3a566c45432f717a1022e1c9fe3dc0b5aaedc2588946bb2b2d09b5b97804b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8ba6684d74f43ab080478dfe81dcd77b0d29d9f01263af86f076faf5090bfc99",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2011-03-22T17:46:57Z",
    "title_canon_sha256": "b47e23fe938a20203ece134d9212927fe4cda79fd07f5b855a9d3039c60ab2e7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1103.4325",
    "kind": "arxiv",
    "version": 11
  }
}