Pith Number

pith:KLV3M7XV

pith:2016:KLV3M7XVSHZNQ2OBFWFX7AW2MN

not attested not anchored not stored refs pending

Refining Lagrange's four-square theorem

Zhi-Wei Sun

arxiv:1604.06723 v14 · 2016-04-22 · math.NT

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{KLV3M7XVSHZNQ2OBFWFX7AW2MN}

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	2026-05-18T00:52:50.336849Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

52ebb67ef591f2d869c12d8b7f82da635a2618ddc4c52c4c3c319b3191253562

Aliases

arxiv: 1604.06723 · arxiv_version: 1604.06723v14 · doi: 10.48550/arxiv.1604.06723 · pith_short_12: KLV3M7XVSHZN · pith_short_16: KLV3M7XVSHZNQ2OB · pith_short_8: KLV3M7XV

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/KLV3M7XVSHZNQ2OBFWFX7AW2MN \
  | 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: 52ebb67ef591f2d869c12d8b7f82da635a2618ddc4c52c4c3c319b3191253562

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f0d56e6a123b756f2f935fec50a99e4e7c1d91f722f0d278f55136ff2e7922a1",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2016-04-22T16:00:36Z",
    "title_canon_sha256": "d681946f9327f36f4db80271930daadfcdd6f5437a72dd4140a3380b478453cd"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1604.06723",
    "kind": "arxiv",
    "version": 14
  }
}