Pith Number

pith:L7FO4HD7

pith:2009:L7FO4HD7XFQW363YXKGECJLASV

not attested not anchored not stored refs pending

On representation of an integer as a sum by X^2+Y^2+Z^2 and the modular equations of degree 3 and 5

Alexander Berkovich

arxiv:0907.1725 v4 · 2009-07-10 · 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{L7FO4HD7XFQW363YXKGECJLASV}

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	2026-05-18T03:51:48.954684Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5fcaee1c7fb9616dfb78ba8c412560956e58546e24a9a7c1b0840e2d5a996885

Aliases

arxiv: 0907.1725 · arxiv_version: 0907.1725v4 · doi: 10.48550/arxiv.0907.1725 · pith_short_12: L7FO4HD7XFQW · pith_short_16: L7FO4HD7XFQW363Y · pith_short_8: L7FO4HD7

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/L7FO4HD7XFQW363YXKGECJLASV \
  | 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: 5fcaee1c7fb9616dfb78ba8c412560956e58546e24a9a7c1b0840e2d5a996885

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "671e5603e8f272fa0cde50c23b403f099928bc9a1830067a39c00f86f26e60ae",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2009-07-10T05:09:16Z",
    "title_canon_sha256": "318219f0cbf2763d5ee30e4b8572ba92b7cd894015afcefc2a737d62cafb965c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0907.1725",
    "kind": "arxiv",
    "version": 4
  }
}