Pith Number

pith:3QGMT4PG

pith:2008:3QGMT4PG2WCDS7PFDIO7TWZUNB

not attested not anchored not stored refs pending

On almost universal mixed sums of squares and triangular numbers

Ben Kane, Zhi-Wei Sun

arxiv:0808.2761 v5 · 2008-08-20 · 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{3QGMT4PG2WCDS7PFDIO7TWZUNB}

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	2026-05-18T04:42:12.568835Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

dc0cc9f1e6d584397de51a1df9db3468431b17c2fe4fffd2d8de89077bd2709b

Aliases

arxiv: 0808.2761 · arxiv_version: 0808.2761v5 · doi: 10.48550/arxiv.0808.2761 · pith_short_12: 3QGMT4PG2WCD · pith_short_16: 3QGMT4PG2WCDS7PF · pith_short_8: 3QGMT4PG

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/3QGMT4PG2WCDS7PFDIO7TWZUNB \
  | 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: dc0cc9f1e6d584397de51a1df9db3468431b17c2fe4fffd2d8de89077bd2709b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "de54e62b75eb04cf3824d0442b8dc7de9bcd1785eeef1cdb893196e6e83915f4",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2008-08-20T18:09:12Z",
    "title_canon_sha256": "96c5db93225fd51ae1166ffe6f0310652457924a7bb3aaf8b9a06169009928a9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0808.2761",
    "kind": "arxiv",
    "version": 5
  }
}