Pith Number

pith:VVMU7WHG

pith:2005:VVMU7WHG7GMMWJLNWOQBDI7PWM

not attested not anchored not stored refs pending

Mixed sums of squares and triangular numbers

Zhi-Wei Sun

arxiv:math/0505128 v9 · 2005-05-09 · 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{VVMU7WHG7GMMWJLNWOQBDI7PWM}

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	2026-07-04T14:59:59.227968Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ad594fd8e6f998cb256db3a011a3efb306b7f663d39f59ef82fe1f5ddad2ae1f

Aliases

arxiv: math/0505128 · arxiv_version: math/0505128v9 · doi: 10.48550/arxiv.math/0505128 · pith_short_12: VVMU7WHG7GMM · pith_short_16: VVMU7WHG7GMMWJLN · pith_short_8: VVMU7WHG

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/VVMU7WHG7GMMWJLNWOQBDI7PWM \
  | 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: ad594fd8e6f998cb256db3a011a3efb306b7f663d39f59ef82fe1f5ddad2ae1f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3fe06fb680ff4f300e5cc0b71c93b6935ebdc3c96fe5d89395f8f0274ab5beaa",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "",
    "primary_cat": "math.NT",
    "submitted_at": "2005-05-09T15:54:48Z",
    "title_canon_sha256": "c3dbdb1ab7207a389648b1c1b8941e701e9b2c8518a47b05755267f33d3dfa2a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0505128",
    "kind": "arxiv",
    "version": 9
  }
}