Pith Number

pith:LSS4ENGE

pith:2026:LSS4ENGEAJYDX2LJP76IBWR2NS

not attested not anchored not stored refs pending

Every Nonnegative Integer Is a Sum of a Triangular, a Pentagonal, and a Heptagonal Number

Dakai Guo, Ruichen Qiu, Ruyong Feng, Xiao-Shan Gao, Yichuan Cao

arxiv:2606.26035 v1 · 2026-06-24 · math.NT · cs.SC

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{LSS4ENGEAJYDX2LJP76IBWR2NS}

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	2026-06-25T01:18:46.433552Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5ca5c234c402703be9697ffc80da3a6c8970e34dec2733620227b51321775b6b

Aliases

arxiv: 2606.26035 · arxiv_version: 2606.26035v1 · doi: 10.48550/arxiv.2606.26035 · pith_short_12: LSS4ENGEAJYD · pith_short_16: LSS4ENGEAJYDX2LJ · pith_short_8: LSS4ENGE

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/LSS4ENGEAJYDX2LJP76IBWR2NS \
  | 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: 5ca5c234c402703be9697ffc80da3a6c8970e34dec2733620227b51321775b6b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a987762e6d5ced10233119453925624dd6c73b23747fe71da9be48b5d2e3cbdb",
    "cross_cats_sorted": [
      "cs.SC"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2026-06-24T17:11:12Z",
    "title_canon_sha256": "81174f25b1121de515b7fb5fe8de881e5a404359ed072b94fbea19343a94f4b6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.26035",
    "kind": "arxiv",
    "version": 1
  }
}