Pith Number

pith:OPTEFAM7

pith:2025:OPTEFAM7CPAD3Z3DGHB3EBWHVK

not attested not anchored not stored refs pending

Existence and nonexistence of spherical $5$-designs of minimal type

Sho Suda, Wei-Hsuan Yu, Zili Xu

arxiv:2508.18685 v1 · 2025-08-26 · 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{OPTEFAM7CPAD3Z3DGHB3EBWHVK}

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	2026-07-05T11:59:29.261669Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

73e642819f13c03de76331c3b206c7aaa58e59c69b0aba8d88fbb35d85cfe962

Aliases

arxiv: 2508.18685 · arxiv_version: 2508.18685v1 · doi: 10.48550/arxiv.2508.18685 · pith_short_12: OPTEFAM7CPAD · pith_short_16: OPTEFAM7CPAD3Z3D · pith_short_8: OPTEFAM7

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/OPTEFAM7CPAD3Z3DGHB3EBWHVK \
  | 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: 73e642819f13c03de76331c3b206c7aaa58e59c69b0aba8d88fbb35d85cfe962

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "51fb3bb9db4bbfecd09303512b0c0c1416f027fa94609a62cc48ae5f1a9bdb34",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2025-08-26T05:17:05Z",
    "title_canon_sha256": "9cfea42f7019bfd2299065cab1014b78654fe73a3b651248cfcf8502eb48f748"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2508.18685",
    "kind": "arxiv",
    "version": 1
  }
}