Pith Number

pith:Y5PGUPRH

pith:2022:Y5PGUPRHK655LZRZBWAH7U24LX

not attested not anchored not stored refs pending

Absolute Minima of Potentials of a Certain Class of Spherical Designs

Sergiy Borodachov

arxiv:2212.04594 v1 · 2022-12-08 · math.CO · math.OC

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{Y5PGUPRHK655LZRZBWAH7U24LX}

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.

Cited by

1 paper in Pith

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

Receipt and verification

First computed	2026-07-05T05:23:49.455454Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c75e6a3e2757bbd5e6390d807fd35c5dfadafc4d0a5e067d37446907a7faabb0

Aliases

arxiv: 2212.04594 · arxiv_version: 2212.04594v1 · doi: 10.48550/arxiv.2212.04594 · pith_short_12: Y5PGUPRHK655 · pith_short_16: Y5PGUPRHK655LZRZ · pith_short_8: Y5PGUPRH

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/Y5PGUPRHK655LZRZBWAH7U24LX \
  | 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: c75e6a3e2757bbd5e6390d807fd35c5dfadafc4d0a5e067d37446907a7faabb0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "74700f10129c407fdc5f80fb8142fd8d9b02ddb0231fda085021541bd332c617",
    "cross_cats_sorted": [
      "math.OC"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2022-12-08T22:54:27Z",
    "title_canon_sha256": "11bbc14a0ec0d61dab857ea848cef51600afda9d861b66ec76bd9b4188725c7f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2212.04594",
    "kind": "arxiv",
    "version": 1
  }
}