Pith Number

pith:74SW7RT2

pith:2019:74SW7RT2VZWWSGCLSUJP5ZI7WV

not attested not anchored not stored refs pending

Optimal measures for p-frame energies on spheres

Alexey Glazyrin, Dmitriy Bilyk, Josiah Park, Oleksandr Vlasiuk, Ryan Matzke

arxiv:1908.00885 v3 · 2019-08-02 · math.MG · math.CA · 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{74SW7RT2VZWWSGCLSUJP5ZI7WV}

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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

Energy on spheres and discreteness of minimizing measures

Receipt and verification

First computed	2026-07-05T03:09:54.166614Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ff256fc67aae6d69184b9512fee51fb56dd5561837db9566b685c47f2ab8e2f2

Aliases

arxiv: 1908.00885 · arxiv_version: 1908.00885v3 · doi: 10.48550/arxiv.1908.00885 · pith_short_12: 74SW7RT2VZWW · pith_short_16: 74SW7RT2VZWWSGCL · pith_short_8: 74SW7RT2

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/74SW7RT2VZWWSGCLSUJP5ZI7WV \
  | 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: ff256fc67aae6d69184b9512fee51fb56dd5561837db9566b685c47f2ab8e2f2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d6073e05b87ca77a6339b03db35b42dae6fb62398162bc5fd285727f1ae60eb9",
    "cross_cats_sorted": [
      "math.CA",
      "math.CO"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.MG",
    "submitted_at": "2019-08-02T14:40:46Z",
    "title_canon_sha256": "7085f51896f94932cb22c828b470db103dae4427180d38bc50f3178d35dbbed3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1908.00885",
    "kind": "arxiv",
    "version": 3
  }
}