Pith Number

pith:6PNLIYIW

pith:2011:6PNLIYIWTD3V4RMAARPXFAXJ5M

not attested not anchored not stored refs pending

Explicit formulas for the Riesz energy of the $N$th roots of unity

J. S. Brauchart

arxiv:1105.5530 v2 · 2011-05-27 · math-ph · math.MP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{6PNLIYIWTD3V4RMAARPXFAXJ5M}

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	2026-05-18T02:38:26.913224Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f3dab4611698f75e4580045f7282e9eb053760e80d6dc0988a8ea5f504c7cc91

Aliases

arxiv: 1105.5530 · arxiv_version: 1105.5530v2 · doi: 10.48550/arxiv.1105.5530 · pith_short_12: 6PNLIYIWTD3V · pith_short_16: 6PNLIYIWTD3V4RMA · pith_short_8: 6PNLIYIW

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/6PNLIYIWTD3V4RMAARPXFAXJ5M \
  | 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: f3dab4611698f75e4580045f7282e9eb053760e80d6dc0988a8ea5f504c7cc91

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c63fd968ba6411f7e6fe15a25324e9ed1b9f75782574084f1b65533a335ab5d9",
    "cross_cats_sorted": [
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2011-05-27T11:27:02Z",
    "title_canon_sha256": "f4c866778f558a644d507e10321e90c15886e3a8ec4f78a8ddf93fce9c18a7cb"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1105.5530",
    "kind": "arxiv",
    "version": 2
  }
}