Pith Number

pith:BPB7SFMG

pith:2008:BPB7SFMGAMGBBL7STDMSQ3EFXO

not attested not anchored not stored refs pending

The Riesz energy of the $N$-th roots of unity: an asymptotic expansion for large $N$

D. P. Hardin, E. B. Saff, J. S. Brauchart

arxiv:0808.1291 v3 · 2008-08-08 · 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{BPB7SFMGAMGBBL7STDMSQ3EFXO}

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

A discrete approach to Dirichlet L-functions, their special values and zeros

Receipt and verification

First computed	2026-05-18T04:09:53.858381Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0bc3f91586030c10aff298d9286c85bba8d2554a8bcdf82a07c3d2fb73934ddc

Aliases

arxiv: 0808.1291 · arxiv_version: 0808.1291v3 · doi: 10.48550/arxiv.0808.1291 · pith_short_12: BPB7SFMGAMGB · pith_short_16: BPB7SFMGAMGBBL7S · pith_short_8: BPB7SFMG

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/BPB7SFMGAMGBBL7STDMSQ3EFXO \
  | 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: 0bc3f91586030c10aff298d9286c85bba8d2554a8bcdf82a07c3d2fb73934ddc

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e3a68b242d7553a9bf6e5f56a5de8438ea79f4c1bd78f012e83c3558310e2a76",
    "cross_cats_sorted": [
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2008-08-08T20:15:02Z",
    "title_canon_sha256": "00b93618016a9cc627de66372d90743febeae6810282588ce359d3b113bad737"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0808.1291",
    "kind": "arxiv",
    "version": 3
  }
}