Pith Number

pith:AZYJH7YE

pith:2017:AZYJH7YECTIXO2HODJSSBZSFM5

not attested not anchored not stored refs pending

Logarithmic and Riesz Equilibrium for Multiple Sources on the Sphere --- the Exceptional Case

Edward B. Saff, Johann S. Brauchart, Peter D. Dragnev, Robert S. Womersley

arxiv:1706.09346 v1 · 2017-06-28 · math-ph · math.MP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{AZYJH7YECTIXO2HODJSSBZSFM5}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more

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	2026-05-18T00:41:18.914723Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

067093ff0414d17768ee1a6520e6456775b021c8b566cf58196dae36ce3e25e1

Aliases

arxiv: 1706.09346 · arxiv_version: 1706.09346v1 · doi: 10.48550/arxiv.1706.09346 · pith_short_12: AZYJH7YECTIX · pith_short_16: AZYJH7YECTIXO2HO · pith_short_8: AZYJH7YE

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/AZYJH7YECTIXO2HODJSSBZSFM5 \
  | 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: 067093ff0414d17768ee1a6520e6456775b021c8b566cf58196dae36ce3e25e1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "caf12cb1981dbd61ab6f1a9f16e9df281c418661c5a481a14e2ba6109bdca04e",
    "cross_cats_sorted": [
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2017-06-28T16:18:10Z",
    "title_canon_sha256": "2988b4a0955dbe45c0d4f0624d9a07977edd0bb0dcdb3ea3941587660faa87df"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1706.09346",
    "kind": "arxiv",
    "version": 1
  }
}