Pith Number

pith:QQ6RADVW

pith:2016:QQ6RADVW3OS5GPBR4NSUGXJZNJ

not attested not anchored not stored refs pending

Stolarsky principle and energy optimization on the sphere

Dmitriy Bilyk, Feng Dai, Ryan Matzke

arxiv:1611.04420 v1 · 2016-11-14 · math.CA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{QQ6RADVW3OS5GPBR4NSUGXJZNJ}

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	2026-05-18T00:59:16.693567Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

843d100eb6dba5d33c31e365435d396a74d4b6e8a29d748ec03b869371d06ca0

Aliases

arxiv: 1611.04420 · arxiv_version: 1611.04420v1 · doi: 10.48550/arxiv.1611.04420 · pith_short_12: QQ6RADVW3OS5 · pith_short_16: QQ6RADVW3OS5GPBR · pith_short_8: QQ6RADVW

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/QQ6RADVW3OS5GPBR4NSUGXJZNJ \
  | 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: 843d100eb6dba5d33c31e365435d396a74d4b6e8a29d748ec03b869371d06ca0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c77aa22b29b39f712fc6f7f325aceeef19fd00ffae1da49983005e388bf32592",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2016-11-14T15:39:24Z",
    "title_canon_sha256": "d877d0fc6e5d81dbea360f93dc7d24602cdbb1efe946337af7479c5b492ac474"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1611.04420",
    "kind": "arxiv",
    "version": 1
  }
}