Pith Number

pith:VVO4EYXG

pith:2015:VVO4EYXG7CCWOMW6IHJHPVMIWP

not attested not anchored not stored refs pending

Relation between spherical designs through a Hopf map

Takayuki Okuda

arxiv:1506.08414 v1 · 2015-06-28 · math.MG · 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{VVO4EYXG7CCWOMW6IHJHPVMIWP}

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	2026-05-18T01:37:45.379221Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ad5dc262e6f8856732de41d277d588b3e33b5083d21aff3933e957721e4aa7e5

Aliases

arxiv: 1506.08414 · arxiv_version: 1506.08414v1 · doi: 10.48550/arxiv.1506.08414 · pith_short_12: VVO4EYXG7CCW · pith_short_16: VVO4EYXG7CCWOMW6 · pith_short_8: VVO4EYXG

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/VVO4EYXG7CCWOMW6IHJHPVMIWP \
  | 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: ad5dc262e6f8856732de41d277d588b3e33b5083d21aff3933e957721e4aa7e5

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4b88f62540f4a337f36d62a75a77c17e0b2834b6b74ac2688598e747ed7dc297",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.MG",
    "submitted_at": "2015-06-28T15:28:02Z",
    "title_canon_sha256": "cfbe967579ac12813dfe31424eeb9c553f99c1b61fcc5245f5b9a3f3bde22006"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1506.08414",
    "kind": "arxiv",
    "version": 1
  }
}