Pith Number

pith:TKXAZI5E

pith:2008:TKXAZI5EOAKOKJYX7JU6Z4JCXP

not attested not anchored not stored refs pending

Spherical designs via Brouwer fixed point theorem

Andriy V. Bondarenko, Maryna S. Viazovska

arxiv:0811.1416 v1 · 2008-11-10 · math.NA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{TKXAZI5EOAKOKJYX7JU6Z4JCXP}

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	2026-05-18T04:41:25.365250Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9aae0ca3a47014e52717fa69ecf122bbc791e742eba99b9a96ba29d2d124418b

Aliases

arxiv: 0811.1416 · arxiv_version: 0811.1416v1 · doi: 10.48550/arxiv.0811.1416 · pith_short_12: TKXAZI5EOAKO · pith_short_16: TKXAZI5EOAKOKJYX · pith_short_8: TKXAZI5E

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/TKXAZI5EOAKOKJYX7JU6Z4JCXP \
  | 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: 9aae0ca3a47014e52717fa69ecf122bbc791e742eba99b9a96ba29d2d124418b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "bab6aff9d07a06f1306769b2a062a8e354a1e538b3ab6aa687a3b1d6196d55ef",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NA",
    "submitted_at": "2008-11-10T09:20:45Z",
    "title_canon_sha256": "397e56986a24cd431a4d8f89b6acf326d374443195dbbddce50fcf1e7f2775e5"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0811.1416",
    "kind": "arxiv",
    "version": 1
  }
}