Pith Number

pith:HXVFRBUZ

pith:2002:HXVFRBUZ2KHGZ5IQ6YLFTKODK4

not attested not anchored not stored refs pending

The Banach-Tarski paradox or what mathematics and religion have in common

Volker Runde

arxiv:math/0202309 v1 · 2002-02-28 · math.GM

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{HXVFRBUZ2KHGZ5IQ6YLFTKODK4}

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	2026-05-18T01:05:29.748435Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3dea588699d28e6cf510f61659a9c3571c2b19c8398a04e3635c8e361e0cb453

Aliases

arxiv: math/0202309 · arxiv_version: math/0202309v1 · doi: 10.48550/arxiv.math/0202309 · pith_short_12: HXVFRBUZ2KHG · pith_short_16: HXVFRBUZ2KHGZ5IQ · pith_short_8: HXVFRBUZ

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/HXVFRBUZ2KHGZ5IQ6YLFTKODK4 \
  | 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: 3dea588699d28e6cf510f61659a9c3571c2b19c8398a04e3635c8e361e0cb453

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "af0e9d7e865f4abe4b05395c3fa1ba608c3655dbd7efe0985160a1e9032d98f0",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.GM",
    "submitted_at": "2002-02-28T16:59:12Z",
    "title_canon_sha256": "6451bda8584a7eb8110892780085fb6be2181e84ad6bd3092cc9cdfee60252a7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0202309",
    "kind": "arxiv",
    "version": 1
  }
}