Pith Number

pith:VXI34B4S

pith:2025:VXI34B4SENRBNFJC3DZTC2NG2H

not attested not anchored not stored refs pending

Minimal Banach-Tarski decompositions

Cesare Straffelini, Kilian Zambanini

arxiv:2507.17517 v2 · 2025-07-23 · math.LO · math.GR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{VXI34B4SENRBNFJC3DZTC2NG2H}

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	2026-06-19T16:12:46.870753Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

add1be07922362169522d8f33169a6d1e21b3f1a27179dd968b10a0700a38543

Aliases

arxiv: 2507.17517 · arxiv_version: 2507.17517v2 · doi: 10.48550/arxiv.2507.17517 · pith_short_12: VXI34B4SENRB · pith_short_16: VXI34B4SENRBNFJC · pith_short_8: VXI34B4S

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/VXI34B4SENRBNFJC3DZTC2NG2H \
  | 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: add1be07922362169522d8f33169a6d1e21b3f1a27179dd968b10a0700a38543

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f2384da60b4723c2a395cff7a62d811a446c509439dfa6efc61aee508b13b666",
    "cross_cats_sorted": [
      "math.GR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.LO",
    "submitted_at": "2025-07-23T13:52:50Z",
    "title_canon_sha256": "4f4b47b2edd3c7d4693633fbf6dcda8c8f5af8437f54ac8e3f9f8a1c74ed3651"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2507.17517",
    "kind": "arxiv",
    "version": 2
  }
}