Pith Number

pith:ICBKOASN

pith:2011:ICBKOASND4XTIPURSZQJNKBNPD

not attested not anchored not stored refs pending

The Banach-Tarski paradox for flag manifolds

Yohei Komori, Yuriko Umemoto

arxiv:1106.0432 v1 · 2011-06-02 · math.GT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{ICBKOASND4XTIPURSZQJNKBNPD}

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	2026-05-18T04:20:50.400900Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4082a7024d1f2f343e91966096a82d78f4223a8724c7398eaef1051682c18f0e

Aliases

arxiv: 1106.0432 · arxiv_version: 1106.0432v1 · doi: 10.48550/arxiv.1106.0432 · pith_short_12: ICBKOASND4XT · pith_short_16: ICBKOASND4XTIPUR · pith_short_8: ICBKOASN

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/ICBKOASND4XTIPURSZQJNKBNPD \
  | 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: 4082a7024d1f2f343e91966096a82d78f4223a8724c7398eaef1051682c18f0e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "932a215fe71a86e83da53ae19f41c6ecf3fdd4bc82a3e7057832eadaa405411a",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2011-06-02T14:04:57Z",
    "title_canon_sha256": "aac689aec4b494af5eeaa22fda2d60f147cfb3535b98ee4905f420fe537330c5"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1106.0432",
    "kind": "arxiv",
    "version": 1
  }
}