Pith Number

pith:W5UIBYKV

pith:2015:W5UIBYKVUBJVQXKKFJFSTIB5QI

not attested not anchored not stored refs pending

von Neumann's problem and extensions of non-amenable equivalence relations

Adrian Ioana, Daniel Hoff, Lewis Bowen

arxiv:1509.01723 v4 · 2015-09-05 · math.DS · math.GR · math.OA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{W5UIBYKVUBJVQXKKFJFSTIB5QI}

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	2026-05-18T00:33:32.735899Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b76880e155a053585d4a2a4b29a03d82285636530568f8d49c8c5c2ff1930b8a

Aliases

arxiv: 1509.01723 · arxiv_version: 1509.01723v4 · doi: 10.48550/arxiv.1509.01723 · pith_short_12: W5UIBYKVUBJV · pith_short_16: W5UIBYKVUBJVQXKK · pith_short_8: W5UIBYKV

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/W5UIBYKVUBJVQXKKFJFSTIB5QI \
  | 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: b76880e155a053585d4a2a4b29a03d82285636530568f8d49c8c5c2ff1930b8a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ca4b7b5dde6121cff785ed50514883a21651d9492ed0c2f6ac747fdf654dfb19",
    "cross_cats_sorted": [
      "math.GR",
      "math.OA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2015-09-05T17:57:21Z",
    "title_canon_sha256": "4b5b198394ae274e4f60a1576e1d03d0526bbcdaf83d673e69dba753a22cd433"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1509.01723",
    "kind": "arxiv",
    "version": 4
  }
}