Pith Number

pith:Y7AZMX4R

pith:2016:Y7AZMX4RZEPFHVCITM6NCNW6YY

not attested not anchored not stored refs pending

An upper bound for the Tarski numbers of non amenable groups of piecewise projective homeomorphisms

Yash Lodha

arxiv:1604.05997 v2 · 2016-04-20 · 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{Y7AZMX4RZEPFHVCITM6NCNW6YY}

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	2026-05-18T00:48:42.872063Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c7c1965f91c91e53d4489b3cd136dec63459f1922f552ea661fe0d130aaa9c53

Aliases

arxiv: 1604.05997 · arxiv_version: 1604.05997v2 · doi: 10.48550/arxiv.1604.05997 · pith_short_12: Y7AZMX4RZEPF · pith_short_16: Y7AZMX4RZEPFHVCI · pith_short_8: Y7AZMX4R

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/Y7AZMX4RZEPFHVCITM6NCNW6YY \
  | 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: c7c1965f91c91e53d4489b3cd136dec63459f1922f552ea661fe0d130aaa9c53

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f3f9d3526dd422be42d9b2b3e51fb7a7eb440e2d9dfd342ebf67fd4f1c6ec703",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2016-04-20T15:18:11Z",
    "title_canon_sha256": "6e8b58cfad7df4974f2147b394e9854cd016b5aecb1406e9b4513bb6d9b6c654"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1604.05997",
    "kind": "arxiv",
    "version": 2
  }
}