Pith Number

pith:ZGPLBO7L

pith:2009:ZGPLBO7LMF5LFGFNBA5GPTX2NX

not attested not anchored not stored refs pending

A new metric criterion for non-amenability III: Non-amenability of R.Thompson's group F

Azer Akhmedov

arxiv:0902.3849 v8 · 2009-02-23 · 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{ZGPLBO7LMF5LFGFNBA5GPTX2NX}

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.

Cited by

1 paper in Pith

Superharmonic functions on the Lamplighter graph of Thompson's group F

Receipt and verification

First computed	2026-05-18T03:04:14.199837Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c99eb0bbeb617ab298ad083a67cefa6dfbebc3409231af814b2a2cfe8af2f48c

Aliases

arxiv: 0902.3849 · arxiv_version: 0902.3849v8 · doi: 10.48550/arxiv.0902.3849 · pith_short_12: ZGPLBO7LMF5L · pith_short_16: ZGPLBO7LMF5LFGFN · pith_short_8: ZGPLBO7L

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/ZGPLBO7LMF5LFGFNBA5GPTX2NX \
  | 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: c99eb0bbeb617ab298ad083a67cefa6dfbebc3409231af814b2a2cfe8af2f48c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "618ee0f0fb0cc0be6dd34778a8a096484d21861aed965aba4f505960494896a7",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2009-02-23T19:34:49Z",
    "title_canon_sha256": "037b23c2ca472bbb702bfa58492f13e4f99e253ffcd157bad2e40817d71dc0f1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0902.3849",
    "kind": "arxiv",
    "version": 8
  }
}