Pith Number

pith:PHZJCYY7

pith:2010:PHZJCYY7E3FQGT5VTACJUJPJIS

not attested not anchored not stored refs pending

Some non-amenable groups

Aditi Kar, Graham A. Niblo

arxiv:1006.5389 v2 · 2010-06-28 · 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{PHZJCYY7E3FQGT5VTACJUJPJIS}

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	2026-05-18T04:08:44.856068Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

79f291631f26cb034fb598049a25e944803b1dccf24c79c679f83b51c4ba4121

Aliases

arxiv: 1006.5389 · arxiv_version: 1006.5389v2 · doi: 10.48550/arxiv.1006.5389 · pith_short_12: PHZJCYY7E3FQ · pith_short_16: PHZJCYY7E3FQGT5V · pith_short_8: PHZJCYY7

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/PHZJCYY7E3FQGT5VTACJUJPJIS \
  | 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: 79f291631f26cb034fb598049a25e944803b1dccf24c79c679f83b51c4ba4121

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "140084c7f7affc558e39c9f903b5029065b348c39b74241a9d3879eb22438d25",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2010-06-28T16:10:32Z",
    "title_canon_sha256": "29add5daaa5dccb58d553248888f4a0369447c2ff9c7be07031a144bb93029e7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1006.5389",
    "kind": "arxiv",
    "version": 2
  }
}