Pith Number

pith:NAMPN2X5

pith:2003:NAMPN2X52XLFAX4D4BOKAKZGR4

not attested not anchored not stored refs pending

On co-amenability for groups and von Neumann algebras

Nicolas Monod, Sorin Popa

arxiv:math/0301348 v3 · 2003-01-30 · 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{NAMPN2X52XLFAX4D4BOKAKZGR4}

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	2026-07-04T14:49:10.072422Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6818f6eafdd5d6505f83e05ca02b268f249fecf3ab8bc4bb5e5a47f479f15c8d

Aliases

arxiv: math/0301348 · arxiv_version: math/0301348v3 · doi: 10.48550/arxiv.math/0301348 · pith_short_12: NAMPN2X52XLF · pith_short_16: NAMPN2X52XLFAX4D · pith_short_8: NAMPN2X5

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/NAMPN2X52XLFAX4D4BOKAKZGR4 \
  | 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: 6818f6eafdd5d6505f83e05ca02b268f249fecf3ab8bc4bb5e5a47f479f15c8d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "172af5e84c9ccaa1d45dbb1a3a860d82bceeb66b862e26f82942de434394ac32",
    "cross_cats_sorted": [
      "math.OA"
    ],
    "license": "",
    "primary_cat": "math.GR",
    "submitted_at": "2003-01-30T02:02:11Z",
    "title_canon_sha256": "875dd61085be720a19347c098469d15782afbd56333e0e95369984ee84419fe5"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0301348",
    "kind": "arxiv",
    "version": 3
  }
}