Pith Number

pith:ZMDIRPJY

pith:2004:ZMDIRPJY7GJP6AVQTWHTAXROMD

not attested not anchored not stored refs pending

Strong rigidity of II$_1$ factors arising from malleable actions of w-rigid groups, II

Sorin Popa

arxiv:math/0407103 v10 · 2004-07-07 · math.OA · 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{ZMDIRPJY7GJP6AVQTWHTAXROMD}

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	2026-07-04T14:38:53.840716Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cb0688bd38f992ff02b09d8f305e2e60e63f9f1045b12de317e7ecba4744f0b8

Aliases

arxiv: math/0407103 · arxiv_version: math/0407103v10 · doi: 10.48550/arxiv.math/0407103 · pith_short_12: ZMDIRPJY7GJP · pith_short_16: ZMDIRPJY7GJP6AVQ · pith_short_8: ZMDIRPJY

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/ZMDIRPJY7GJP6AVQTWHTAXROMD \
  | 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: cb0688bd38f992ff02b09d8f305e2e60e63f9f1045b12de317e7ecba4744f0b8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a3591766e899a96382b022e4bea734d3caba6c7eaf39c27abeab11f9aa30fe34",
    "cross_cats_sorted": [
      "math.GR"
    ],
    "license": "",
    "primary_cat": "math.OA",
    "submitted_at": "2004-07-07T13:24:34Z",
    "title_canon_sha256": "319bc413f50e5d0981bd11e2d1187626b28470e6b4c3690b45e55f8acb31668a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0407103",
    "kind": "arxiv",
    "version": 10
  }
}