Pith Number

pith:E47DBJIJ

pith:2003:E47DBJIJKDMXG2MPFJVE7LV2UE

not attested not anchored not stored refs pending

Strong Rigidity of II$_1$ Factors Arising from Malleable Actions of w-Rigid Groups, I

Sorin Popa

arxiv:math/0305306 v13 · 2003-05-21 · 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{E47DBJIJKDMXG2MPFJVE7LV2UE}

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	2026-07-04T14:37:19.663908Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

273e30a50950d973698f2a6a4faebaa1058c4368c4deac93e989490bbcc71877

Aliases

arxiv: math/0305306 · arxiv_version: math/0305306v13 · doi: 10.48550/arxiv.math/0305306 · pith_short_12: E47DBJIJKDMX · pith_short_16: E47DBJIJKDMXG2MP · pith_short_8: E47DBJIJ

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/E47DBJIJKDMXG2MPFJVE7LV2UE \
  | 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: 273e30a50950d973698f2a6a4faebaa1058c4368c4deac93e989490bbcc71877

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "326fc699b5c3fd7f0d876d70903f2ba13050df6c1cb4caa592f14344295b4896",
    "cross_cats_sorted": [
      "math.GR"
    ],
    "license": "",
    "primary_cat": "math.OA",
    "submitted_at": "2003-05-21T19:56:31Z",
    "title_canon_sha256": "ccfd66a9a933d2d8a47ff0a9a9b00f39d0b8cbdcc3d40c3f21abc8bdbed5ecf7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0305306",
    "kind": "arxiv",
    "version": 13
  }
}