Pith Number

pith:4LYKPT34

pith:2009:4LYKPT345HPENPIMF67WSZNUIN

not attested not anchored not stored refs pending

On the classification of inductive limits of II$_1$ factors with spectral gap

Sorin Popa

arxiv:0910.2241 v1 · 2009-10-13 · 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{4LYKPT345HPENPIMF67WSZNUIN}

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	2026-07-04T15:54:24.720205Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e2f0a7cf7ce9de46bd0c2fbf6965b4436a1783eddc8616a3936feeb229a8b803

Aliases

arxiv: 0910.2241 · arxiv_version: 0910.2241v1 · doi: 10.48550/arxiv.0910.2241 · pith_short_12: 4LYKPT345HPE · pith_short_16: 4LYKPT345HPENPIM · pith_short_8: 4LYKPT34

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/4LYKPT345HPENPIMF67WSZNUIN \
  | 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: e2f0a7cf7ce9de46bd0c2fbf6965b4436a1783eddc8616a3936feeb229a8b803

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f0e95da22c1dc5720a21066ebbd7f8d6bcec0fbd2f85bfa41961aa07f4c2e24a",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OA",
    "submitted_at": "2009-10-13T18:58:20Z",
    "title_canon_sha256": "8ab731965c880d30c5183578d59652571084ce3e8b2b8e727c5a894cebd64329"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0910.2241",
    "kind": "arxiv",
    "version": 1
  }
}