Pith Number

pith:5ZTLQ6OK

pith:2025:5ZTLQ6OKYX77JXJS5TUQ6CDULH

not attested not anchored not stored refs pending

Compressible subalgebras in II$_1$ factors

Sorin Popa

arxiv:2510.17076 v2 · 2025-10-20 · 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{5ZTLQ6OKYX77JXJS5TUQ6CDULH}

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	2026-07-01T01:17:11.479223Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ee66b879cac5fff4dd32ece90f087459fb5c8045d836eb0b5d9fbf162158d676

Aliases

arxiv: 2510.17076 · arxiv_version: 2510.17076v2 · doi: 10.48550/arxiv.2510.17076 · pith_short_12: 5ZTLQ6OKYX77 · pith_short_16: 5ZTLQ6OKYX77JXJS · pith_short_8: 5ZTLQ6OK

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/5ZTLQ6OKYX77JXJS5TUQ6CDULH \
  | 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: ee66b879cac5fff4dd32ece90f087459fb5c8045d836eb0b5d9fbf162158d676

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4ae83cf330d206334bbe48758fa890f703bd8d45ad1075b08d18138933ab6b9e",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OA",
    "submitted_at": "2025-10-20T01:06:58Z",
    "title_canon_sha256": "9dab433212ed06c5ab83adf8360adfcff5f8a0895f74ef0a40c35c100d83e2de"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2510.17076",
    "kind": "arxiv",
    "version": 2
  }
}