Pith Number

pith:RH7HYHOF

pith:2017:RH7HYHOFQVHHG3YFJ2LAD2QN2P

not attested not anchored not stored refs pending

Asymptotic orthogonalization of subalgebras in II$_1$ factors

Sorin Popa

arxiv:1707.07317 v3 · 2017-07-23 · 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{RH7HYHOFQVHHG3YFJ2LAD2QN2P}

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	2026-05-18T00:02:49.830839Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

89fe7c1dc5854e736f054e9601ea0dd3d06b98228bda4abb1b2989bd9f2b3983

Aliases

arxiv: 1707.07317 · arxiv_version: 1707.07317v3 · doi: 10.48550/arxiv.1707.07317 · pith_short_12: RH7HYHOFQVHH · pith_short_16: RH7HYHOFQVHHG3YF · pith_short_8: RH7HYHOF

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/RH7HYHOFQVHHG3YFJ2LAD2QN2P \
  | 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: 89fe7c1dc5854e736f054e9601ea0dd3d06b98228bda4abb1b2989bd9f2b3983

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e3850316c4e9ab14422220f76b231150d5cbe64d27896eab54c44619aa8bbece",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OA",
    "submitted_at": "2017-07-23T15:57:26Z",
    "title_canon_sha256": "aca8cc4082de7ec21a34ad7c76b65199b201a3b966af384c66b864fc90900fa5"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1707.07317",
    "kind": "arxiv",
    "version": 3
  }
}