Pith Number

pith:QVA7KKJV

pith:2016:QVA7KKJVCXS2KZB5J7B5XHHOAO

not attested not anchored not stored refs pending

The Rank Theorem and $L^2$-invariants in Free Entropy: Global Upper Bounds

Kenley Jung

arxiv:1602.04726 v1 · 2016-02-15 · 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{QVA7KKJVCXS2KZB5J7B5XHHOAO}

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.

Cited by

1 paper in Pith

An $\ell^2$ Obstruction for Elementary Embeddings of Hyperbolic Groups

Receipt and verification

First computed	2026-05-18T01:20:49.321555Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8541f5293515e5a5643d4fc3db9cee03b69e5ece2472d07068f2c2bacdc350f4

Aliases

arxiv: 1602.04726 · arxiv_version: 1602.04726v1 · doi: 10.48550/arxiv.1602.04726 · pith_short_12: QVA7KKJVCXS2 · pith_short_16: QVA7KKJVCXS2KZB5 · pith_short_8: QVA7KKJV

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/QVA7KKJVCXS2KZB5J7B5XHHOAO \
  | 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: 8541f5293515e5a5643d4fc3db9cee03b69e5ece2472d07068f2c2bacdc350f4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f2bb052dc7edf9b743e144fd5b2ec6057f5d7fbdadcecfe97bab893307abea2b",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OA",
    "submitted_at": "2016-02-15T16:24:33Z",
    "title_canon_sha256": "c988ce26cd6b39fefdb031564763e1788750d517872cc5d0294c3093f7808100"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1602.04726",
    "kind": "arxiv",
    "version": 1
  }
}