Pith Number

pith:PH3GA3DN

pith:2022:PH3GA3DNK45T5XVJC6CNM5ZYK2

not attested not anchored not stored refs pending

Schur Multipliers of $C^*$-algebras, group-invariant compactification and applications to amenability and percolation

Chiranjib Mukherjee, Konstantin Recke

arxiv:2211.11411 v3 · 2022-11-21 · math.OA · math.GR · math.PR

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{PH3GA3DNK45T5XVJC6CNM5ZYK2}

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

Coarse embeddability, $L^1$-compression and Percolations on General Graphs

Receipt and verification

First computed	2026-07-05T08:46:50.584970Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

79f6606c6d573b3edea91784d67738568a95ee053d0d5e67099b6737235efc68

Aliases

arxiv: 2211.11411 · arxiv_version: 2211.11411v3 · doi: 10.48550/arxiv.2211.11411 · pith_short_12: PH3GA3DNK45T · pith_short_16: PH3GA3DNK45T5XVJ · pith_short_8: PH3GA3DN

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/PH3GA3DNK45T5XVJC6CNM5ZYK2 \
  | 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: 79f6606c6d573b3edea91784d67738568a95ee053d0d5e67099b6737235efc68

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e980947a4b3e1a70bfd3a8fca13c53e12febeb7458aadf2f98a78d4307fec352",
    "cross_cats_sorted": [
      "math.GR",
      "math.PR"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.OA",
    "submitted_at": "2022-11-21T12:48:26Z",
    "title_canon_sha256": "82e42429ec3f2776015eeb1db104c7e93006f7b7dfcb3985cc260472fe384e10"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2211.11411",
    "kind": "arxiv",
    "version": 3
  }
}