Pith Number

pith:KQ4WAK57

pith:2023:KQ4WAK57VBX6PI3QPNJ2DVDHGG

not attested not anchored not stored refs pending

On Diximier's averaging theorem for operators in type ${\rm II}_1$ factors

Junsheng Fang, Shilin Wen, Zhaolin Yao

arxiv:2303.10602 v1 · 2023-03-19 · 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{KQ4WAK57VBX6PI3QPNJ2DVDHGG}

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	2026-07-05T05:52:34.330634Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5439602bbfa86fe7a3707b53a1d46731b0e8a37ad05f0932395de0a74e7727e4

Aliases

arxiv: 2303.10602 · arxiv_version: 2303.10602v1 · doi: 10.48550/arxiv.2303.10602 · pith_short_12: KQ4WAK57VBX6 · pith_short_16: KQ4WAK57VBX6PI3Q · pith_short_8: KQ4WAK57

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/KQ4WAK57VBX6PI3QPNJ2DVDHGG \
  | 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: 5439602bbfa86fe7a3707b53a1d46731b0e8a37ad05f0932395de0a74e7727e4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ecc5f7fde8ea233a06c0db3adb52e476f6c474e328e5a39a71fbce6cffa03867",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.OA",
    "submitted_at": "2023-03-19T08:39:20Z",
    "title_canon_sha256": "80601bd7240672f56bf21be46ce5ec9f1b8be7f73af4f6b66896942c4a7cdafe"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2303.10602",
    "kind": "arxiv",
    "version": 1
  }
}