Pith Number

pith:FMDX6X2M

pith:2017:FMDX6X2MUAJOOGKAYJAZGEYAO5

not attested not anchored not stored refs pending

A combinatorial result on asymptotic independence relations for random matrices with non-commutative entries

Mihai Popa, Zhiwei Hao

arxiv:1704.06324 v1 · 2017-04-20 · 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{FMDX6X2MUAJOOGKAYJAZGEYAO5}

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	2026-05-18T00:45:59.992301Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2b077f5f4ca012e71940c241931300776497a35e433baeea663c446073170f1a

Aliases

arxiv: 1704.06324 · arxiv_version: 1704.06324v1 · doi: 10.48550/arxiv.1704.06324 · pith_short_12: FMDX6X2MUAJO · pith_short_16: FMDX6X2MUAJOOGKA · pith_short_8: FMDX6X2M

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/FMDX6X2MUAJOOGKAYJAZGEYAO5 \
  | 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: 2b077f5f4ca012e71940c241931300776497a35e433baeea663c446073170f1a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "71e6fb8d243eec042ce3f505a2101c09eaab8eb99beb0e985464d468af9286bc",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OA",
    "submitted_at": "2017-04-20T20:12:37Z",
    "title_canon_sha256": "1d998f8b7613b1e2f6bfb43851c34363ff1cb926a234509cd418dba9881d8110"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1704.06324",
    "kind": "arxiv",
    "version": 1
  }
}