Pith Number

pith:CZP53TQX

pith:2012:CZP53TQXIDID6EMK7SJ7PPSWUK

not attested not anchored not stored refs pending

Real Second Order Freeness and Haar Orthogonal Matrices

James A. Mingo (Queen's University), Mihai Popa (Queen's University)

arxiv:1210.6097 v3 · 2012-10-23 · math.OA · 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{CZP53TQXIDID6EMK7SJ7PPSWUK}

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	2026-05-18T01:53:44.541846Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

165fddce1740d03f118afc93f7be56a28189891fcd8991d8055491a411340349

Aliases

arxiv: 1210.6097 · arxiv_version: 1210.6097v3 · doi: 10.48550/arxiv.1210.6097 · pith_short_12: CZP53TQXIDID · pith_short_16: CZP53TQXIDID6EMK · pith_short_8: CZP53TQX

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/CZP53TQXIDID6EMK7SJ7PPSWUK \
  | 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: 165fddce1740d03f118afc93f7be56a28189891fcd8991d8055491a411340349

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "58ccf48ae4f12506b531bd4f9b3c3dac75220259253a840b21a3719d498f05fc",
    "cross_cats_sorted": [
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OA",
    "submitted_at": "2012-10-23T00:56:34Z",
    "title_canon_sha256": "4fed3099f07dfc857c947fcbe1c48b02de99b25d88b4e893f2662670483ad821"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1210.6097",
    "kind": "arxiv",
    "version": 3
  }
}