Pith Number

pith:2SHF3YTF

pith:2016:2SHF3YTF4VK4LVTN6PEPVT2WPS

not attested not anchored not stored refs pending

Mixtures of classical and free independence

Janusz Wysoczanski, Roland Speicher

arxiv:1603.08758 v3 · 2016-03-29 · 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{2SHF3YTF4VK4LVTN6PEPVT2WPS}

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	2026-05-18T01:15:38.139036Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d48e5de265e555c5d66df3c8facf567ca94e9d58bf7840fc38607f196a47b888

Aliases

arxiv: 1603.08758 · arxiv_version: 1603.08758v3 · doi: 10.48550/arxiv.1603.08758 · pith_short_12: 2SHF3YTF4VK4 · pith_short_16: 2SHF3YTF4VK4LVTN · pith_short_8: 2SHF3YTF

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/2SHF3YTF4VK4LVTN6PEPVT2WPS \
  | 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: d48e5de265e555c5d66df3c8facf567ca94e9d58bf7840fc38607f196a47b888

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c5493615e4c7f2dfb913171855abd34fc91cd65daa6bf67af5d07fc5d9361107",
    "cross_cats_sorted": [
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OA",
    "submitted_at": "2016-03-29T13:14:30Z",
    "title_canon_sha256": "8148348733a2cbb6a734f8af55cdfea06d5d56c5bae1568d0b4f6b54d3b69ad2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1603.08758",
    "kind": "arxiv",
    "version": 3
  }
}