Pith Number

pith:6I2PVUIK

pith:2010:6I2PVUIK36K3CHU62DKIUG4DXS

not attested not anchored not stored refs pending

On the operator-valued analogues of the semicircle, arcsine and Bernoulli laws

Mihai Popa, Serban T. Belinschi, Victor Vinnikov

arxiv:1008.5205 v2 · 2010-08-31 · 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{6I2PVUIK36K3CHU62DKIUG4DXS}

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	2026-05-18T04:39:18.071545Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f234fad10adf95b11e9ed0d48a1b83bc89e0b67b995185ab26381433637fdb78

Aliases

arxiv: 1008.5205 · arxiv_version: 1008.5205v2 · doi: 10.48550/arxiv.1008.5205 · pith_short_12: 6I2PVUIK36K3 · pith_short_16: 6I2PVUIK36K3CHU6 · pith_short_8: 6I2PVUIK

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/6I2PVUIK36K3CHU62DKIUG4DXS \
  | 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: f234fad10adf95b11e9ed0d48a1b83bc89e0b67b995185ab26381433637fdb78

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7ac6907dd2566b480bb2e45531a880647279b1bf071ae7589664bf976218fc7b",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OA",
    "submitted_at": "2010-08-31T03:12:20Z",
    "title_canon_sha256": "451911ae44069fae1da0485dba28fc20ee993989c24b9cdee44825120372084c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1008.5205",
    "kind": "arxiv",
    "version": 2
  }
}