Pith Number

pith:6CW2LKTY

pith:2001:6CW2LKTYHXFB4YAYCJUUSQP4XG

not attested not anchored not stored refs pending

A disjointness type property of conditional expectation operators

Beata Randrianantoanina

arxiv:math/0112181 v1 · 2001-12-18 · math.FA

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{6CW2LKTYHXFB4YAYCJUUSQP4XG}

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	2026-05-18T01:05:29.849150Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f0ada5aa783dca1e601812694941fcb9a9758788792f9869c6ea323978296663

Aliases

arxiv: math/0112181 · arxiv_version: math/0112181v1 · doi: 10.48550/arxiv.math/0112181 · pith_short_12: 6CW2LKTYHXFB · pith_short_16: 6CW2LKTYHXFB4YAY · pith_short_8: 6CW2LKTY

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/6CW2LKTYHXFB4YAYCJUUSQP4XG \
  | 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: f0ada5aa783dca1e601812694941fcb9a9758788792f9869c6ea323978296663

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "278c7db68cd884c08aa01c017e3d974af423aecc8a8e49f646b1f2a4b0d0a414",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.FA",
    "submitted_at": "2001-12-18T17:13:40Z",
    "title_canon_sha256": "df65de0da6c96261a00ebb87bb1a2c99c03a83cb94c5cb6fed768e407e8b51f3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0112181",
    "kind": "arxiv",
    "version": 1
  }
}