Pith Number

pith:2T2XNFEI

pith:2011:2T2XNFEIQK5J4RNFYNEPH7TPRF

not attested not anchored not stored refs pending

On optimal stationary couplings between stationary processes

Ludger Rueschendorf, Tomonari Sei

arxiv:1108.4086 v1 · 2011-08-20 · 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{2T2XNFEIQK5J4RNFYNEPH7TPRF}

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	2026-05-18T04:14:56.188981Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d4f576948882ba9e45a5c348f3fe6f8967bfb9287daa31fa3f29f6af0d3ee4dc

Aliases

arxiv: 1108.4086 · arxiv_version: 1108.4086v1 · doi: 10.48550/arxiv.1108.4086 · pith_short_12: 2T2XNFEIQK5J · pith_short_16: 2T2XNFEIQK5J4RNF · pith_short_8: 2T2XNFEI

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/2T2XNFEIQK5J4RNFYNEPH7TPRF \
  | 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: d4f576948882ba9e45a5c348f3fe6f8967bfb9287daa31fa3f29f6af0d3ee4dc

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "faba88d459d2d2b037b0aec36175b14add3e5f7280850d97148688c74b344cac",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2011-08-20T03:45:18Z",
    "title_canon_sha256": "76a0b54096fca94dddeb7fd369b4b49cf245e7cfe0b3ff839c17a820481103dd"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1108.4086",
    "kind": "arxiv",
    "version": 1
  }
}