Pith Number

pith:R6ZT3JTZ

pith:2013:R6ZT3JTZIBKDMSICA4W7J7O2GO

not attested not anchored not stored refs pending

From Kleisli Categories to Commutative C*-algebras: Probabilistic Gelfand Duality

Bart P. F. Jacobs (Radboud University Nijmegen), Robert W. J. Furber (Radboud University Nijmegen)

arxiv:1303.1115 v8 · 2013-03-05 · math.CT · cs.LO

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Add to your LaTeX paper

\usepackage{pith}
\pithnumber{R6ZT3JTZIBKDMSICA4W7J7O2GO}

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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.

Cited by

1 paper in Pith

A synthetic approach to Markov kernels, conditional independence and theorems on sufficient statistics

Receipt and verification

First computed	2026-05-18T00:53:11.185344Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8fb33da6794054364902072df4fdda33a90298dba1485d302228583837243c64

Aliases

arxiv: 1303.1115 · arxiv_version: 1303.1115v8 · doi: 10.48550/arxiv.1303.1115 · pith_short_12: R6ZT3JTZIBKD · pith_short_16: R6ZT3JTZIBKDMSIC · pith_short_8: R6ZT3JTZ

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/R6ZT3JTZIBKDMSICA4W7J7O2GO \
  | 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: 8fb33da6794054364902072df4fdda33a90298dba1485d302228583837243c64

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5ed1814d18ddc25c21da9c4baee3361fd3dff0abb3887f9daf93135e5cec034b",
    "cross_cats_sorted": [
      "cs.LO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CT",
    "submitted_at": "2013-03-05T17:44:20Z",
    "title_canon_sha256": "bf40842e279aa0d52658f063b243170a43799f6fb873b9ce9082f2e63a26b330"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1303.1115",
    "kind": "arxiv",
    "version": 8
  }
}