Pith Number

pith:GSRTQV6C

pith:2026:GSRTQV6CWQZGDTRBVLI7XCVZGZ

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Interpreting De Finetti's theorem in the Category of Integrable Cones (long version)

Crubill\'e Rapha\"elle

Connecting categorical De Finetti theorem to linear logic exponentials characterizes total elements of !Bool

arxiv:2605.15402 v1 · 2026-05-14 · cs.LO

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Claims

C1strongest claim

We establish a connection between two results in the literature on probabilistic semantics: a formulation of De Finetti's theorem in the language of category theory due to Jacobs and Staton, and the generic construction of the free exponential of Linear Logic by Melliès et al, that has been instantiated in the model of probabilistic coherence spaces by Crubillé et al. We then use this connection to give a characterization of the total elements of the probabilistic coherence space !Bool.

C2weakest assumption

Making this connection formal requires technical developments on the relationship between the category of stochastic kernels and the category of integrable cones.

C3one line summary

Establishes a formal connection between Jacobs-Staton categorical De Finetti theorem and Melliès free exponential in linear logic, instantiated in probabilistic coherence spaces, then characterizes total elements of !Bool.

References

55 extracted · 55 resolved · 0 Pith anchors

[1] Andrea Asperti and Giuseppe Longo 1991

[2] The unsung de finetti’s first paper about exchangeability.Rendiconti di Matematica e delle sue applicazioni, 28:1–17, 2008 2008

[3] Element-free probability distributions and ran- dom partitions 2024 · doi:10.1145/3661814.3662131

[4] On convergence determining and separating classes of functions.Stochastic processes and their applications, 120(10):1898–1907, 2010 1907

[5] Disintegration and Bayesian inversion via string diagrams 2019 · doi:10.1017/s0960129518000488

Formal links

1 machine-checked theorem link

Receipt and verification

First computed	2026-05-20T00:00:56.734203Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

34a33857c2b43261ce21aad1fb8ab93647c624e3d71d013864b1b1e3e88a5aab

Aliases

arxiv: 2605.15402 · arxiv_version: 2605.15402v1 · doi: 10.48550/arxiv.2605.15402 · pith_short_12: GSRTQV6CWQZG · pith_short_16: GSRTQV6CWQZGDTRB · pith_short_8: GSRTQV6C

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/GSRTQV6CWQZGDTRBVLI7XCVZGZ \
  | 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: 34a33857c2b43261ce21aad1fb8ab93647c624e3d71d013864b1b1e3e88a5aab

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "18a85e7035d567f669d093ee33a411d25d0732c95843a8e4615da29f24c9063d",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.LO",
    "submitted_at": "2026-05-14T20:37:17Z",
    "title_canon_sha256": "25ee75a220087a5c6d2c30b3487597d704885beb2b51027c7b767dffe055a33d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.15402",
    "kind": "arxiv",
    "version": 1
  }
}