Pith Number

pith:SEQTVGXR

pith:2026:SEQTVGXREBQ6NJ27UPORUOOQCB

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Verifying Exact Samplers for Continuous Distributions with a Discrete Program Logic

Alejandro Aguirre, Joseph Tassarotti, Kwing Hei Li, Lars Birkedal, Markus de Medeiros, Puming Liu

A higher-order separation logic proves exact samplers for continuous distributions correct.

arxiv:2605.13526 v1 · 2026-05-13 · cs.LO

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Claims

C1strongest claim

We present Continuous-Eris, a higher-order separation logic for verifying the correctness of exact sampling algorithms for computable distributions. To demonstrate Continuous-Eris, we verify the correctness of computable samplers for the uniform, Gaussian, and Laplace distributions, as well as a library for exact real arithmetic for working with generated samples. All of the results in this paper have been verified in the Rocq proof assistant.

C2weakest assumption

The underlying programming language semantics for probabilistic choice, higher-order functions, and mutable state are faithfully captured by the separation logic rules, and the model of computable reals correctly represents lazy digit generation without hidden approximation.

C3one line summary

Continuous-Eris is a new separation logic, fully verified in Rocq, that proves correctness of exact samplers for uniform, Gaussian, and Laplace distributions plus an exact real arithmetic library.

References

16 extracted · 16 resolved · 0 Pith anchors

[1] 1 Nathanael L. Ackerman, Cameron E. Freer, and Daniel M. Roy. On the computability of conditional probability.J. ACM, 66(3):23:1–23:40, 2019.doi:10.1145/3321699. 2 Alejandro Aguirre, Philipp G. Haselw 2019 · doi:10.1145/3321699

[2] 5 Kevin Batz, Joost-Pieter Katoen, Francesca Randone, and Tobias Winkler 2016 · doi:10.4230/lipics.icalp.2016.107

[3] Quickstrom: property-based acceptance testing with ltl specifications · doi:10.1145/3519939.3523721

[4] A domain-theoretic approach to brownian motion and general continuous stochastic processes 2014

[5] Narayan Kumar, and Patrick Totzke 2020 · doi:10.1145/2603088.2603102

Receipt and verification

First computed	2026-05-18T02:44:24.309674Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

91213a9af12061e6a75fa3dd1a39d01069a2e97a2c7d3c37bbee19135ecaab04

Aliases

arxiv: 2605.13526 · arxiv_version: 2605.13526v1 · doi: 10.48550/arxiv.2605.13526 · pith_short_12: SEQTVGXREBQ6 · pith_short_16: SEQTVGXREBQ6NJ27 · pith_short_8: SEQTVGXR

Agent API

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/SEQTVGXREBQ6NJ27UPORUOOQCB \
  | 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: 91213a9af12061e6a75fa3dd1a39d01069a2e97a2c7d3c37bbee19135ecaab04

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3692aaf252ed8b1b1275424aefaf96e87009fc56df75197610f80a8887849854",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cs.LO",
    "submitted_at": "2026-05-13T13:39:31Z",
    "title_canon_sha256": "ce9b349437b50d37a84d53b7c6a971ca41d679e03b6b05e8e1617addd5b2b844"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.13526",
    "kind": "arxiv",
    "version": 1
  }
}