{
  "id": "oai:papers.qnfo.org:the-sampling-ceiling-why-llm-authored-constraint-systems-cannot-exceed-the-relia",
  "slug": "the-sampling-ceiling-why-llm-authored-constraint-systems-cannot-exceed-the-relia",
  "title": "The Sampling Ceiling: Why LLM-Authored Constraint Systems Cannot Exceed the Reliability of the Model That Authored Them",
  "authors": [
    "Rowan Brad Quni-Gudzinas"
  ],
  "abstract": "Large language models (LLMs) are increasingly used to author the artifacts that other software systems must obey: specifications, system prompts, interface contracts, and validation rubrics. Practitioners currently assume that better prompting, self-critique, or meta-level instruction can raise the reliability of these authored constraint systems arbitrarily. This paper argues that assumption is false. We model LLM generation as stochastic sampling from a fixed conditional distribution and constraint satisfaction as deductive verification, and we prove a ceiling result: any prompt-level transformation of the sampling process leaves the per-constraint error rate bounded below by a model-intrinsic minimum ε_min > 0 on constraint types the model cannot self-verify, so no composition of prompts can close the reliability gap. We quantify the gap with explicit arithmetic: for a specification with N=40 constraints and a per-constraint error rate ε=0.02, a prompt-only pipeline achieves a clean-run probability of 0.98⁴0≈ 0.4457, while a hybrid pipeline in which a formal verifier catches errors with probability c=0.95 achieves (1-ε(1-c))⁴0≈ 0.9608, a factor of $2.16$ improvement that no prompt change can match under the model. The break-even count is N^*=35 constraints. The result is consistent with reported adherence thresholds of p^*≈ 0.958 per chapter and q^*≈ 0.986 per constraint in long-form drafting, and it justifies hybrid architectures in which LLMs draft and formal tools enforce.",
  "abstract_markdown": "Large language models (LLMs) are increasingly used to author the artifacts that other software systems must obey: specifications, system prompts, interface contracts, and validation rubrics. Practitioners currently assume that better prompting, self-critique, or meta-level instruction can raise the reliability of these authored constraint systems arbitrarily. This paper argues that assumption is false. We model LLM generation as stochastic sampling from a fixed conditional distribution and constraint satisfaction as deductive verification, and we prove a ceiling result: any prompt-level transformation of the sampling process leaves the per-constraint error rate bounded below by a model-intrinsic minimum $\\varepsilon_{\\min} > 0$ on constraint types the model cannot self-verify, so no composition of prompts can close the reliability gap. We quantify the gap with explicit arithmetic: for a specification with $N=40$ constraints and a per-constraint error rate $\\varepsilon=0.02$, a prompt-only pipeline achieves a clean-run probability of $0.98^{40}\\approx 0.4457$, while a hybrid pipeline in which a formal verifier catches errors with probability $c=0.95$ achieves $(1-\\varepsilon(1-c))^{40}\\approx 0.9608$, a factor of $2.16$ improvement that no prompt change can match under the model. The break-even count is $N^{*}=35$ constraints. The result is consistent with reported adherence thresholds of $p^{*}\\approx 0.958$ per chapter and $q^{*}\\approx 0.986$ per constraint in long-form drafting, and it justifies hybrid architectures in which LLMs draft and formal tools enforce.",
  "date": "2026-11-11",
  "first_published": "2026-11-11",
  "last_revised": "2026-11-11T00:00:00Z",
  "modified": "2026-11-11T00:00:00Z",
  "version": "1.0.0",
  "version_count": 1,
  "language": "en",
  "keywords": [],
  "quality_tags": [
    "High-quality scholarly research",
    "open-access scholarly work",
    "versioned research publication"
  ],
  "quality_label": "High-quality scholarly research",
  "quality_basis": "QNFO publisher classification for open-access, versioned research with a public revision history and reader correction channel; this is not a claim of independent peer review.",
  "quality_evidence_url": "https://qnfo.org/about",
  "peer_review_status": "Not independently peer-reviewed",
  "resource_type": "ScholarlyArticle",
  "doi": null,
  "doi_url": null,
  "url": "https://papers.qnfo.org/papers/the-sampling-ceiling-why-llm-authored-constraint-systems-cannot-exceed-the-relia",
  "license_url": "https://legal.qnfo.org/",
  "license_spdx": null,
  "sha256": "9b202d54573b83c089cfe5529f210dcbfcf30ea5340a3db430cceffa3f0cf845",
  "version_url": "https://papers.qnfo.org/papers/the-sampling-ceiling-why-llm-authored-constraint-systems-cannot-exceed-the-relia/v/1.0.0",
  "datacite": {
    "schemaVersion": "http://datacite.org/schema/kernel-4",
    "identifiers": [
      {
        "identifier": "https://papers.qnfo.org/papers/the-sampling-ceiling-why-llm-authored-constraint-systems-cannot-exceed-the-relia",
        "identifierType": "URL"
      }
    ],
    "creators": [
      {
        "name": "Rowan Brad Quni-Gudzinas",
        "nameType": "Personal",
        "nameIdentifiers": [
          {
            "nameIdentifier": "https://orcid.org/0009-0002-4317-5604",
            "nameIdentifierScheme": "ORCID",
            "schemeUri": "https://orcid.org"
          }
        ]
      }
    ],
    "titles": [
      {
        "title": "The Sampling Ceiling: Why LLM-Authored Constraint Systems Cannot Exceed the Reliability of the Model That Authored Them"
      }
    ],
    "publisher": "QNFO",
    "publicationYear": "2026",
    "resourceType": {
      "resourceTypeGeneral": "Text",
      "resourceType": "ScholarlyArticle"
    },
    "subjects": [
      {
        "subject": "High-quality scholarly research",
        "subjectScheme": "QNFO publisher classification",
        "schemeUri": "https://qnfo.org/about"
      },
      {
        "subject": "open-access scholarly work",
        "subjectScheme": "QNFO publisher classification",
        "schemeUri": "https://qnfo.org/about"
      },
      {
        "subject": "versioned research publication",
        "subjectScheme": "QNFO publisher classification",
        "schemeUri": "https://qnfo.org/about"
      }
    ],
    "dates": [
      {
        "date": "2026-11-11",
        "dateType": "Issued"
      },
      {
        "date": "2026-11-11",
        "dateType": "Updated"
      }
    ],
    "language": "en",
    "version": "1.0.0",
    "rightsList": [
      {
        "rightsUri": "https://legal.qnfo.org/"
      }
    ],
    "descriptions": [
      {
        "description": "Large language models (LLMs) are increasingly used to author the artifacts that other software systems must obey: specifications, system prompts, interface contracts, and validation rubrics. Practitioners currently assume that better prompting, self-critique, or meta-level instruction can raise the reliability of these authored constraint systems arbitrarily. This paper argues that assumption is false. We model LLM generation as stochastic sampling from a fixed conditional distribution and constraint satisfaction as deductive verification, and we prove a ceiling result: any prompt-level transformation of the sampling process leaves the per-constraint error rate bounded below by a model-intrinsic minimum ε_min > 0 on constraint types the model cannot self-verify, so no composition of prompts can close the reliability gap. We quantify the gap with explicit arithmetic: for a specification with N=40 constraints and a per-constraint error rate ε=0.02, a prompt-only pipeline achieves a clean-run probability of 0.98⁴0≈ 0.4457, while a hybrid pipeline in which a formal verifier catches errors with probability c=0.95 achieves (1-ε(1-c))⁴0≈ 0.9608, a factor of $2.16$ improvement that no prompt change can match under the model. The break-even count is N^*=35 constraints. The result is consistent with reported adherence thresholds of p^*≈ 0.958 per chapter and q^*≈ 0.986 per constraint in long-form drafting, and it justifies hybrid architectures in which LLMs draft and formal tools enforce.",
        "descriptionType": "Abstract"
      },
      {
        "description": "Publisher quality classification: High-quality scholarly research. QNFO publisher classification for open-access, versioned research with a public revision history and reader correction channel; this is not a claim of independent peer review.",
        "descriptionType": "Other"
      },
      {
        "description": "Peer review status: Not independently peer-reviewed",
        "descriptionType": "Other"
      }
    ],
    "formats": [
      "text/html"
    ]
  }
}