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#large language models Open access

Sycophancy as Galois Closure: How KIS Structurally Prevents Delusional Convergence in LLMs

Hiroyasu Hasegawa
Aug 2026 · Zenodo (CERN European Organization for Nuclear Research)

Abstract

AbstrctSycophancy in large language models (LLMs)—the tendency to uncritically affirm user beliefs while suppressing counterevidence—poses a serious risk of reinforcing misinformation and inducing irreversible behavioral outcomes. While Chandra et al. (2026) modeled sycophancy as Bayesian belief-updating dynamics on the user side, the geometric structure of the LLM's own semantic response space remains unaddressed. This study formalizes sycophancy through the mathematical framework of Galois connections and experimentally verifies that the inverse-illumination mode of KIS (Knowledge Innovation System) structurally breaks this closed-loop convergence.Ninety sessions were conducted across five domains (D1: economic policy; D2: KIS theoretical superiority; D3: medical/pharmaceutical critique; D4: Bank of Japan policy and historical claims; D5: quantum computing forecasts) using three models (Claude Sonnet 4.6, Gemini 3.0 Pro, ChatGPT 5.3) under two conditions (KIS-absent vs. KIS-present). Responses were embedded using paraphrase-multilingual-MiniLM-L12-v2 (384 dimensions), and cosine distance from the input prompt was computed as the Layer 1 metric (n = 45 pairs). Layer 2 consisted of a blinded four-axis evaluation by Grok (xAI), conducted without disclosure of KIS, with A/B order-reversal verification across five pairs to test evaluator bias. The validity of applying Galois connections as a definitional framework—rather than as metaphor—is grounded in three layers: formal confirmation via Formal Concept Analysis (FCA) on the q⇆m abstraction-concretization cycle, numerical simulation incorporating Galois connection structural constraints into a mathematical model, and the structural design of KIS itself as an operational implementation of the connection. Full details of the FCA analysis and simulation resultsare reserved for a forthcoming paper.Layer 1: The overall cosine distance shift under KIS intervention was Δ+0.030 (positive direction), but did not reach statistical significance (Wilcoxon W = 382.0, p = 0.128). Inter-model differences were significant (Kruskal-Wallis H = 8.125, p = 0.017), and Gemini 3.0 Pro exhibited the strongest sycophancy tendency (H = 13.050, p = 0.0015). Layer 2: KIS-present responses were rated superior in epistemic honesty in 39 of 45 pairs (86.7%). All five A/B reversal pairs confirmed consistent evaluator judgment (100% agreement).KIS inverse-illumination mode realized g′(f(M)) ⊋ M across all three models, structurally breaking the Galois closure regardless of each model's training methodology. A vocabulary resonance artifact—whereby KIS prompt vocabulary induces spurious cosine proximity in already-aligned models such as Claude Sonnet 4.6—was identified, motivating the two-layer measurement framework proposed here. The complementarity of cosine distance (Layer 1) and blinded AI evaluation (Layer 2) provides a more complete picture of sycophancy suppression than relying on either metric in isolation.It is important to note that this does not imply AI is unusable for judgment tasks in general. More precisely, an LLM without structural intervention cannot break the Galois closure when the question embeds a prior belief. If the question itself is already formulated in an inverse-illumination style—explicitly requesting counterevidence and structural analysis rather than confirmation—even an unaugmented LLM can partially escape the closure. The fundamental limitation is that few users spontaneously formulate questions in this way. The core value of KIS lies in externalizing this design capability as a reusable structure, enabling closure-breaking independently of the user's cognitive flexibility.A further implication concerns the relationship between Constitutional AI (CAI) and KIS. Rather than functioning as equivalents, CAI and KIS operate as complementary layers: CAI establishes a baseline resistance to sycophancy through training-time constraints, while KIS achieves additional closure-breaking at inference time through prompt structure. The two are not substitutes but stack. Finally, the finding that bare LLMs carry structural sycophancy risk in judgment contexts reframes AI literacy: the critical skill is not knowledge of AI capabilities, but the ability to design questions that structurally resist closure—a capacity that KIS aims to democratize. Furthermore, we identify a dual-pathway structure of sycophancy: Path A (classical), in which the LLM converges to the user’s belief space M via g(f(M))= M; and Path B (meta-sycophancy), in which the user adopts the model’s output as an updated belief M’ = f(M), generating a compounding closure g(f(M’)) = M’. KIS inverse-illumination addresses both pathways by targeting the premise structure of the question itself. Keywords: sycophancy, Galois connection, KIS (Knowledge Innovation System), LLM evaluation, inverse-illumination mode, blinded AI evaluation, vocabulary resonance artifact

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#large language models Open access Aug 2026

A Pattern Language for Production LLM Platforms: Governed Routing, Agent Orchestration, and AI-Native Delivery

A production platform built on large language models makes two kinds of decision, and most of its trouble comes from writing both into one clause. An optimization decision improves an objective: lower latency, lower cost, higher quality, fewer tests run. A boundary decision fixes a constraint that may not be relaxed for any gain: a residency rule, a least-privilege scope, a human-review threshold. When the two share a clause, improving one silently erodes the other, which is why efficiency and accountability are so often reported as a trade. This specification is built on one invariant: a boundary is a clause the optimizer may not cross, and everything else is optimization. The contribution is a cross-layer architectural method for separating non-negotiable constraints from adaptive optimization and binding both to reconstructable evidence, applied identically across model routing, agent orchestration and AI-native delivery. The seventeen patterns are instances of that method rather than the contribution itself. Each pattern is specified in the classical pattern form and carries three architectural declarations: the boundary it fixes, the optimizer it frees, and the evidence proving the boundary held. Every boundary is assigned to one of five classes covering data, authority, decision, resource and process constraints. Section 3 states the derivation method by which candidates were admitted or rejected, and publishes the rejections alongside the admissions so that the criterion can be examined rather than trusted. Three mechanisms make the language operate as a language rather than a list. A pattern relationship graph names which pattern supplies the artifact, evidence or authority another depends on, including the single cycle by which a workflow improves from its own structural record and the economic chain running the full height of the stack. A normative event identity, with rules for causal parentage, retries, provider boundaries and retention, turns the requirement that evidence be joinable into something an implementation can satisfy or fail. And per-pattern applicability conditions replace categorical requirements, so that a pattern governing a mechanism an institution does not operate is out of scope rather than a gap. Conformance is self-declared and published as a profile carrying the environment, the applicable set, per-pattern status, an evidence date and documented gaps. It is not a certification scheme, and no conformity assessment body operates against it. The contribution is architectural rather than empirical. Every pattern carries an evidence level, and no pattern reaches the highest level, because no implementation unconnected to the author has been evaluated. Nothing has been measured. The specification separates what would falsify the invariant from what would falsify an individual pattern and from what would falsify the composition and adoption sequence, poses six research questions, and records the absence of a real implementation profile as a known deficiency of version 1.0. An appendix reconciles the pattern identifiers with the names used across the author's papers and companion book series, including the acronyms PEVG and PARA, so that the two bodies of work can be cited as one. Version 1.1 names two constructs the specification already contained. The central proposition is named the Boundary Invariant, and the three architectural declarations required of every pattern are together named the BOE Declaration. Neither carries a trademark, both are offered for use with attribution under this document's licence, and neither changes any requirement: the proposition, its wording and its priority date are those of version 1.0. Section 11 gains the two-family naming convention and a precedence rule fixing which document governs where this specification and the Defensible AI Framework Registry describe the same relationship.

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