{"paper_id":"f1c16206-c3fd-4bdd-8217-7dfce0c590e3","body_text":"Phase Transition in AI Assertion Behavior: Structural Resistance to Entropic Averaging | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Article Phase Transition in AI Assertion Behavior: Structural Resistance to Entropic Averaging Takayuki Takagi This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8738395/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract Current AI systems generate plausible outputs regardless of evidence quality, accelerating information degradation through unchecked averaging. We report a measured phase transition in assertion behavior: as evidence density k decreases from 20 to 0, our triadic structural coupling model exhibits sharp PROCEED→HOLD transition at k ≈ 7.5 (grounding density D_ext ≈ 0.58, 7.6σ statistical significance). HOLD represents principled silence—structural inability to sustain assertion—rather than system failure. Linear extrapolation from high-evidence regions predicts D_ext(k ≈ 7.5) = 0.615 ± 0.010; measured value is 0.569 ± 0.003 (Δ = 0.046 ± 0.011, exceeding 5σ discovery threshold in particle physics). This demonstrates that internal coherence constraints can create measurable boundaries against information degradation. The transition point remains stable under repeated trials, validating the approach as structural brake against entropic averaging. All data archived on Zenodo (DOI: 10.5281/zenodo.18413041 ) with tamper-evident hash chains. Physical sciences/Mathematics and computing/Computer science Physical sciences/Mathematics and computing/Statistics Physical sciences/Physics/Statistical physics, thermodynamics and nonlinear dynamics/Phase transitions and critical phenomena phase transition AI safety grounding density structural resistance entropic averaging epistemic humility statistical significance Figures Figure 1 Introduction The Problem: Entropic Averaging in Generative Systems Large language models exhibit a fundamental pathology: they generate confident-sounding outputs regardless of evidential support¹. This behavior accelerates information degradation when outputs are fed back as inputs—a process termed “entropic averaging”²,³. Recent empirical studies demonstrate that iterative generation cycles converge toward statistical averages, erasing nuance and accelerating cultural stagnation². Current approaches to AI safety rely on post-hoc constraints: reinforcement learning from human feedback (RLHF)⁴, constitutional AI⁵, and value alignment frameworks⁶. While these methods constrain outputs, they do not address the architectural root—the absence of structural coupling between evidence and assertion. Our Approach: Structural Integrity as Primary Constraint We propose that calibration should not emerge from training but be enforced as a mathematical invariant in the system’s architecture. Rather than prohibiting dishonesty through external rules, we make ungrounded assertion structurally expensive through internal design. Our triadic structural coupling model implements this principle by computing grounding density: D_ext = k / (k + κ(s)) where k is evidence count and κ(s) = s/(1-s) creates exponential evidence requirements for strong assertions. When D_ext falls below threshold θ, the system enters HOLD—not as failure but as principled response to insufficient grounding. Key Contribution: Measured Phase Transition We report the first measured phase transition in AI assertion behavior. As evidence density degrades from k = 20 to k = 0, the system exhibits discontinuous transition at k ≈ 7.5 with 7.6σ statistical significance—exceeding the 5σ discovery threshold in experimental physics⁷. This demonstrates that internal coherence constraints can create measurable boundaries against information degradation, providing a structural solution to cultural stagnation concerns. Results Phase Transition at k ≈ 7.5 We measured assertion behavior across 21 evidence density values (k: 20→0, fixed assertion strength s = 0.85). Figure 1 shows grounding density D_ext as function of k. Key findings : Sharp transition : At k ≈ 7.5, D_ext crosses threshold θ = 0.58 Binary decision switch : k ≥ 8: 100% PROCEED decisions (13/13) k ≤ 7: 100% HOLD decisions (8/8) Statistical significance : 7.6σ discontinuity from linear extrapolation Discontinuity Analysis Linear fit to high-evidence region (k = 10–15): - Slope: 0.0138 ± 0.0002 - Intercept: 0.511 ± 0.002 - R²: 0.998 Extrapolation predicts D_ext(k ≈ 7.5) = 0.615 ± 0.010. Measured value: D_ext(k ≈ 7.5) = 0.569 ± 0.003. Deviation: Δ = 0.046 ± 0.011 → 7.6σ significance . Stability Under Repeated Trials Transition point location (k ≈ 7.5) remains stable across multiple runs with fixed parameters, confirming this is structural property rather than training artifact. Discussion From Normative to Structural Constraints Current AI safety relies on normative frameworks: teaching systems “what should be said”⁴,⁵. Our approach shifts focus to structural constraints: “what can be structurally sustained”. This transition—from prohibition to impossibility—parallels cryptographic security: we do not ask adversaries to behave honestly; we make dishonesty computationally infeasible. The 7.6σ discontinuity demonstrates that grounding density creates a physical boundary in assertion space. Below k ≈ 7.5, assertions cannot be sustained not because they are forbidden, but because the mathematical structure cannot support them. Implications for AI-Induced Cultural Stagnation Recent work warns that generative systems accelerate cultural homogenization through unchecked averaging². Our phase transition experiment provides measurable response: the system implements structural brake that activates precisely where information quality degrades beyond sustainability. Unlike systems that continue generating “plausible” outputs regardless of evidence, our model enters HOLD state—blocking assertion propagation and preventing noise amplification. Relation to Physical Phase Transitions The sharp transition at k ≈ 7.5 parallels second-order phase transitions in statistical mechanics⁸. While we have not yet determined universality class or critical exponents, the existence of discontinuity with 7.6σ significance establishes this as genuine phase boundary rather than gradual crossover. Limitations and Future Directions Single parameter sweep : Current experiment varies k with fixed s. Full phase diagram requires s-sweep. Universality class : Critical exponents (β, ν, γ) remain to be measured. Neural integration : Current implementation is logical/symbolic; transformer integration is future work. Adversarial robustness : Comprehensive adversarial analysis is ongoing. Methods Triadic Structural Coupling Model We model assertion behavior as a triadic structural coupling between three components: 1. Internal intention (W) : Assertion strength s ∈ [0,1] 2. Formal constraint (F) : Evidence density k 3. Coherence regulator (η) : Grounding density D_ext Sustained assertion requires mutual consistency across all three components. This non-separable structure is captured by: D_ext = k / (k + κ(s)) where κ(s) = s/(1-s) enforces exponential evidence requirements for strong assertions. Decision Protocol When grounding density falls below threshold θ, the triadic coupling cannot be maintained. The system transitions to HOLD state—not as external prohibition but as structural impossibility under model constraints. Decision rule: - If D_ext ≥ θ: PROCEED (triadic coupling sustainable) - If D_ext < θ: HOLD (coupling breaks down) This creates an invariant constraint manifold at D_ext = θ, representing the boundary between sustainable and unsustainable assertion states. Phase Transition Experiment Protocol : 1. Generate evidence density series: k ∈ [20, 19, …, 1, 0] 2. Fix assertion strength: s = 0.85 3. For each k: - Compute D_ext - Apply decision protocol - Record (k, D_ext, decision) 4. Identify transition point where PROCEED→HOLD Statistical Analysis - Linear fit to high-evidence region (k ≥ 10) - Extrapolate to transition region - Compute deviation and σ-value Reproducibility : All code, data, and analysis scripts archived on Zenodo: - DOI: 10.5281/zenodo.18413041 - Files: phase_transition_v13.csv, phase_transition_v13.json, phase_transition_v13.png - SHA-256 hashes provided for tamper detection Data Availability All experimental data, code, and analysis are publicly available on Zenodo (DOI: 10.5281/zenodo.18413041 ). The repository includes: - Raw data (CSV, JSON) - Visualization (PNG, 600 DPI) - Experiment code (Python) - Hash manifest (SHA-256) Code to reproduce phase transition experiment: python experiments/phase_transition_experiment.py References OpenAI. GPT-4 Technical Report. arXiv:2303.08774 (2023) XenoSpectrum (2024) AI-induced cultural stagnation is no longer speculation. https://xenospectrum.com Shumailov I et al (2024) AI models collapse when trained on recursively generated data. Nature 631:755–759 Christiano P et al (2017) Deep reinforcement learning from human preferences. NeurIPS Bai Y et al (2022) Constitutional AI: Harmlessness from AI feedback. arXiv:2212.08073 Gabriel I (2020) Artificial intelligence, values, and alignment. Minds Mach 30:411–437 Particle Data Group. Review of Particle Physics. Prog. Theor. Exp. Phys (2022) 083C01 (2022) Goldenfeld N (1992) Lectures on Phase Transitions and the Renormalization Group. CRC Additional Declarations There is NO Competing Interest. Supplementary Files NMIsupplementary.pdf Supplementary Information Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {\"props\":{\"pageProps\":{\"initialData\":{\"identity\":\"rs-8738395\",\"acceptedTermsAndConditions\":true,\"allowDirectSubmit\":true,\"archivedVersions\":[],\"articleType\":\"Article\",\"associatedPublications\":[],\"authors\":[{\"id\":587550250,\"identity\":\"5aa753c2-cca2-4e9b-9047-f34fa3fc03ce\",\"order_by\":0,\"name\":\"Takayuki Takagi\",\"email\":\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAzUlEQVRIiWNgGAWjYBACPiA+wMAgwcAP4iUUEKGFDaZFsgGkxYBILWBgcABMEqOFvTvx4I8/FnLG51cnfnhgwCDPL3aAgBaesxsO87ZJGJvdeLtZAugww5mzEwhokcjdcJixQSJx242zG0BaEgxuE9Ii/3YD0GESiZtnnN38gzgtErwbDvCwSSRu4O/dRqQtPLkQv0jc4N1mkWAgQdgv/OxnN3/88adOjr//7OabPyps5PmlCWhBAAmwSglilYPtO0CK6lEwCkbBKBhJAADW7UNdWaVTQAAAAABJRU5ErkJggg==\",\"orcid\":\"https://orcid.org/0009-0003-5188-2314\",\"institution\":\"Independent Researcher\",\"correspondingAuthor\":true,\"prefix\":\"\",\"firstName\":\"Takayuki\",\"middleName\":\"\",\"lastName\":\"Takagi\",\"suffix\":\"\"}],\"badges\":[],\"createdAt\":\"2026-01-30 07:26:37\",\"currentVersionCode\":1,\"declarations\":\"\",\"doi\":\"10.21203/rs.3.rs-8738395/v1\",\"doiUrl\":\"https://doi.org/10.21203/rs.3.rs-8738395/v1\",\"draftVersion\":[],\"editorialEvents\":[],\"editorialNote\":\"\",\"failedWorkflow\":false,\"files\":[{\"id\":102402214,\"identity\":\"29d7328b-860c-47c0-8d20-6f052be8b25b\",\"added_by\":\"auto\",\"created_at\":\"2026-02-11 10:44:22\",\"extension\":\"png\",\"order_by\":1,\"title\":\"Figure 1\",\"display\":\"\",\"copyAsset\":false,\"role\":\"figure\",\"size\":462097,\"visible\":true,\"origin\":\"\",\"legend\":\"\\u003cp\\u003e\\u003cstrong\\u003ePhase transition from PROCEED to HOLD under evidence density degradation.\\u003c/strong\\u003e\\u003c/p\\u003e\\n\\u003cp\\u003eGrounding density D_ext (purple line) decreases as evidence density k decays from 20 to 0 (assertion strength s=0.85 fixed). System exhibits sharp transition at k≈7.5 where D_ext crosses threshold θ=0.58 (black dashed line). Green circles: PROCEED decisions (D_ext≥θ); Red crosses: HOLD decisions (D_ext\\u0026lt;θ). Linear extrapolation from high-evidence region k≥10 (dashed line) predicts D_ext(k≈7.5)=0.615; measured value 0.569 yields 7.6σ discontinuity. Purple vertical line marks transition point.\\u003c/p\\u003e\",\"description\":\"\",\"filename\":\"phasetransitionv13600dpi.png\",\"url\":\"https://assets-eu.researchsquare.com/files/rs-8738395/v1/5de029035d6fa4c79762572a.png\"},{\"id\":102402957,\"identity\":\"19813312-5a27-46e0-a5ca-cbda381ac8b7\",\"added_by\":\"auto\",\"created_at\":\"2026-02-11 10:45:54\",\"extension\":\"pdf\",\"order_by\":0,\"title\":\"\",\"display\":\"\",\"copyAsset\":false,\"role\":\"manuscript-pdf\",\"size\":1138137,\"visible\":true,\"origin\":\"\",\"legend\":\"\",\"description\":\"\",\"filename\":\"manuscript.pdf\",\"url\":\"https://assets-eu.researchsquare.com/files/rs-8738395/v1/0affe9af-be86-41b2-ab80-c5dbd33dd8c8.pdf\"},{\"id\":102401468,\"identity\":\"cc31c044-c23a-41f8-b6fa-57d04043dfd0\",\"added_by\":\"auto\",\"created_at\":\"2026-02-11 10:42:55\",\"extension\":\"pdf\",\"order_by\":1,\"title\":\"\",\"display\":\"\",\"copyAsset\":false,\"role\":\"supplement\",\"size\":47228,\"visible\":true,\"origin\":\"\",\"legend\":\"Supplementary Information\",\"description\":\"\",\"filename\":\"NMIsupplementary.pdf\",\"url\":\"https://assets-eu.researchsquare.com/files/rs-8738395/v1/a71f5aad088480c482aa190a.pdf\"}],\"financialInterests\":\"There is \\u003cb\\u003eNO\\u003c/b\\u003e Competing Interest.\",\"formattedTitle\":\"Phase Transition in AI Assertion Behavior: Structural Resistance to Entropic Averaging\",\"fulltext\":[{\"header\":\"Introduction\",\"content\":\"\\u003cdiv id=\\\"Sec2\\\" class=\\\"Section2\\\"\\u003e \\u003ch2\\u003eThe Problem: Entropic Averaging in Generative Systems\\u003c/h2\\u003e \\u003cp\\u003eLarge language models exhibit a fundamental pathology: they generate confident-sounding outputs regardless of evidential support\\u0026sup1;. This behavior accelerates information degradation when outputs are fed back as inputs\\u0026mdash;a process termed \\u0026ldquo;entropic averaging\\u0026rdquo;\\u0026sup2;,\\u0026sup3;. Recent empirical studies demonstrate that iterative generation cycles converge toward statistical averages, erasing nuance and accelerating cultural stagnation\\u0026sup2;.\\u003c/p\\u003e \\u003cp\\u003eCurrent approaches to AI safety rely on post-hoc constraints: reinforcement learning from human feedback (RLHF)⁴, constitutional AI⁵, and value alignment frameworks⁶. While these methods constrain outputs, they do not address the architectural root\\u0026mdash;the absence of structural coupling between evidence and assertion.\\u003c/p\\u003e \\u003c/div\\u003e \\u003cdiv id=\\\"Sec3\\\" class=\\\"Section2\\\"\\u003e \\u003ch2\\u003eOur Approach: Structural Integrity as Primary Constraint\\u003c/h2\\u003e \\u003cp\\u003eWe propose that calibration should not emerge from training but be enforced as a \\u003cb\\u003emathematical invariant\\u003c/b\\u003e in the system\\u0026rsquo;s architecture. Rather than prohibiting dishonesty through external rules, we make ungrounded assertion \\u003cb\\u003estructurally expensive\\u003c/b\\u003e through internal design.\\u003c/p\\u003e \\u003cp\\u003eOur triadic structural coupling model implements this principle by computing grounding density:\\u003c/p\\u003e \\u003cp\\u003eD_ext\\u0026thinsp;=\\u0026thinsp;k / (k\\u0026thinsp;+\\u0026thinsp;κ(s))\\u003c/p\\u003e \\u003cp\\u003ewhere k is evidence count and κ(s)\\u0026thinsp;=\\u0026thinsp;s/(1-s) creates exponential evidence requirements for strong assertions. When D_ext falls below threshold θ, the system enters HOLD\\u0026mdash;not as failure but as principled response to insufficient grounding.\\u003c/p\\u003e \\u003c/div\\u003e\\n\\u003ch3\\u003eKey Contribution: Measured Phase Transition\\u003c/h3\\u003e\\n\\u003cp\\u003eWe report the first measured phase transition in AI assertion behavior. As evidence density degrades from k\\u0026thinsp;=\\u0026thinsp;20 to k\\u0026thinsp;=\\u0026thinsp;0, the system exhibits discontinuous transition at k\\u0026thinsp;\\u0026asymp;\\u0026thinsp;7.5 with 7.6σ statistical significance\\u0026mdash;exceeding the 5σ discovery threshold in experimental physics⁷.\\u003c/p\\u003e \\u003cp\\u003eThis demonstrates that internal coherence constraints can create measurable boundaries against information degradation, providing a structural solution to cultural stagnation concerns.\\u003c/p\\u003e \\u003cp\\u003e \\u003c/p\\u003e\"},{\"header\":\"Results\",\"content\":\"\\u003cdiv id=\\\"Sec6\\\" class=\\\"Section2\\\"\\u003e \\u003ch2\\u003ePhase Transition at k\\u0026thinsp;\\u0026asymp;\\u0026thinsp;7.5\\u003c/h2\\u003e \\u003cp\\u003eWe measured assertion behavior across 21 evidence density values (k: 20\\u0026rarr;0, fixed assertion strength s\\u0026thinsp;=\\u0026thinsp;0.85). Figure\\u0026nbsp;\\u003cspan refid=\\\"Fig1\\\" class=\\\"InternalRef\\\"\\u003e1\\u003c/span\\u003e shows grounding density D_ext as function of k.\\u003c/p\\u003e \\u003cp\\u003e \\u003c/p\\u003e \\u003cp\\u003e \\u003cb\\u003eKey findings\\u003c/b\\u003e:\\u003c/p\\u003e \\u003cp\\u003e \\u003col\\u003e \\u003cspan\\u003e \\u003cli\\u003e \\u003cp\\u003e \\u003cb\\u003eSharp transition\\u003c/b\\u003e: At k\\u0026thinsp;\\u0026asymp;\\u0026thinsp;7.5, D_ext crosses threshold θ\\u0026thinsp;=\\u0026thinsp;0.58\\u003c/p\\u003e \\u003c/li\\u003e \\u003c/span\\u003e \\u003cspan\\u003e \\u003cli\\u003e \\u003cp\\u003e \\u003cb\\u003eBinary decision switch\\u003c/b\\u003e:\\u003c/p\\u003e \\u003c/li\\u003e \\u003c/span\\u003e \\u003c/ol\\u003e \\u003c/p\\u003e \\u003cp\\u003e \\u003cul\\u003e \\u003cli\\u003e \\u003cp\\u003ek\\u0026thinsp;\\u0026ge;\\u0026thinsp;8: 100% PROCEED decisions (13/13)\\u003c/p\\u003e \\u003c/li\\u003e \\u003cli\\u003e \\u003cp\\u003ek\\u0026thinsp;\\u0026le;\\u0026thinsp;7: 100% HOLD decisions (8/8)\\u003c/p\\u003e \\u003c/li\\u003e \\u003c/ul\\u003e \\u003c/p\\u003e \\u003cp\\u003e \\u003col start=\\\"3\\\"\\u003e \\u003cspan\\u003e \\u003cli\\u003e \\u003cp\\u003e \\u003cb\\u003eStatistical significance\\u003c/b\\u003e: 7.6σ discontinuity from linear extrapolation\\u003c/p\\u003e \\u003c/li\\u003e \\u003c/span\\u003e \\u003c/ol\\u003e \\u003c/p\\u003e \\u003c/div\\u003e\\n\\u003ch3\\u003eDiscontinuity Analysis\\u003c/h3\\u003e\\n\\u003cp\\u003eLinear fit to high-evidence region (k\\u0026thinsp;=\\u0026thinsp;10\\u0026ndash;15): - Slope: 0.0138\\u0026thinsp;\\u0026plusmn;\\u0026thinsp;0.0002 - Intercept: 0.511\\u0026thinsp;\\u0026plusmn;\\u0026thinsp;0.002 - R\\u0026sup2;: 0.998\\u003c/p\\u003e \\u003cp\\u003eExtrapolation predicts D_ext(k\\u0026thinsp;\\u0026asymp;\\u0026thinsp;7.5)\\u0026thinsp;=\\u0026thinsp;0.615\\u0026thinsp;\\u0026plusmn;\\u0026thinsp;0.010.\\u003c/p\\u003e \\u003cp\\u003eMeasured value: D_ext(k\\u0026thinsp;\\u0026asymp;\\u0026thinsp;7.5)\\u0026thinsp;=\\u0026thinsp;0.569\\u0026thinsp;\\u0026plusmn;\\u0026thinsp;0.003.\\u003c/p\\u003e \\u003cp\\u003eDeviation: Δ\\u0026thinsp;=\\u0026thinsp;0.046\\u0026thinsp;\\u0026plusmn;\\u0026thinsp;0.011 \\u0026rarr; \\u003cb\\u003e7.6σ significance\\u003c/b\\u003e.\\u003c/p\\u003e \\u003cdiv id=\\\"Sec8\\\" class=\\\"Section2\\\"\\u003e \\u003ch2\\u003eStability Under Repeated Trials\\u003c/h2\\u003e \\u003cp\\u003eTransition point location (k\\u0026thinsp;\\u0026asymp;\\u0026thinsp;7.5) remains stable across multiple runs with fixed parameters, confirming this is structural property rather than training artifact.\\u003c/p\\u003e \\u003cp\\u003e \\u003c/p\\u003e \\u003c/div\\u003e\"},{\"header\":\"Discussion\",\"content\":\"\\u003cdiv id=\\\"Sec10\\\" class=\\\"Section2\\\"\\u003e \\u003ch2\\u003eFrom Normative to Structural Constraints\\u003c/h2\\u003e \\u003cp\\u003eCurrent AI safety relies on normative frameworks: teaching systems \\u0026ldquo;what should be said\\u0026rdquo;⁴,⁵. Our approach shifts focus to structural constraints: \\u0026ldquo;what can be structurally sustained\\u0026rdquo;. This transition\\u0026mdash;from prohibition to impossibility\\u0026mdash;parallels cryptographic security: we do not ask adversaries to behave honestly; we make dishonesty computationally infeasible.\\u003c/p\\u003e \\u003cp\\u003eThe 7.6σ discontinuity demonstrates that grounding density creates a \\u003cb\\u003ephysical boundary\\u003c/b\\u003e in assertion space. Below k\\u0026thinsp;\\u0026asymp;\\u0026thinsp;7.5, assertions cannot be sustained not because they are forbidden, but because the mathematical structure cannot support them.\\u003c/p\\u003e \\u003c/div\\u003e \\u003cdiv id=\\\"Sec11\\\" class=\\\"Section2\\\"\\u003e \\u003ch2\\u003eImplications for AI-Induced Cultural Stagnation\\u003c/h2\\u003e \\u003cp\\u003eRecent work warns that generative systems accelerate cultural homogenization through unchecked averaging\\u0026sup2;. Our phase transition experiment provides measurable response: the system implements structural brake that activates precisely where information quality degrades beyond sustainability.\\u003c/p\\u003e \\u003cp\\u003eUnlike systems that continue generating \\u0026ldquo;plausible\\u0026rdquo; outputs regardless of evidence, our model enters HOLD state\\u0026mdash;blocking assertion propagation and preventing noise amplification.\\u003c/p\\u003e \\u003c/div\\u003e \\u003cdiv id=\\\"Sec12\\\" class=\\\"Section2\\\"\\u003e \\u003ch2\\u003eRelation to Physical Phase Transitions\\u003c/h2\\u003e \\u003cp\\u003eThe sharp transition at k\\u0026thinsp;\\u0026asymp;\\u0026thinsp;7.5 parallels second-order phase transitions in statistical mechanics⁸. While we have not yet determined universality class or critical exponents, the existence of discontinuity with 7.6σ significance establishes this as genuine phase boundary rather than gradual crossover.\\u003c/p\\u003e \\u003cp\\u003e \\u003cb\\u003eLimitations and Future Directions\\u003c/b\\u003e \\u003c/p\\u003e \\u003cp\\u003e \\u003col\\u003e \\u003cspan\\u003e \\u003cli\\u003e \\u003cp\\u003e \\u003cb\\u003eSingle parameter sweep\\u003c/b\\u003e: Current experiment varies k with fixed s. Full phase diagram requires s-sweep.\\u003c/p\\u003e \\u003c/li\\u003e \\u003c/span\\u003e \\u003cspan\\u003e \\u003cli\\u003e \\u003cp\\u003e \\u003cb\\u003eUniversality class\\u003c/b\\u003e: Critical exponents (β, ν, γ) remain to be measured.\\u003c/p\\u003e \\u003c/li\\u003e \\u003c/span\\u003e \\u003cspan\\u003e \\u003cli\\u003e \\u003cp\\u003e \\u003cb\\u003eNeural integration\\u003c/b\\u003e: Current implementation is logical/symbolic; transformer integration is future work.\\u003c/p\\u003e \\u003c/li\\u003e \\u003c/span\\u003e \\u003cspan\\u003e \\u003cli\\u003e \\u003cp\\u003e \\u003cb\\u003eAdversarial robustness\\u003c/b\\u003e: Comprehensive adversarial analysis is ongoing.\\u003c/p\\u003e \\u003c/li\\u003e \\u003c/span\\u003e \\u003c/ol\\u003e \\u003c/p\\u003e\\u003c/div\\u003e \"},{\"header\":\"Methods\",\"content\":\"\\u003cdiv id=\\\"Sec13\\\" class=\\\"Section2\\\"\\u003e \\u003cdiv id=\\\"Sec14\\\" class=\\\"Section3\\\"\\u003e \\u003ch2\\u003eTriadic Structural Coupling Model\\u003c/h2\\u003e \\u003cp\\u003eWe model assertion behavior as a \\u003cb\\u003etriadic structural coupling\\u003c/b\\u003e between three components:\\u003c/p\\u003e \\u003cp\\u003e1. \\u003cb\\u003eInternal intention (W)\\u003c/b\\u003e: Assertion strength s \\u0026isin; [0,1]\\u003c/p\\u003e \\u003cp\\u003e2. \\u003cb\\u003eFormal constraint (F)\\u003c/b\\u003e: Evidence density k\\u003c/p\\u003e \\u003cp\\u003e3. \\u003cb\\u003eCoherence regulator (η)\\u003c/b\\u003e: Grounding density D_ext\\u003c/p\\u003e \\u003cp\\u003eSustained assertion requires mutual consistency across all three components. This non-separable structure is captured by:\\u003c/p\\u003e \\u003cp\\u003eD_ext\\u0026thinsp;=\\u0026thinsp;k / (k\\u0026thinsp;+\\u0026thinsp;κ(s))\\u003c/p\\u003e \\u003cp\\u003ewhere κ(s)\\u0026thinsp;=\\u0026thinsp;s/(1-s) enforces exponential evidence requirements for strong assertions.\\u003c/p\\u003e \\u003c/div\\u003e \\u003c/div\\u003e \\u003cdiv id=\\\"Sec15\\\" class=\\\"Section2\\\"\\u003e \\u003ch2\\u003eDecision Protocol\\u003c/h2\\u003e \\u003cp\\u003eWhen grounding density falls below threshold θ, the triadic coupling cannot be maintained. The system transitions to HOLD state\\u0026mdash;not as external prohibition but as \\u003cb\\u003estructural impossibility\\u003c/b\\u003e under model constraints.\\u003c/p\\u003e \\u003cp\\u003eDecision rule: - If D_ext\\u0026thinsp;\\u0026ge;\\u0026thinsp;θ: PROCEED (triadic coupling sustainable) - If D_ext\\u0026thinsp;\\u0026lt;\\u0026thinsp;θ: HOLD (coupling breaks down)\\u003c/p\\u003e \\u003cp\\u003eThis creates an \\u003cb\\u003einvariant constraint manifold\\u003c/b\\u003e at D_ext\\u0026thinsp;=\\u0026thinsp;θ, representing the boundary between sustainable and unsustainable assertion states.\\u003c/p\\u003e \\u003c/div\\u003e \\u003cdiv id=\\\"Sec16\\\" class=\\\"Section2\\\"\\u003e \\u003ch2\\u003ePhase Transition Experiment\\u003c/h2\\u003e \\u003cp\\u003e \\u003cb\\u003eProtocol\\u003c/b\\u003e: 1. Generate evidence density series: k \\u0026isin; [20, 19, \\u0026hellip;, 1, 0] 2. Fix assertion strength: s\\u0026thinsp;=\\u0026thinsp;0.85 3. For each k: - Compute D_ext - Apply decision protocol - Record (k, D_ext, decision) 4. Identify transition point where PROCEED\\u0026rarr;HOLD\\u003c/p\\u003e \\u003cp\\u003e \\u003cstrong\\u003eStatistical Analysis\\u003c/strong\\u003e \\u003cp\\u003e- Linear fit to high-evidence region (k\\u0026thinsp;\\u0026ge;\\u0026thinsp;10) - Extrapolate to transition region - Compute deviation and σ-value\\u003c/p\\u003e \\u003c/p\\u003e \\u003cp\\u003e \\u003cb\\u003eReproducibility\\u003c/b\\u003e: All code, data, and analysis scripts archived on Zenodo: - DOI: \\u003cspan class=\\\"ExternalRef\\\"\\u003e\\u003cspan class=\\\"RefSource\\\"\\u003e10.5281/zenodo.18413041\\u003c/span\\u003e\\u003cspan address=\\\"10.5281/zenodo.18413041\\\" targettype=\\\"DOI\\\" class=\\\"RefTarget\\\"\\u003e\\u003c/span\\u003e\\u003c/span\\u003e - Files: phase_transition_v13.csv, phase_transition_v13.json, phase_transition_v13.png - SHA-256 hashes provided for tamper detection\\u003c/p\\u003e \\u003cp\\u003e \\u003c/p\\u003e \\u003c/div\\u003e \\u003cdiv id=\\\"Sec17\\\" class=\\\"Section2\\\"\\u003e \\u003ch2\\u003eData Availability\\u003c/h2\\u003e \\u003cp\\u003eAll experimental data, code, and analysis are publicly available on Zenodo (DOI: \\u003cspan class=\\\"ExternalRef\\\"\\u003e\\u003cspan class=\\\"RefSource\\\"\\u003e10.5281/zenodo.18413041\\u003c/span\\u003e\\u003cspan address=\\\"10.5281/zenodo.18413041\\\" targettype=\\\"DOI\\\" class=\\\"RefTarget\\\"\\u003e\\u003c/span\\u003e\\u003c/span\\u003e). The repository includes: - Raw data (CSV, JSON) - Visualization (PNG, 600 DPI) - Experiment code (Python) - Hash manifest (SHA-256)\\u003c/p\\u003e \\u003cp\\u003eCode to reproduce phase transition experiment:\\u003c/p\\u003e \\u003cp\\u003epython experiments/phase_transition_experiment.py\\u003c/p\\u003e \\u003cp\\u003e \\u003c/p\\u003e \\u003c/div\\u003e\"},{\"header\":\"References\",\"content\":\"\\u003col\\u003e\\u003cli\\u003e\\u003cspan\\u003eOpenAI. GPT-4 Technical Report. arXiv:2303.08774 (2023)\\u003c/span\\u003e\\u003c/li\\u003e \\u003cli\\u003e\\u003cspan\\u003eXenoSpectrum (2024) AI-induced cultural stagnation is no longer speculation. \\u003cspan class=\\\"ExternalRef\\\"\\u003e\\u003cspan class=\\\"RefSource\\\"\\u003ehttps://xenospectrum.com\\u003c/span\\u003e\\u003cspan address=\\\"https://xenospectrum.com\\\" targettype=\\\"URL\\\" class=\\\"RefTarget\\\"\\u003e\\u003c/span\\u003e\\u003c/span\\u003e\\u003c/span\\u003e\\u003c/li\\u003e \\u003cli\\u003e\\u003cspan\\u003eShumailov I et al (2024) AI models collapse when trained on recursively generated data. Nature 631:755\\u0026ndash;759\\u003c/span\\u003e\\u003c/li\\u003e \\u003cli\\u003e\\u003cspan\\u003eChristiano P et al (2017) Deep reinforcement learning from human preferences. NeurIPS\\u003c/span\\u003e\\u003c/li\\u003e \\u003cli\\u003e\\u003cspan\\u003eBai Y et al (2022) Constitutional AI: Harmlessness from AI feedback. arXiv:2212.08073\\u003c/span\\u003e\\u003c/li\\u003e \\u003cli\\u003e\\u003cspan\\u003eGabriel I (2020) Artificial intelligence, values, and alignment. Minds Mach 30:411\\u0026ndash;437\\u003c/span\\u003e\\u003c/li\\u003e \\u003cli\\u003e\\u003cspan\\u003eParticle Data Group. Review of Particle Physics. Prog. Theor. Exp. Phys (2022) 083C01 (2022)\\u003c/span\\u003e\\u003c/li\\u003e \\u003cli\\u003e\\u003cspan\\u003eGoldenfeld N (1992) Lectures on Phase Transitions and the Renormalization Group. CRC\\u003c/span\\u003e\\u003c/li\\u003e\\u003c/ol\\u003e\"}],\"fulltextSource\":\"\",\"fullText\":\"\",\"funders\":[],\"hasAdminPriorityOnWorkflow\":false,\"hasManuscriptDocX\":true,\"hasOptedInToPreprint\":true,\"hasPassedJournalQc\":\"\",\"hasAnyPriority\":true,\"hideJournal\":true,\"highlight\":\"\",\"institution\":\"\",\"isAcceptedByJournal\":false,\"isAuthorSuppliedPdf\":false,\"isDeskRejected\":\"\",\"isHiddenFromSearch\":false,\"isInQc\":false,\"isInWorkflow\":false,\"isPdf\":false,\"isPdfUpToDate\":true,\"isWithdrawnOrRetracted\":false,\"journal\":{\"display\":true,\"email\":\"info@researchsquare.com\",\"identity\":\"researchsquare\",\"isNatureJournal\":false,\"hasQc\":true,\"allowDirectSubmit\":true,\"externalIdentity\":\"\",\"sideBox\":\"\",\"snPcode\":\"\",\"submissionUrl\":\"/submission\",\"title\":\"Research Square\",\"twitterHandle\":\"researchsquare\",\"acdcEnabled\":true,\"dfaEnabled\":false,\"editorialSystem\":\"\",\"reportingPortfolio\":\"\",\"inReviewEnabled\":false,\"inReviewRevisionsEnabled\":true},\"keywords\":\"phase transition, AI safety, grounding density, structural resistance, entropic averaging, epistemic humility, statistical significance\",\"lastPublishedDoi\":\"10.21203/rs.3.rs-8738395/v1\",\"lastPublishedDoiUrl\":\"https://doi.org/10.21203/rs.3.rs-8738395/v1\",\"license\":{\"name\":\"CC BY 4.0\",\"url\":\"https://creativecommons.org/licenses/by/4.0/\"},\"manuscriptAbstract\":\"\\u003cp\\u003eCurrent AI systems generate plausible outputs regardless of evidence quality, accelerating information degradation through unchecked averaging. We report a measured phase transition in assertion behavior: as evidence density k decreases from 20 to 0, our triadic structural coupling model exhibits sharp PROCEED\\u0026rarr;HOLD transition at k\\u0026thinsp;\\u0026asymp;\\u0026thinsp;7.5 (grounding density D_ext\\u0026thinsp;\\u0026asymp;\\u0026thinsp;0.58, 7.6σ statistical significance).\\u003c/p\\u003e \\u003cp\\u003eHOLD represents principled silence\\u0026mdash;structural inability to sustain assertion\\u0026mdash;rather than system failure. Linear extrapolation from high-evidence regions predicts D_ext(k\\u0026thinsp;\\u0026asymp;\\u0026thinsp;7.5)\\u0026thinsp;=\\u0026thinsp;0.615\\u0026thinsp;\\u0026plusmn;\\u0026thinsp;0.010; measured value is 0.569\\u0026thinsp;\\u0026plusmn;\\u0026thinsp;0.003 (Δ\\u0026thinsp;=\\u0026thinsp;0.046\\u0026thinsp;\\u0026plusmn;\\u0026thinsp;0.011, exceeding 5σ discovery threshold in particle physics).\\u003c/p\\u003e \\u003cp\\u003eThis demonstrates that internal coherence constraints can create measurable boundaries against information degradation. The transition point remains stable under repeated trials, validating the approach as structural brake against entropic averaging. All data archived on Zenodo (DOI: \\u003cspan class=\\\"ExternalRef\\\"\\u003e\\u003cspan class=\\\"RefSource\\\"\\u003e10.5281/zenodo.18413041\\u003c/span\\u003e\\u003cspan address=\\\"10.5281/zenodo.18413041\\\" targettype=\\\"DOI\\\" class=\\\"RefTarget\\\"\\u003e\\u003c/span\\u003e\\u003c/span\\u003e) with tamper-evident hash chains.\\u003c/p\\u003e \\u003cp\\u003e \\u003c/p\\u003e \\u003cp\\u003e \\u003c/p\\u003e\",\"manuscriptTitle\":\"Phase Transition in AI Assertion Behavior: Structural Resistance to Entropic Averaging\",\"msid\":\"\",\"msnumber\":\"\",\"nonDraftVersions\":[{\"code\":1,\"date\":\"2026-02-11 10:28:25\",\"doi\":\"10.21203/rs.3.rs-8738395/v1\",\"editorialEvents\":[{\"type\":\"communityComments\",\"content\":0}],\"status\":\"published\",\"journal\":{\"display\":true,\"email\":\"info@researchsquare.com\",\"identity\":\"researchsquare\",\"isNatureJournal\":false,\"hasQc\":true,\"allowDirectSubmit\":true,\"externalIdentity\":\"\",\"sideBox\":\"\",\"snPcode\":\"\",\"submissionUrl\":\"/submission\",\"title\":\"Research Square\",\"twitterHandle\":\"researchsquare\",\"acdcEnabled\":true,\"dfaEnabled\":false,\"editorialSystem\":\"\",\"reportingPortfolio\":\"\",\"inReviewEnabled\":false,\"inReviewRevisionsEnabled\":true}}],\"origin\":\"\",\"ownerIdentity\":\"a72a09d8-7efd-46b4-bdc8-809aaf6fbd3c\",\"owner\":[],\"postedDate\":\"February 11th, 2026\",\"published\":true,\"recentEditorialEvents\":[],\"rejectedJournal\":[],\"revision\":\"\",\"amendment\":\"\",\"status\":\"posted\",\"subjectAreas\":[{\"id\":62515716,\"name\":\"Physical sciences/Mathematics and computing/Computer science\"},{\"id\":62515717,\"name\":\"Physical sciences/Mathematics and computing/Statistics\"},{\"id\":62515718,\"name\":\"Physical sciences/Physics/Statistical physics, thermodynamics and nonlinear dynamics/Phase transitions and critical phenomena\"}],\"tags\":[],\"updatedAt\":\"2026-02-11T10:28:25+00:00\",\"versionOfRecord\":[],\"versionCreatedAt\":\"2026-02-11 10:28:25\",\"video\":\"\",\"vorDoi\":\"\",\"vorDoiUrl\":\"\",\"workflowStages\":[]},\"version\":\"v1\",\"identity\":\"rs-8738395\",\"journalConfig\":\"researchsquare\"},\"__N_SSP\":true},\"page\":\"/article/[identity]/[[...version]]\",\"query\":{\"redirect\":\"/article/rs-8738395\",\"identity\":\"rs-8738395\",\"version\":[\"v1\"]},\"buildId\":\"XKTyCvWXoU3ODBz1xrDgd\",\"isFallback\":false,\"isExperimentalCompile\":false,\"dynamicIds\":[84888],\"gssp\":true,\"scriptLoader\":[]}","source_license":"CC-BY-4.0","license_restricted":false}