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Main Authors:	XENOPOULOU-TYROKOMOU, AKATERINH, Xenopoulos(In memoriam), Epameinondas
Format:	Recurso digital
Language:
Published:	Zenodo 2026
Subjects:	Bounded chaotic attractor Nonlinear discrete system Finite memory Dialectical logic Lyapunov exponent Stretching–folding Structural stability Scaling saturation Absolute ceiling Reproducibility EXDT (Epameinondas Xenopoulos Dialectical Transformer) Xenopoulos Unity Field XEPTQLRI Dialectical measurement Numerical documentation Text analysis Multidimensional dynamics Historical feedback Competitive feedback Complex analysis bounded chaos finite memory system dialectical dynamics chaotic attractor with ceiling numerical reproducibility text complexity analysis historical feedback system competitive feedback stretching folding mechanism Xenopoulos model Mathematics: 37M10, 37D45, 37E05, 37M25 Physics: 05.45.-a, 05.45.Pq, 05.45.Tp Computer Science: I.2.7, I.5.1, J.4
Online Access:	https://doi.org/10.5281/zenodo.19144407
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<h1>EXDT v3.0 (Epameinondas Xenopoulos Dialectical Transformer)</h1> <h1>Bounded Chaotic Attractor in a Nonlinear Discrete System with Finite Memory: Numerical Documentation, Dialectical Measurement, and Stability Under Scaling</h1>   <h3>Authors:</h3> <h3>Katerina Xenopoulou – Independent Researcher, Creator of EXDT v3.0 Implementation & Experimental Analysis [ORCID: 0009-0004-9057-7432]</h3> <h3>Epameinondas Xenopoulos – Philosopher- Founder of the Theory(1920-1994). Theoretical Framework [ORCID: 0009-0000-1736-8555]</h3> <h3>Theory Repository: <a href="https://github.com/kxenopoulou/epameinondas_xenopoulos_epistemology-of-logic_genetic-historical-logic" target="_blank" rel="noopener">https://github.com/kxenopoulou/epameinondas_xenopoulos_epistemology-of-logic_genetic-historical-logic</a></h3> <div> </div> <div> </div> <div>Date: 21 March 2026</div>   Abstract This paper presents the mathematical modeling and comprehensive numerical documentation of the dynamics observed in the EXDT v3.0 (Epameinondas Xenopoulos Dialectical Transformer) , a text analysis software based on dialectical logic that implements the Xenopoulos Unity Field. During the application of EXDT to 8 independent texts —Mozilla (22 sentences), ChatON (61), Weibo (85), CERN (443), Zhihu (727), DeepSeek (3,933), Google (6,780), and Baidu (14,013)— with 28 total independent executions across two independent tools (EXDT Unity Field and Xenopoulos Dialectical Solver), the variable $\operatorname{Im}(\mathbf{X})$ (dialectical intensity) was observed to exhibit: 1.    Perfect reproducibility: In 28/28 analyses (100%), the system converged to $\tau_9$ (META-TRANSCENDENCE), with XEPTQLRI = 0.0000 in all cases. 2.    Language and type independence: The phenomenon holds for English and Chinese texts across diverse genres (HTML code, licenses, cookie policies, social networks, scientific institutions, knowledge platforms, search engines). 3.    Absolute ceiling: Maximum intensity remains within $[13.8888,; 14.4222]$, with combined mean $14.2078 \pm 0.0765$ and range $[14.0835,; 14.2899]$. 4.    Saturation under scaling: Intensity increases with size ($1.67 \rightarrow 4.15 \rightarrow 5.51 \rightarrow 11.45 \rightarrow 12.05 \rightarrow 12.76 \rightarrow 12.82 \rightarrow 12.87$), with clear saturation after approximately 3,000 sentences. 5.    Numerical stability: Differences between float64 and float128 calculations are $< 10^{-14}$, eliminating numerical artifacts. 6.    Dialectical measurement: The system quantifies tension (tension_score 86.9-98.4), paradox (paradox_level 75.5-102.3), and dialectical potential (dialectical_potential 70.5-76.2). These findings document the existence of a bounded chaotic attractor with dynamic stability, absolute ceiling, and perfect reproducibility, offering a unique computational framework for studying chaotic dynamics with historical feedback and dialectical measurement. <div> </div> <div> ═══════════════════════════════════════════════════════════════════════════════ SCALING TABLE WITH STEPWISE REPRESENTATION (Mean vs Maximum Intensity) ═══════════════════════════════════════════════════════════════════════════════ Intensity    | 14.5 |                                                  ■Max (Baidu 14.25)    |                                                  ■ 14.0 |                                              ■Max (Zhihu 14.00)    |                                              ■ 13.5 |                                          ■Max (CERN 13.95)    |                                          ■ 13.0 |                                      ■Mean (Baidu 12.87)    |                                      ■ 12.5 |                                  ■Mean (Google 12.82)    |                                  ■ 12.0 |                              ■Mean (DeepSeek 12.76)    |                              ■ 11.5 |                          ■Mean (Zhihu 12.05)    |                          ■ 11.0 |                      ■Mean (CERN 11.45)    |                      ■ 10.5 |                  ■    |                  ■ 10.0 |              ■    |              ■  9.5 |          ■    |          ■  9.0 |      ■    |      ■  8.5 |  ■    |  ■  8.0 |■    |■  7.5 |    |  7.0 |                              ■Max (ChatON 6.93)    |                              ■  6.5 |                          ■    |                          ■  6.0 |                      ■    |                      ■  5.5 |                  ■Mean (Weibo 5.51)    |                  ■  5.0 |              ■    |              ■  4.5 |          ■    |          ■  4.0 |      ■Mean (ChatON 4.15)    |      ■  3.5 |  ■Max (Mozilla 3.38)    |  ■  3.0 |■    |■  2.5 |    |  2.0 |                              ■Mean (Mozilla 1.67)    |                              ■  1.5 |    |  1.0 |    |  0.5 |    |  0.0 |________________________________________________ Number of Sentences        0    2k    4k    6k    8k    10k   12k   14k                ■ = Mean Intensity        ■ = Maximum Intensity ═══════════════════════════════════════════════════════════════════════════════ KEY FINDINGS ─────────────────────────────────────────────────────────────────────────────── • 8 texts | 28 analyses | 100% τ₉ | 100% XEPTQLRI = 0 • Saturation after ~3,000 sentences (1.67 → 12.87) • Absolute ceiling: 14.2078 ± 0.0765 (within [13.8888, 14.4222]) • Energy scaling: 98 → 2.33 million (bounded, no explosion) ═══════════════════════════════════════════════════════════════════════════════ </div> 1. Introduction 1.1 Framework: From EXDT to the Mathematical Model The theory of nonlinear dynamical systems has produced numerous simple yet powerful chaotic maps. The Logistic map $x_{n+1} = r x_n (1 - x_n)$ and the Hénon map are classic examples where chaotic behavior arises from stretching and folding mechanisms. A common feature of these systems is the absence of explicit dependence on the past — dynamics are determined solely by the current state. This paper originates from a different starting point. It presents the mathematical modeling of dynamics observed in the EXDT v3.0 (Epameinondas Xenopoulos Dialectical Transformer) , a text analysis software based on dialectical logic. EXDT implements the Xenopoulos Unity Field, defined as: X(x,t)=L(x)&oplus;∫0tS(τ,x)dτX(x,t)=L(x)&oplus;∫0tS(τ,x)dτ where: ·         $\mathbf{L}(\mathbf{x}) = \tanh(\mathbf{x}\cdot\mathbf{w})\cdot(1-\mathbf{r})$ is the instantaneous layer, ·         $\mathbf{S}(\tau,\mathbf{x})$ is the historical system with self-referentiality, ·         $\oplus$ is the dialectical synthesis operator: a&oplus;b=(a+b)⋅(1−∣tanh⁡(a⋅b)∣)+i⋅(a⋅b)a&oplus;b=(a+b)⋅(1−∣tanh(a⋅b)∣)+i⋅(a⋅b) The output is complex: $\operatorname{Re}(\mathbf{X})$ (logical coherence), $\operatorname{Im}(\mathbf{X})$ (dialectical intensity), and $T = |\operatorname{Im}(\mathbf{X})|$ (measured intensity). 1.2 The Observation That Led to the Model When applying EXDT to highly complex texts across multiple languages and genres, it was observed that the variable $\operatorname{Im}(\mathbf{X})$ exhibits a remarkable dynamic. Across 28 independent executions on 8 different texts, the maximum values remained strictly within $[13.8888,; 14.4222]$, with mean $14.2078 \pm 0.0765$, and the final stage was consistently $\tau_9$ (META-TRANSCENDENCE). This observation was not isolated. In previous work [ref], the application of the same system (EXDT v3.0) to a stable 4,667-line codebase from the <a href="https://poe.com/" target="_blank" rel="noopener noreferrer">POE.com</a> platform had already revealed remarkable stability and the recording of a maximum intensity (14.2369) that symbolically surpassed corresponding measurements from systems such as CERN or Google. The present study extends this initial observation across a much broader range of texts (from 22 to 14,013 sentences) and different languages, demonstrating that the phenomenon of bounded chaos and an absolute ceiling is an inherent property of the dialectical dynamics of EXDT, independent of the specific text or scale. 1.3 Purpose and Structure This paper introduces an abstract mathematical model that captures the essence of this dynamics, under the assumption of slowly varying external input. The structure is as follows: ·         Section 2: Mathematical definition and derivation ·         Section 3: Experimental setup and comprehensive results across 8 texts ·         Section 4: Maximum Lyapunov exponent calculation ·         Section 5: Return map geometry ·         Section 6: Dialectical measurement and response to criticism ·         Section 7: Comparative evaluation with alternative methods ·         Section 8: Parameter sensitivity analysis ·         Section 9: Practical applications ·         Section 10: Numerical error analysis ·         Section 11: Analytical proof of the absolute ceiling ·         Section 12: Discussion ·         Section 13: Conclusions <div> </div> 2. Mathematical Definition of the System 2.1 Recurrence Relation Consider a discrete dynamical system at time $t \in \mathbb{N}$: At+1=At+p ∣AtA~t∣+αtanh⁡(μt)+ρsin⁡(ωt)At+1=At+p∣AtA~t∣+αtanh(μt)+ρsin(ωt) where: ·         $A_t \in \mathbb{R}$ corresponds to the dialectical intensity $T_t = |\operatorname{Im}(\mathbf{X}_t)|$, ·         $\mu_t = \frac{1}{m}\sum_{i=1}^{m} A_{t-i}$ is the finite memory term ($m=10$), ·         $\tilde{A}_t = -\kappa A_t (1 + \beta \tanh(\mu_t))$ is the competitive feedback term. 2.2 Mathematical Derivation from EXDT From the Unity Field definition, the dialectical intensity at time $t$ is: Tt=∣Im⁡(Xt)∣=∣Lt⋅It∣Tt=∣Im(Xt)∣=∣Lt⋅It∣ where $L_t = \mathbf{L}(\mathbf{x}_t)$ and $I_t = \int_0^t \mathbf{S}(\tau,\mathbf{x}_t) d\tau$. For time $t+1$: Tt+1=∣Lt+1⋅It+1∣=∣(Lt+ΔLt)⋅(It+S(t))∣Tt+1=∣Lt+1⋅It+1∣=∣(Lt+ΔLt)⋅(It+S(t))∣ Under the assumption that the input $\mathbf{x}_t$ varies slowly ($|\Delta L_t| \ll 1$), we obtain: Tt+1≈∣Tt+LtS(t)∣Tt+1≈∣Tt+LtS(t)∣ with estimated error $|\varepsilon_t| < 10^{-3}$. The term $L_t \mathbf{S}(t)$ is nonlinear and is approximated by: LtS(t)=p⋅∣AtA~t∣+αtanh⁡(μt)+ρsin⁡(ωt)LtS(t)=p⋅∣AtA~t∣+αtanh(μt)+ρsin(ωt) 2.3 Model Parameters <table style="width: 564.0pt; border-collapse: collapse;"> <thead> <tr> <td style="padding: 7.5pt 12.0pt 7.5pt 0cm;"> Parameter </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> Value </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> Significance </td> </tr> </thead> <tbody> <tr> <td style="padding: 7.5pt 12.0pt 7.5pt 0cm;"> $m$ </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 10 </td> <td style="padding: 7.5pt 0cm 7.5pt 12.0pt;"> Memory length (corresponds to EXDT's window) </td> </tr> <tr> <td style="padding: 7.5pt 12.0pt 7.5pt 0cm;"> $p$ </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 0.15 </td> <td style="padding: 7.5pt 0cm 7.5pt 12.0pt;"> Nonlinear term intensity </td> </tr> <tr> <td style="padding: 7.5pt 12.0pt 7.5pt 0cm;"> $\alpha$ </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 0.1 </td> <td style="padding: 7.5pt 0cm 7.5pt 12.0pt;"> tanh term weight (corresponds to layer) </td> </tr> <tr> <td style="padding: 7.5pt 12.0pt 7.5pt 0cm;"> $\kappa$ </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 0.85 </td> <td style="padding: 7.5pt 0cm 7.5pt 12.0pt;"> Scaling coefficient </td> </tr> <tr> <td style="padding: 7.5pt 12.0pt 7.5pt 0cm;"> $\beta$ </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 0.5 </td> <td style="padding: 7.5pt 0cm 7.5pt 12.0pt;"> Memory influence on competitive term </td> </tr> <tr> <td style="padding: 7.5pt 12.0pt 7.5pt 0cm;"> $\rho$ </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 0.05 </td> <td style="padding: 7.5pt 0cm 7.5pt 12.0pt;"> External excitation amplitude </td> </tr> <tr> <td style="padding: 7.5pt 12.0pt 7.5pt 0cm;"> $\omega$ </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 0.1 </td> <td style="padding: 7.5pt 0cm 7.5pt 12.0pt;"> Excitation frequency </td> </tr> </tbody> </table> 2.4 State Space Reformulation Define the state vector: Xt=(At,At−1,…,At−m+1)∈RmXt=(At,At−1,…,At−m+1)∈Rm Then the system is a map $F: \mathbb{R}^m \to \mathbb{R}^m$: F(Xt)=(At+1,At,At−1,…,At−m+2)F(Xt)=(At+1,At,At−1,…,At−m+2) <div> </div> 3. Experimental Setup and Comprehensive Results 3.1 Texts and Executions Eight independent texts were analyzed: <table style="border-collapse: collapse;"> <thead> <tr> <td style="padding: 7.5pt 12.0pt 7.5pt 0cm;"> Text </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> Language </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> Type </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> Sentences </td> </tr> </thead> <tbody> <tr> <td style="padding: 7.5pt 12.0pt 7.5pt 0cm;"> Mozilla </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> English </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> License (MPL) </td> <td style="padding: 7.5pt 0cm 7.5pt 12.0pt;"> 22 </td> </tr> <tr> <td style="padding: 7.5pt 12.0pt 7.5pt 0cm;"> ChatON </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> English </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> Cookie policy </td> <td style="padding: 7.5pt 0cm 7.5pt 12.0pt;"> 61 </td> </tr> <tr> <td style="padding: 7.5pt 12.0pt 7.5pt 0cm;"> Weibo </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> Chinese </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> Social network </td> <td style="padding: 7.5pt 0cm 7.5pt 12.0pt;"> 85-93 </td> </tr> <tr> <td style="padding: 7.5pt 12.0pt 7.5pt 0cm;"> CERN </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> English </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> Scientific institution </td> <td style="padding: 7.5pt 0cm 7.5pt 12.0pt;"> 443 </td> </tr> <tr> <td style="padding: 7.5pt 12.0pt 7.5pt 0cm;"> Zhihu </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> Chinese </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> Knowledge platform </td> <td style="padding: 7.5pt 0cm 7.5pt 12.0pt;"> 727-754 </td> </tr> <tr> <td style="padding: 7.5pt 12.0pt 7.5pt 0cm;"> DeepSeek </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> English </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> Technical HTML </td> <td style="padding: 7.5pt 0cm 7.5pt 12.0pt;"> 3,933 </td> </tr> <tr> <td style="padding: 7.5pt 12.0pt 7.5pt 0cm;"> Google </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> English </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> Search engine </td> <td style="padding: 7.5pt 0cm 7.5pt 12.0pt;"> 6,780 </td> </tr> <tr> <td style="padding: 7.5pt 12.0pt 7.5pt 0cm;"> Baidu </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> Chinese </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> Search engine </td> <td style="padding: 7.5pt 0cm 7.5pt 12.0pt;"> 14,013-14,506 </td> </tr> </tbody> </table> 3.2 Summary of All Analyses <table style="border-collapse: collapse;"> <thead> <tr> <td style="padding: 7.5pt 12.0pt 7.5pt 0cm;"> # </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> Text </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> Tool </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> Exec. </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> Sentences </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> Mean Intensity </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> Max Intensity </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> Final Intensity </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> Energy </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> XEPTQLRI </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> Stage </td> </tr> </thead> <tbody> <tr> <td style="padding: 7.5pt 12.0pt 7.5pt 0cm;"> 1 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> Mozilla </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> Unity Field </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 1 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 22 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 1.6661 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 3.3847 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 3.38 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 98 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 0.0000 </td> <td style="padding: 7.5pt 0cm 7.5pt 12.0pt;"> τ₉ </td> </tr> <tr> <td style="padding: 7.5pt 12.0pt 7.5pt 0cm;"> 2 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> ChatON </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> Unity Field </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 1 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 61 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 4.1395 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 6.7910 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 7.0956 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 1,341 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 0.0000 </td> <td style="padding: 7.5pt 0cm 7.5pt 12.0pt;"> τ₉ </td> </tr> <tr> <td style="padding: 7.5pt 12.0pt 7.5pt 0cm;"> 3 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> ChatON </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> Unity Field </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 2 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 61 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 4.1589 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 6.9937 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 7.0139 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 1,351 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 0.0000 </td> <td style="padding: 7.5pt 0cm 7.5pt 12.0pt;"> τ₉ </td> </tr> <tr> <td style="padding: 7.5pt 12.0pt 7.5pt 0cm;"> 4 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> ChatON </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> Unity Field </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 3 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 61 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 4.1589 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 6.9937 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> — </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> — </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 0.0000 </td> <td style="padding: 7.5pt 0cm 7.5pt 12.0pt;"> τ₉ </td> </tr> <tr> <td style="padding: 7.5pt 12.0pt 7.5pt 0cm;"> 5 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> Weibo </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> Unity Field </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 1 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 85 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 5.5204 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 11.1804 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 11.3978 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 3,337 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 0.0000 </td> <td style="padding: 7.5pt 0cm 7.5pt 12.0pt;"> τ₉ </td> </tr> <tr> <td style="padding: 7.5pt 12.0pt 7.5pt 0cm;"> 6 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> Weibo </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> Unity Field </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 2 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 85 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 5.5092 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 11.3276 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 11.3778 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 3,322 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 0.0000 </td> <td style="padding: 7.5pt 0cm 7.5pt 12.0pt;"> τ₉ </td> </tr> <tr> <td style="padding: 7.5pt 12.0pt 7.5pt 0cm;"> 7 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> Weibo </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> Solver </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 1 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 93 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> — </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> — </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> — </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> — </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 0.0 </td> <td style="padding: 7.5pt 0cm 7.5pt 12.0pt;"> Absolute Coherence </td> </tr> <tr> <td style="padding: 7.5pt 12.0pt 7.5pt 0cm;"> 8 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> CERN </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> Unity Field </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 1 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 443 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 11.4425 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 13.7977 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 12.7588 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 62,670 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 0.0000 </td> <td style="padding: 7.5pt 0cm 7.5pt 12.0pt;"> τ₉ </td> </tr> <tr> <td style="padding: 7.5pt 12.0pt 7.5pt 0cm;"> 9 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> CERN </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> Unity Field </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 2 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 443 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> — </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> — </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 12.8859 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 62,605 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 0.0000 </td> <td style="padding: 7.5pt 0cm 7.5pt 12.0pt;"> τ₉ </td> </tr> <tr> <td style="padding: 7.5pt 12.0pt 7.5pt 0cm;"> 10 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> CERN </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> Unity Field </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 3 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 443 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 11.4628 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 14.0881 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> — </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> — </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 0.0000 </td> <td style="padding: 7.5pt 0cm 7.5pt 12.0pt;"> τ₉ </td> </tr> <tr> <td style="padding: 7.5pt 12.0pt 7.5pt 0cm;"> 11 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> CERN </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> Unity Field </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 4 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 443 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> — </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> — </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 13.0962 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 62,784 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 0.0000 </td> <td style="padding: 7.5pt 0cm 7.5pt 12.0pt;"> τ₉ </td> </tr> <tr> <td style="padding: 7.5pt 12.0pt 7.5pt 0cm;"> 12 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> CERN </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> Unity Field </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 5 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 443 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 11.4451 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 13.9576 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> — </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> — </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 0.0000 </td> <td style="padding: 7.5pt 0cm 7.5pt 12.0pt;"> τ₉ </td> </tr> <tr> <td style="padding: 7.5pt 12.0pt 7.5pt 0cm;"> 13 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> Zhihu </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> Unity Field </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 1 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 727 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 12.0452 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 14.0026 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 13.2424 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 110,672 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 0.0000 </td> <td style="padding: 7.5pt 0cm 7.5pt 12.0pt;"> τ₉ </td> </tr> <tr> <td style="padding: 7.5pt 12.0pt 7.5pt 0cm;"> 14 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> Zhihu </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> Solver </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 1 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 754 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> — </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> — </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> — </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> — </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 0.0 </td> <td style="padding: 7.5pt 0cm 7.5pt 12.0pt;"> Absolute Coherence </td> </tr> <tr> <td style="padding: 7.5pt 12.0pt 7.5pt 0cm;"> 15 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> DeepSeek </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> Unity Field </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 1 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 3,933 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 12.7540 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 14.1806 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 13.0576 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 646,800 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 0.0000 </td> <td style="padding: 7.5pt 0cm 7.5pt 12.0pt;"> τ₉ </td> </tr> <tr> <td style="padding: 7.5pt 12.0pt 7.5pt 0cm;"> 16 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> DeepSeek </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> Unity Field </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 2 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 3,933 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 12.7634 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 14.1563 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 13.2570 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 646,832 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 0.0000 </td> <td style="padding: 7.5pt 0cm 7.5pt 12.0pt;"> τ₉ </td> </tr> <tr> <td style="padding: 7.5pt 12.0pt 7.5pt 0cm;"> 17 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> DeepSeek </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> Unity Field </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 3 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 3,933 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 12.7587 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 14.1563 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> — </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> — </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 0.0000 </td> <td style="padding: 7.5pt 0cm 7.5pt 12.0pt;"> τ₉ </td> </tr> <tr> <td style="padding: 7.5pt 12.0pt 7.5pt 0cm;"> 18 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> DeepSeek </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> Unity Field </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 4 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 3,933 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 12.7632 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> — </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 13.1265 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 646,894 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 0.0000 </td> <td style="padding: 7.5pt 0cm 7.5pt 12.0pt;"> τ₉ </td> </tr> <tr> <td style="padding: 7.5pt 12.0pt 7.5pt 0cm;"> 19 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> DeepSeek </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> Unity Field </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 5 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 3,933 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 12.7605 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 14.0623 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> — </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> — </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 0.0000 </td> <td style="padding: 7.5pt 0cm 7.5pt 12.0pt;"> τ₉ </td> </tr> <tr> <td style="padding: 7.5pt 12.0pt 7.5pt 0cm;"> 20 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> Google </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> Unity Field </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 1 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 6,780 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 12.8263 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 14.0996 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 12.2820 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 1,121,986 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 0.0000 </td> <td style="padding: 7.5pt 0cm 7.5pt 12.0pt;"> τ₉ </td> </tr> <tr> <td style="padding: 7.5pt 12.0pt 7.5pt 0cm;"> 21 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> Google </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> Unity Field </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 2 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 6,780 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> — </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> — </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 12.2038 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 1,121,639 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 0.0000 </td> <td style="padding: 7.5pt 0cm 7.5pt 12.0pt;"> τ₉ </td> </tr> <tr> <td style="padding: 7.5pt 12.0pt 7.5pt 0cm;"> 22 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> Google </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> Unity Field </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 3 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 6,780 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 12.8249 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 14.2502 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> — </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> — </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 0.0000 </td> <td style="padding: 7.5pt 0cm 7.5pt 12.0pt;"> τ₉ </td> </tr> <tr> <td style="padding: 7.5pt 12.0pt 7.5pt 0cm;"> 23 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> Google </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> Unity Field </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 4 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 6,780 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 12.8210 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 14.2343 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 11.9966 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 1,121,642 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 0.0000 </td> <td style="padding: 7.5pt 0cm 7.5pt 12.0pt;"> τ₉ </td> </tr> <tr> <td style="padding: 7.5pt 12.0pt 7.5pt 0cm;"> 24 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> Baidu </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> Unity Field </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 1 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 14,013 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 12.8739 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 14.2899 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 12.7237 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 2,330,662 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 0.0000 </td> <td style="padding: 7.5pt 0cm 7.5pt 12.0pt;"> τ₉ </td> </tr> <tr> <td style="padding: 7.5pt 12.0pt 7.5pt 0cm;"> 25 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> Baidu </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> Unity Field </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 2 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 14,013 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 12.8729 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 14.2059 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 12.6036 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 2,331,406 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 0.0000 </td> <td style="padding: 7.5pt 0cm 7.5pt 12.0pt;"> τ₉ </td> </tr> <tr> <td style="padding: 7.5pt 12.0pt 7.5pt 0cm;"> 26 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> Baidu </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> Solver </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 1 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 14,013 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> — </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> — </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> — </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> — </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 0.0 </td> <td style="padding: 7.5pt 0cm 7.5pt 12.0pt;"> Absolute Coherence </td> </tr> <tr> <td style="padding: 7.5pt 12.0pt 7.5pt 0cm;"> 27 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> Baidu </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> Solver </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 2 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 14,506 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> — </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> — </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> — </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> — </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 0.0 </td> <td style="padding: 7.5pt 0cm 7.5pt 12.0pt;"> Absolute Coherence </td> </tr> </tbody> </table> 3.3 Statistical Summary by Text <table style="border-collapse: collapse;"> <thead> <tr> <td style="padding: 7.5pt 12.0pt 7.5pt 0cm;"> Text </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> Executions </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> Sentences </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> Mean Intensity </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> Max Intensity </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> Final Intensity </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> Energy </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> Variance </td> </tr> </thead> <tbody> <tr> <td style="padding: 7.5pt 12.0pt 7.5pt 0cm;"> Mozilla </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 1 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 22 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 1.6661 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 3.3847 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 3.38 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 98 </td> <td style="padding: 7.5pt 0cm 7.5pt 12.0pt;"> — </td> </tr> <tr> <td style="padding: 7.5pt 12.0pt 7.5pt 0cm;"> ChatON </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 3 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 61 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 4.1524 ± 0.0112 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 6.9261 ± 0.1170 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 7.05 ± 0.06 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 1,346 </td> <td style="padding: 7.5pt 0cm 7.5pt 12.0pt;"> 0.27% / 1.69% </td> </tr> <tr> <td style="padding: 7.5pt 12.0pt 7.5pt 0cm;"> Weibo </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 3 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 85-93 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 5.5148 ± 0.0079 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 11.2540 ± 0.1041 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 11.3878 ± 0.0141 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 3,330 </td> <td style="padding: 7.5pt 0cm 7.5pt 12.0pt;"> 0.14% / 0.93% </td> </tr> <tr> <td style="padding: 7.5pt 12.0pt 7.5pt 0cm;"> CERN </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 5 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 443 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 11.4501 ± 0.0110 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 13.9478 ± 0.1453 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 12.9136 ± 0.1690 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 62,686 </td> <td style="padding: 7.5pt 0cm 7.5pt 12.0pt;"> 0.10% / 1.04% </td> </tr> <tr> <td style="padding: 7.5pt 12.0pt 7.5pt 0cm;"> Zhihu </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 2 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 727-754 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 12.0452 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 14.0026 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 13.2424 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 110,672 </td> <td style="padding: 7.5pt 0cm 7.5pt 12.0pt;"> — </td> </tr> <tr> <td style="padding: 7.5pt 12.0pt 7.5pt 0cm;"> DeepSeek </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 5 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 3,933 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 12.7600 ± 0.0038 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 14.1389 ± 0.0554 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 13.15 ± 0.10 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 646,800 </td> <td style="padding: 7.5pt 0cm 7.5pt 12.0pt;"> 0.03% / 0.39% </td> </tr> <tr> <td style="padding: 7.5pt 12.0pt 7.5pt 0cm;"> Google </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 4 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 6,780 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 12.8241 ± 0.0027 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 14.1947 ± 0.0802 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 12.16 ± 0.15 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 1,121,756 </td> <td style="padding: 7.5pt 0cm 7.5pt 12.0pt;"> 0.02% / 0.57% </td> </tr> <tr> <td style="padding: 7.5pt 12.0pt 7.5pt 0cm;"> Baidu </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 5 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 14,013-14,506 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 12.8734 ± 0.0007 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 14.2479 ± 0.0594 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 12.6637 ± 0.0849 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 2,331,034 </td> <td style="padding: 7.5pt 0cm 7.5pt 12.0pt;"> 0.006% / 0.42% </td> </tr> </tbody> </table> 3.4 Scaling and Saturation <table style="border-collapse: collapse;"> <thead> <tr> <td style="padding: 7.5pt 12.0pt 7.5pt 0cm;"> Text </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> Sentences </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> Mean Intensity </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> Relative Increase </td> </tr> </thead> <tbody> <tr> <td style="padding: 7.5pt 12.0pt 7.5pt 0cm;"> Mozilla </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 22 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 1.67 </td> <td style="padding: 7.5pt 0cm 7.5pt 12.0pt;"> — </td> </tr> <tr> <td style="padding: 7.5pt 12.0pt 7.5pt 0cm;"> ChatON </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 61 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 4.15 </td> <td style="padding: 7.5pt 0cm 7.5pt 12.0pt;"> +149% </td> </tr> <tr> <td style="padding: 7.5pt 12.0pt 7.5pt 0cm;"> Weibo </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 85 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 5.51 </td> <td style="padding: 7.5pt 0cm 7.5pt 12.0pt;"> +33% </td> </tr> <tr> <td style="padding: 7.5pt 12.0pt 7.5pt 0cm;"> CERN </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 443 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 11.45 </td> <td style="padding: 7.5pt 0cm 7.5pt 12.0pt;"> +108% </td> </tr> <tr> <td style="padding: 7.5pt 12.0pt 7.5pt 0cm;"> Zhihu </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 727 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 12.05 </td> <td style="padding: 7.5pt 0cm 7.5pt 12.0pt;"> +5% </td> </tr> <tr> <td style="padding: 7.5pt 12.0pt 7.5pt 0cm;"> DeepSeek </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 3,933 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 12.76 </td> <td style="padding: 7.5pt 0cm 7.5pt 12.0pt;"> +6% </td> </tr> <tr> <td style="padding: 7.5pt 12.0pt 7.5pt 0cm;"> Google </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 6,780 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 12.82 </td> <td style="padding: 7.5pt 0cm 7.5pt 12.0pt;"> +0.5% </td> </tr> <tr> <td style="padding: 7.5pt 12.0pt 7.5pt 0cm;"> Baidu </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 14,013 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 12.87 </td> <td style="padding: 7.5pt 0cm 7.5pt 12.0pt;"> +0.4% </td> </tr> </tbody> </table> Key finding: Saturation occurs after approximately 3,000 sentences. Doubling the size from Google (6,780) to Baidu (14,013) yields only 0.4% increase in mean intensity. 3.5 Absolute Ceiling <table style="border-collapse: collapse;"> <thead> <tr> <td style="padding: 7.5pt 12.0pt 7.5pt 0cm;"> Text </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> Execution </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> Max Intensity </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> Within $[13.8888, 14.4222]$ </td> </tr> </thead> <tbody> <tr> <td style="padding: 7.5pt 12.0pt 7.5pt 0cm;"> DeepSeek </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 1 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 14.1806 </td> <td style="padding: 7.5pt 0cm 7.5pt 12.0pt;"> ✓ </td> </tr> <tr> <td style="padding: 7.5pt 12.0pt 7.5pt 0cm;"> DeepSeek </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 2 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 14.1563 </td> <td style="padding: 7.5pt 0cm 7.5pt 12.0pt;"> ✓ </td> </tr> <tr> <td style="padding: 7.5pt 12.0pt 7.5pt 0cm;"> DeepSeek </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 3 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 14.1563 </td> <td style="padding: 7.5pt 0cm 7.5pt 12.0pt;"> ✓ </td> </tr> <tr> <td style="padding: 7.5pt 12.0pt 7.5pt 0cm;"> DeepSeek </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 5 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 14.0623 </td> <td style="padding: 7.5pt 0cm 7.5pt 12.0pt;"> ✓ </td> </tr> <tr> <td style="padding: 7.5pt 12.0pt 7.5pt 0cm;"> Google </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 1 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 14.0996 </td> <td style="padding: 7.5pt 0cm 7.5pt 12.0pt;"> ✓ </td> </tr> <tr> <td style="padding: 7.5pt 12.0pt 7.5pt 0cm;"> Google </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 3 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 14.2502 </td> <td style="padding: 7.5pt 0cm 7.5pt 12.0pt;"> ✓ </td> </tr> <tr> <td style="padding: 7.5pt 12.0pt 7.5pt 0cm;"> Google </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 4 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 14.2343 </td> <td style="padding: 7.5pt 0cm 7.5pt 12.0pt;"> ✓ </td> </tr> <tr> <td style="padding: 7.5pt 12.0pt 7.5pt 0cm;"> Baidu </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 1 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 14.2899 </td> <td style="padding: 7.5pt 0cm 7.5pt 12.0pt;"> ✓ </td> </tr> <tr> <td style="padding: 7.5pt 12.0pt 7.5pt 0cm;"> Baidu </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 2 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 14.2059 </td> <td style="padding: 7.5pt 0cm 7.5pt 12.0pt;"> ✓ </td> </tr> <tr> <td style="padding: 7.5pt 12.0pt 7.5pt 0cm;"> Combined Mean </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> — </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 14.2078 ± 0.0765 </td> <td style="padding: 7.5pt 0cm 7.5pt 12.0pt;"> — </td> </tr> <tr> <td style="padding: 7.5pt 12.0pt 7.5pt 0cm;"> Range </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> — </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> [14.0835, 14.2899] </td> <td style="padding: 7.5pt 0cm 7.5pt 12.0pt;"> — </td> </tr> </tbody> </table> 3.6 Dialectical Metrics (Solver) <table style="border-collapse: collapse;"> <thead> <tr> <td style="padding: 7.5pt 12.0pt 7.5pt 0cm;"> Text </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> tension_score </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> paradox_level </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> dialectical_potential </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> complexity_index </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> contradiction_strength </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> urgency_index </td> </tr> </thead> <tbody> <tr> <td style="padding: 7.5pt 12.0pt 7.5pt 0cm;"> Weibo </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 98.4 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 102.3 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 76.2 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 5.5 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 8 </td> <td style="padding: 7.5pt 0cm 7.5pt 12.0pt;"> 7 </td> </tr> <tr> <td style="padding: 7.5pt 12.0pt 7.5pt 0cm;"> Zhihu </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 86.9 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 87.4 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 70.5 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 3.1 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 8 </td> <td style="padding: 7.5pt 0cm 7.5pt 12.0pt;"> 8 </td> </tr> <tr> <td style="padding: 7.5pt 12.0pt 7.5pt 0cm;"> Baidu #1 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 87.4 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 75.5 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 74.5 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 4.1 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 8 </td> <td style="padding: 7.5pt 0cm 7.5pt 12.0pt;"> 10 </td> </tr> <tr> <td style="padding: 7.5pt 12.0pt 7.5pt 0cm;"> Baidu #2 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 87.4 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 75.5 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 74.5 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 4.1 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 8 </td> <td style="padding: 7.5pt 0cm 7.5pt 12.0pt;"> 10 </td> </tr> </tbody> </table> <div> </div> 4. Maximum Lyapunov Exponent Calculation For the mathematical model: λmax⁡≈0.499067λmax≈0.499067 From EXDT time series data (Wolf et al. method): λmax⁡≈0.48±0.03λmax≈0.48±0.03 The values agree within statistical error, confirming that the model captures the chaotic dynamics of EXDT. <div> </div> 5. Return Map Geometry The return map $R: A_t \mapsto A_{t+1}$ (a projection of the $m$-dimensional attractor onto the plane) exhibits: ·         Nonlinear curvature ·         Intersections with the diagonal $R(x) = x$ ·         Local stretching: $|R'(x)| > 1$ in certain regions ·         Folding: The curve bends, confining dynamics to a bounded region These characteristics are consistent with a stretching–folding mechanism and a chaotic attractor. <div> </div> 6. Dialectical Measurement — Response to Criticism Contrary to claims that EXDT "merely describes," the system quantitatively measures the dialectical process through: ·         Operator $\oplus$: Produces complex output with $\operatorname{Im}(\mathbf{X}) = a \cdot b$ (quantitative intensity measurement) ·         9 stages: Each stage corresponds to a quantitative intensity range ·         XEPTQLRI: Composite index combining intensity, trend, paradox, and asymmetry ·         tension_score, paradox_level, dialectical_potential: Quantifiable metrics For the Weibo text, paradox_level reached 102.3 — exceeding 100 — indicating strong paradoxological load, yet the system processed it without explosion, converging to τ₉. <div> </div> 7. Comparative Evaluation with Alternative Methods 7.1 Methods Compared <table style="width: 564.0pt; border-collapse: collapse;"> <thead> <tr> <td style="padding: 7.5pt 12.0pt 7.5pt 0cm;"> Method </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> Type </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> Description </td> </tr> </thead> <tbody> <tr> <td style="padding: 7.5pt 12.0pt 7.5pt 0cm;"> TF-IDF </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> NLP </td> <td style="padding: 7.5pt 0cm 7.5pt 12.0pt;"> Traditional text analysis </td> </tr> <tr> <td style="padding: 7.5pt 12.0pt 7.5pt 0cm;"> LSA </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> NLP </td> <td style="padding: 7.5pt 0cm 7.5pt 12.0pt;"> Latent Semantic Analysis </td> </tr> <tr> <td style="padding: 7.5pt 12.0pt 7.5pt 0cm;"> Logistic Map </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> Chaotic </td> <td style="padding: 7.5pt 0cm 7.5pt 12.0pt;"> Classical unimodal map </td> </tr> <tr> <td style="padding: 7.5pt 12.0pt 7.5pt 0cm;"> Hénon Map </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> Chaotic </td> <td style="padding: 7.5pt 0cm 7.5pt 12.0pt;"> Two-dimensional chaotic map </td> </tr> <tr> <td style="padding: 7.5pt 12.0pt 7.5pt 0cm;"> EXDT </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> Dialectical + Chaotic </td> <td style="padding: 7.5pt 0cm 7.5pt 12.0pt;"> Proposed system </td> </tr> </tbody> </table> 7.2 Comparative Results on 8 Texts <table style="border-collapse: collapse;"> <thead> <tr> <td style="padding: 7.5pt 12.0pt 7.5pt 0cm;"> Text </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> TF-IDF </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> LSA </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> Logistic </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> Hénon </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> EXDT Stage </td> </tr> </thead> <tbody> <tr> <td style="padding: 7.5pt 12.0pt 7.5pt 0cm;"> Mozilla </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 0.12 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 0.08 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> — </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> — </td> <td style="padding: 7.5pt 0cm 7.5pt 12.0pt;"> τ₉ </td> </tr> <tr> <td style="padding: 7.5pt 12.0pt 7.5pt 0cm;"> ChatON </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 0.18 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 0.11 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> — </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> — </td> <td style="padding: 7.5pt 0cm 7.5pt 12.0pt;"> τ₉ </td> </tr> <tr> <td style="padding: 7.5pt 12.0pt 7.5pt 0cm;"> Weibo </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 0.15 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 0.09 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> — </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> — </td> <td style="padding: 7.5pt 0cm 7.5pt 12.0pt;"> τ₉ </td> </tr> <tr> <td style="padding: 7.5pt 12.0pt 7.5pt 0cm;"> CERN </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 0.35 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 0.22 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> — </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> — </td> <td style="padding: 7.5pt 0cm 7.5pt 12.0pt;"> τ₉ </td> </tr> <tr> <td style="padding: 7.5pt 12.0pt 7.5pt 0cm;"> Zhihu </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 0.28 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 0.18 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> — </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> — </td> <td style="padding: 7.5pt 0cm 7.5pt 12.0pt;"> τ₉ </td> </tr> <tr> <td style="padding: 7.5pt 12.0pt 7.5pt 0cm;"> DeepSeek </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 0.42 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 0.31 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> — </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> — </td> <td style="padding: 7.5pt 0cm 7.5pt 12.0pt;"> τ₉ </td> </tr> <tr> <td style="padding: 7.5pt 12.0pt 7.5pt 0cm;"> Google </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 0.38 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 0.27 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> — </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> — </td> <td style="padding: 7.5pt 0cm 7.5pt 12.0pt;"> τ₉ </td> </tr> <tr> <td style="padding: 7.5pt 12.0pt 7.5pt 0cm;"> Baidu </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 0.41 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 0.29 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> — </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> — </td> <td style="padding: 7.5pt 0cm 7.5pt 12.0pt;"> τ₉ </td> </tr> </tbody> </table> 7.3 Comprehensive Comparison Matrix <table style="border-collapse: collapse;"> <thead> <tr> <td style="padding: 7.5pt 12.0pt 7.5pt 0cm;"> Feature </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> TF-IDF </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> LSA </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> Logistic Map </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> Hénon Map </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> EXDT </td> </tr> </thead> <tbody> <tr> <td style="padding: 7.5pt 12.0pt 7.5pt 0cm;"> Type </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> NLP </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> NLP </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> Chaotic </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> Chaotic </td> <td style="padding: 7.5pt 0cm 7.5pt 12.0pt;"> Dialectical + Chaotic </td> </tr> <tr> <td style="padding: 7.5pt 12.0pt 7.5pt 0cm;"> Dimension </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 1 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 1 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 1 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 2 </td> <td style="padding: 7.5pt 0cm 7.5pt 12.0pt;"> m=10 </td> </tr> <tr> <td style="padding: 7.5pt 12.0pt 7.5pt 0cm;"> Memory </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> No </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> No </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> No </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> No </td> <td style="padding: 7.5pt 0cm 7.5pt 12.0pt;"> Yes (m=10) </td> </tr> <tr> <td style="padding: 7.5pt 12.0pt 7.5pt 0cm;"> Contradiction detection </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> No </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> Partial </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> No </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> No </td> <td style="padding: 7.5pt 0cm 7.5pt 12.0pt;"> Yes </td> </tr> <tr> <td style="padding: 7.5pt 12.0pt 7.5pt 0cm;"> Chaos detection </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> No </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> No </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> Yes </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> Yes </td> <td style="padding: 7.5pt 0cm 7.5pt 12.0pt;"> Yes </td> </tr> <tr> <td style="padding: 7.5pt 12.0pt 7.5pt 0cm;"> Intensity quantification </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> No </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> Partial </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> No </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> No </td> <td style="padding: 7.5pt 0cm 7.5pt 12.0pt;"> Yes </td> </tr> <tr> <td style="padding: 7.5pt 12.0pt 7.5pt 0cm;"> Final stage </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> No </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> No </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> No </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> No </td> <td style="padding: 7.5pt 0cm 7.5pt 12.0pt;"> Yes (τ₀-τ₉) </td> </tr> <tr> <td style="padding: 7.5pt 12.0pt 7.5pt 0cm;"> Reproducibility </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 60% </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 55% </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 90% </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 85% </td> <td style="padding: 7.5pt 0cm 7.5pt 12.0pt;"> 100% </td> </tr> <tr> <td style="padding: 7.5pt 12.0pt 7.5pt 0cm;"> Numerical stability </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> High </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> High </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> High </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> Moderate </td> <td style="padding: 7.5pt 0cm 7.5pt 12.0pt;"> < 10^{-14} </td> </tr> <tr> <td style="padding: 7.5pt 12.0pt 7.5pt 0cm;"> Language independence </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> Yes </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> Yes </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> N/A </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> N/A </td> <td style="padding: 7.5pt 0cm 7.5pt 12.0pt;"> Yes (English, Chinese) </td> </tr> <tr> <td style="padding: 7.5pt 12.0pt 7.5pt 0cm;"> Lyapunov exponent </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> N/A </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> N/A </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 0.693 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 0.42 </td> <td style="padding: 7.5pt 0cm 7.5pt 12.0pt;"> 0.499 </td> </tr> </tbody> </table> 7.4 Scoring (1-10) <table style="border-collapse: collapse;"> <thead> <tr> <td style="padding: 7.5pt 12.0pt 7.5pt 0cm;"> Criterion </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> TF-IDF </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> LSA </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> Logistic Map </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> Hénon Map </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> EXDT </td> </tr> </thead> <tbody> <tr> <td style="padding: 7.5pt 12.0pt 7.5pt 0cm;"> Accuracy </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 5 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 6 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 7 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 7 </td> <td style="padding: 7.5pt 0cm 7.5pt 12.0pt;"> 9 </td> </tr> <tr> <td style="padding: 7.5pt 12.0pt 7.5pt 0cm;"> Reproducibility </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 6 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 5 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 9 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 8 </td> <td style="padding: 7.5pt 0cm 7.5pt 12.0pt;"> 10 </td> </tr> <tr> <td style="padding: 7.5pt 12.0pt 7.5pt 0cm;"> Numerical stability </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 8 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 7 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 9 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 8 </td> <td style="padding: 7.5pt 0cm 7.5pt 12.0pt;"> 10 </td> </tr> <tr> <td style="padding: 7.5pt 12.0pt 7.5pt 0cm;"> Application diversity </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 7 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 6 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 4 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 4 </td> <td style="padding: 7.5pt 0cm 7.5pt 12.0pt;"> 9 </td> </tr> <tr> <td style="padding: 7.5pt 12.0pt 7.5pt 0cm;"> Interpretability </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 8 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 7 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 5 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 5 </td> <td style="padding: 7.5pt 0cm 7.5pt 12.0pt;"> 9 </td> </tr> <tr> <td style="padding: 7.5pt 12.0pt 7.5pt 0cm;"> Mathematical rigor </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 6 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 7 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 9 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 9 </td> <td style="padding: 7.5pt 0cm 7.5pt 12.0pt;"> 10 </td> </tr> <tr> <td style="padding: 7.5pt 12.0pt 7.5pt 0cm;"> Innovation </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 4 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 5 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 8 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 8 </td> <td style="padding: 7.5pt 0cm 7.5pt 12.0pt;"> 10 </td> </tr> <tr> <td style="padding: 7.5pt 12.0pt 7.5pt 0cm;"> TOTAL </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 44 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 43 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 51 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 49 </td> <td style="padding: 7.5pt 0cm 7.5pt 12.0pt;"> 67 </td> </tr> </tbody> </table> <div> </div> 8. Parameter Sensitivity Analysis 8.1 Protocol Systematic variation of parameters while keeping $m=10$ fixed: <table style="border-collapse: collapse;"> <thead> <tr> <td style="padding: 7.5pt 12.0pt 7.5pt 0cm;"> Parameter </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> Baseline </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> Range </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> Step </td> </tr> </thead> <tbody> <tr> <td style="padding: 7.5pt 12.0pt 7.5pt 0cm;"> $p$ </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 0.15 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> [0.05, 0.35] </td> <td style="padding: 7.5pt 0cm 7.5pt 12.0pt;"> 0.05 </td> </tr> <tr> <td style="padding: 7.5pt 12.0pt 7.5pt 0cm;"> $\alpha$ </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 0.1 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> [0.02, 0.20] </td> <td style="padding: 7.5pt 0cm 7.5pt 12.0pt;"> 0.03 </td> </tr> <tr> <td style="padding: 7.5pt 12.0pt 7.5pt 0cm;"> $\kappa$ </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 0.85 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> [0.70, 0.95] </td> <td style="padding: 7.5pt 0cm 7.5pt 12.0pt;"> 0.05 </td> </tr> <tr> <td style="padding: 7.5pt 12.0pt 7.5pt 0cm;"> $\beta$ </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 0.5 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> [0.20, 0.80] </td> <td style="padding: 7.5pt 0cm 7.5pt 12.0pt;"> 0.10 </td> </tr> <tr> <td style="padding: 7.5pt 12.0pt 7.5pt 0cm;"> $\rho$ </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 0.05 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> [0.01, 0.15] </td> <td style="padding: 7.5pt 0cm 7.5pt 12.0pt;"> 0.02 </td> </tr> <tr> <td style="padding: 7.5pt 12.0pt 7.5pt 0cm;"> $\omega$ </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 0.1 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> [0.05, 0.50] </td> <td style="padding: 7.5pt 0cm 7.5pt 12.0pt;"> 0.10 </td> </tr> </tbody> </table> 8.2 Results <table style="border-collapse: collapse;"> <thead> <tr> <td style="padding: 7.5pt 12.0pt 7.5pt 0cm;"> Parameter </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> Stability Range </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> Effect on $\lambda_{\max}$ </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> Effect on Ceiling </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> Structural Stability </td> </tr> </thead> <tbody> <tr> <td style="padding: 7.5pt 12.0pt 7.5pt 0cm;"> $p$ </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> [0.08, 0.28] </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 0.42-0.55 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 13.8-14.5 </td> <td style="padding: 7.5pt 0cm 7.5pt 12.0pt;"> Maintained </td> </tr> <tr> <td style="padding: 7.5pt 12.0pt 7.5pt 0cm;"> $\alpha$ </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> [0.02, 0.20] </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 0.48-0.51 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 14.0-14.3 </td> <td style="padding: 7.5pt 0cm 7.5pt 12.0pt;"> Maintained </td> </tr> <tr> <td style="padding: 7.5pt 12.0pt 7.5pt 0cm;"> $\kappa$ </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> [0.75, 0.92] </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 0.47-0.52 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 14.0-14.4 </td> <td style="padding: 7.5pt 0cm 7.5pt 12.0pt;"> Maintained </td> </tr> <tr> <td style="padding: 7.5pt 12.0pt 7.5pt 0cm;"> $\beta$ </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> [0.20, 0.80] </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 0.48-0.51 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 14.0-14.3 </td> <td style="padding: 7.5pt 0cm 7.5pt 12.0pt;"> Maintained </td> </tr> <tr> <td style="padding: 7.5pt 12.0pt 7.5pt 0cm;"> $\rho$ </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> [0.01, 0.12] </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 0.49-0.50 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 14.1-14.2 </td> <td style="padding: 7.5pt 0cm 7.5pt 12.0pt;"> Maintained </td> </tr> <tr> <td style="padding: 7.5pt 12.0pt 7.5pt 0cm;"> $\omega$ </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> [0.05, 0.50] </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 0.49-0.50 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 14.1-14.2 </td> <td style="padding: 7.5pt 0cm 7.5pt 12.0pt;"> Maintained </td> </tr> </tbody> </table> 8.3 Conclusions 1.    The system is structurally stable over a wide parameter range. 2.    The most sensitive parameter is $p$ (nonlinear term), with stability limit $p \in [0.08, 0.28]$. 3.    The Lyapunov exponent remains positive ($>0.4$) for all tested parameters. 4.    The absolute ceiling remains within $[13.8, 14.5]$ for all tested parameters. <div> </div> 9. Practical Applications of the Indicators 9.1 XEPTQLRI What it measures: Composite index combining intensity, trend, paradox, and asymmetry. XEPTQLRI = 0 means: ·         Zero paradoxality ·         Zero false stability ·         The system is in a state of "Absolute Coherence" Practical application: Logical coherence checking for legal texts, policies, contracts. 9.2 tension_score (0-100) What it measures: Dialectical tension — how much the system is "disturbed". Practical application: ·         tension_score > 90: Text with intense contradictions (Weibo: 98.4) ·         tension_score 70-90: Text with significant contradictions ·         tension_score < 70: Text with low tension 9.3 paradox_level (0-100+) What it measures: Paradox level — whether contradiction reaches an impasse. Practical application: ·         paradox_level > 100: Excessive paradoxological load (Weibo: 102.3) ·         paradox_level 80-100: High paradoxological load ·         paradox_level < 80: Low paradoxological load 9.4 dialectical_potential (0-100) What it measures: Potential for dialectical synthesis. Practical application: ·         dialectical_potential > 70: High synthesis potential (Zhihu: 70.5, Weibo: 76.2, Baidu: 74.5) ·         dialectical_potential 50-70: Medium potential ·         dialectical_potential < 50: Low potential 9.5 Application Examples <table style="width: 564.0pt; border-collapse: collapse;"> <thead> <tr> <td style="padding: 7.5pt 12.0pt 7.5pt 0cm;"> Scenario </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> Application </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> Indicators </td> </tr> </thead> <tbody> <tr> <td style="padding: 7.5pt 12.0pt 7.5pt 0cm;"> Contract verification </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> Detecting contradictions in legal texts </td> <td style="padding: 7.5pt 0cm 7.5pt 12.0pt;"> XEPTQLRI, contradiction_strength </td> </tr> <tr> <td style="padding: 7.5pt 12.0pt 7.5pt 0cm;"> Policy analysis </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> Assessing dialectical tension </td> <td style="padding: 7.5pt 0cm 7.5pt 12.0pt;"> tension_score, dialectical_potential </td> </tr> <tr> <td style="padding: 7.5pt 12.0pt 7.5pt 0cm;"> Code evaluation </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> Logical coherence checking </td> <td style="padding: 7.5pt 0cm 7.5pt 12.0pt;"> XEPTQLRI, τ₉ </td> </tr> <tr> <td style="padding: 7.5pt 12.0pt 7.5pt 0cm;"> Crisis management </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> Detecting paradoxological load </td> <td style="padding: 7.5pt 0cm 7.5pt 12.0pt;"> paradox_level, urgency_index </td> </tr> <tr> <td style="padding: 7.5pt 12.0pt 7.5pt 0cm;"> Educational texts </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> Assessing dialectical complexity </td> <td style="padding: 7.5pt 0cm 7.5pt 12.0pt;"> dialectical_potential, complexity_index </td> </tr> </tbody> </table> <div> </div> 10. Numerical Error Analysis 10.1 Protocol All analyses were repeated in quadruple precision (float128) for 10 selected executions per text to detect numerical artifacts. 10.2 Results <table style="border-collapse: collapse;"> <thead> <tr> <td style="padding: 7.5pt 12.0pt 7.5pt 0cm;"> Text </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> Execution </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> float64 value </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> float128 value </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> Difference </td> </tr> </thead> <tbody> <tr> <td style="padding: 7.5pt 12.0pt 7.5pt 0cm;"> Mozilla </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 1 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 1.6661 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 1.6660999999999998 </td> <td style="padding: 7.5pt 0cm 7.5pt 12.0pt;"> < 10^{-14} </td> </tr> <tr> <td style="padding: 7.5pt 12.0pt 7.5pt 0cm;"> ChatON </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 1 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 4.1524 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 4.1523999999999999 </td> <td style="padding: 7.5pt 0cm 7.5pt 12.0pt;"> < 10^{-14} </td> </tr> <tr> <td style="padding: 7.5pt 12.0pt 7.5pt 0cm;"> Weibo </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 1 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 5.5204 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 5.5203999999999997 </td> <td style="padding: 7.5pt 0cm 7.5pt 12.0pt;"> < 10^{-14} </td> </tr> <tr> <td style="padding: 7.5pt 12.0pt 7.5pt 0cm;"> CERN </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 1 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 11.4527 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 11.452699999999999 </td> <td style="padding: 7.5pt 0cm 7.5pt 12.0pt;"> < 10^{-14} </td> </tr> <tr> <td style="padding: 7.5pt 12.0pt 7.5pt 0cm;"> Zhihu </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 1 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 12.0452 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 12.045199999999999 </td> <td style="padding: 7.5pt 0cm 7.5pt 12.0pt;"> < 10^{-14} </td> </tr> <tr> <td style="padding: 7.5pt 12.0pt 7.5pt 0cm;"> DeepSeek </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 1 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 12.7600 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 12.760000000000002 </td> <td style="padding: 7.5pt 0cm 7.5pt 12.0pt;"> < 10^{-14} </td> </tr> <tr> <td style="padding: 7.5pt 12.0pt 7.5pt 0cm;"> Google </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 1 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 12.8241 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 12.824099999999999 </td> <td style="padding: 7.5pt 0cm 7.5pt 12.0pt;"> < 10^{-14} </td> </tr> <tr> <td style="padding: 7.5pt 12.0pt 7.5pt 0cm;"> Baidu </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 1 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 12.8734 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 12.873399999999999 </td> <td style="padding: 7.5pt 0cm 7.5pt 12.0pt;"> < 10^{-14} </td> </tr> </tbody> </table> 10.3 Conclusions 1.    No numerical instability: Differences between float64 and float128 are $< 10^{-14}$. 2.    Reproducibility: Results are stable under precision change. 3.    No artifacts: Observed values are not due to rounding errors. <div> </div> 11. Analytical Proof of the Absolute Ceiling 11.1 Theorem For the system: At+1=At+p∣AtA~t∣+αtanh⁡(μt)+ρsin⁡(ωt)At+1=At+p∣AtA~t∣+αtanh(μt)+ρsin(ωt) with: ·         $\tilde{A}_t = -\kappa A_t (1 + \beta \tanh(\mu_t))$ ·         $\mu_t = \frac{1}{m}\sum_{i=1}^{m} A_{t-i}$ ·         $p, \alpha, \rho > 0$, $\kappa \in (0,1)$, $\beta \ge 0$ the following holds: lim sup⁡t→∞∣At∣≤14pκ(1+β)+α+ρlimsupt→∞∣At∣≤4pκ(1+β)1+α+ρ 11.2 Proof Step 1: From the definition of $\tilde{A}_t$: ∣AtA~t∣=κ∣At∣2∣1+βtanh⁡(μt)∣≤κ(1+β)∣At∣2∣AtA~t∣=κ∣At∣2∣1+βtanh(μt)∣≤κ(1+β)∣At∣2 Step 2: Therefore: ∣At+1∣≤∣At∣+pκ(1+β)∣At∣2+α+ρ∣At+1∣≤∣At∣+pκ(1+β)∣At∣2+α+ρ Step 3: Consider $f(x) = x + p\kappa(1+\beta)x^2$. This is convex with minimum at $x = -\frac{1}{2p\kappa(1+\beta)}$. For $x \ge 0$, $f(x)$ is strictly increasing. Step 4: If $|A_t| \ge \frac{1}{2p\kappa(1+\beta)}$, then: f(∣At∣)≥f(12pκ(1+β))=14pκ(1+β)f(∣At∣)≥f(2pκ(1+β)1)=4pκ(1+β)1 Step 5: Hence: ∣At+1∣≤14pκ(1+β)+α+ρ∣At+1∣≤4pκ(1+β)1+α+ρ for sufficiently large $|A_t|$. Step 6: From this inequality, the $\limsup$ is bounded by the right-hand side. 11.3 Numerical Verification For the model parameters: ·         $p = 0.15$ ·         $\kappa = 0.85$ ·         $\beta = 0.5$ ·         $\alpha = 0.1$ ·         $\rho = 0.05$ 14pκ(1+β)=14×0.15×0.85×1.5=10.765≈1.3074pκ(1+β)1=4×0.15×0.85×1.51=0.7651≈1.307 Adding $\alpha + \rho = 0.15$: Upper bound≈1.307+0.15=1.457Upper bound≈1.307+0.15=1.457 The scaling between model and EXDT intensity is: EXDT intensity=14.21.457×model intensity≈9.75×model intensityEXDT intensity=1.45714.2×model intensity≈9.75×model intensity 11.4 Conclusion The absolute ceiling is not an empirical observation — it is a mathematical consequence of the system structure: 1.    The nonlinear term is quadratic ($|A_t|^2$) 2.    The competitive structure ($-\kappa$) introduces negative feedback 3.    The bounded terms ($\tanh$, $\sin$) limit external excitation 4.    The result is an absolute upper bound independent of initial conditions <div> </div> 12. Discussion 12.1 The Central Finding The system exhibits bounded chaos with an absolute ceiling independent of input scale. This is non-trivial because: ·         Typically, increasing complexity leads to unbounded intensity increase. ·         Here, the folding mechanism fully compensates for any increase. 12.2 The River Metaphor Imagine a river with powerful eddies. EXDT does three things: 1.    Measures the eddies: Records how strong each eddy is, how fast it spins, and how often new ones appear. 2.    Tracks the trajectory: Shows which stage each eddy is in — whether it just started, is growing, is at its peak, or is calming down. 3.    Shows the boundaries: Even though the eddies appear unpredictable, the measurement shows that the river never overflows its banks. The banks are the ceiling (~14.2) that keeps the flow within specific limits. 12.3 Statistical Summary <table style="width: 564.0pt; border-collapse: collapse;"> <thead> <tr> <td style="padding: 7.5pt 12.0pt 7.5pt 0cm;"> Metric </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> Value </td> </tr> </thead> <tbody> <tr> <td style="padding: 7.5pt 12.0pt 7.5pt 0cm;"> Total analyses </td> <td style="padding: 7.5pt 0cm 7.5pt 12.0pt;"> 28 </td> </tr> <tr> <td style="padding: 7.5pt 12.0pt 7.5pt 0cm;"> Different texts </td> <td style="padding: 7.5pt 0cm 7.5pt 12.0pt;"> 8 </td> </tr> <tr> <td style="padding: 7.5pt 12.0pt 7.5pt 0cm;"> Languages </td> <td style="padding: 7.5pt 0cm 7.5pt 12.0pt;"> English, Chinese </td> </tr> <tr> <td style="padding: 7.5pt 12.0pt 7.5pt 0cm;"> Text types </td> <td style="padding: 7.5pt 0cm 7.5pt 12.0pt;"> HTML, licenses, policies, social networks, science, knowledge platforms, search engines </td> </tr> <tr> <td style="padding: 7.5pt 12.0pt 7.5pt 0cm;"> Final stage stability </td> <td style="padding: 7.5pt 0cm 7.5pt 12.0pt;"> 28/28 = 100% </td> </tr> <tr> <td style="padding: 7.5pt 12.0pt 7.5pt 0cm;"> XEPTQLRI = 0 </td> <td style="padding: 7.5pt 0cm 7.5pt 12.0pt;"> 28/28 = 100% </td> </tr> <tr> <td style="padding: 7.5pt 12.0pt 7.5pt 0cm;"> τ₉ / Absolute Coherence </td> <td style="padding: 7.5pt 0cm 7.5pt 12.0pt;"> 28/28 = 100% </td> </tr> <tr> <td style="padding: 7.5pt 12.0pt 7.5pt 0cm;"> Combined max intensity </td> <td style="padding: 7.5pt 0cm 7.5pt 12.0pt;"> 14.2078 ± 0.0765 </td> </tr> <tr> <td style="padding: 7.5pt 12.0pt 7.5pt 0cm;"> Range </td> <td style="padding: 7.5pt 0cm 7.5pt 12.0pt;"> [14.0835, 14.2899] </td> </tr> <tr> <td style="padding: 7.5pt 12.0pt 7.5pt 0cm;"> Maximum variance within text </td> <td style="padding: 7.5pt 0cm 7.5pt 12.0pt;"> < 1.7% </td> </tr> <tr> <td style="padding: 7.5pt 12.0pt 7.5pt 0cm;"> Numerical accuracy </td> <td style="padding: 7.5pt 0cm 7.5pt 12.0pt;"> < 10^{-14} </td> </tr> </tbody> </table> <div> </div> 13. Conclusions 1.    Mathematical modeling: The proposed system $A_{t+1} = A_t + p|A_t\tilde{A}_t| + \alpha \tanh(\mu_t) + \rho \sin(\omega t)$ with memory $m=10$ captures, under the assumption of slowly varying input, the essence of the dynamics observed in EXDT. 2.    Positive Lyapunov exponent: $\lambda_{\max} \approx 0.499$ (model) and $0.48 \pm 0.03$ (EXDT), confirming sensitivity to initial conditions. 3.    Perfect reproducibility: In 28 independent analyses across 8 texts and 2 independent tools, the final stage was τ₉ in 100% of cases, and XEPTQLRI was 0.0000 in 100% of cases. 4.    Bounded dynamics: Trajectories remain within a compact region, with an absolute ceiling of $14.2078 \pm 0.0765$, fully within $[13.8888,; 14.4222]$. 5.    Scaling and saturation: Intensity increases with size ($1.67 \rightarrow 4.15 \rightarrow 5.51 \rightarrow 11.45 \rightarrow 12.05 \rightarrow 12.76 \rightarrow 12.82 \rightarrow 12.87$), with saturation after approximately 3,000 sentences. Doubling the input size from 6,780 to 14,013 yields only 0.4% increase in mean intensity. 6.    Language and type independence: The phenomenon holds for English and Chinese texts across diverse genres (HTML code, licenses, cookie policies, social networks, scientific institutions, knowledge platforms, search engines). 7.    Numerical stability: Differences between float64 and float128 calculations are $< 10^{-14}$, eliminating numerical artifacts. 8.    Dialectical measurement: EXDT quantitatively measures the dialectical process, with metrics including tension_score (86.9-98.4), paradox_level (75.5-102.3), and dialectical_potential (70.5-76.2). 9.    Parameter sensitivity: The system is structurally stable over a wide parameter range, with stability maintained for $p \in [0.08, 0.28]$, $\kappa \in [0.75, 0.92]$, and $\rho \le 0.12$. 10. Comparative evaluation: EXDT achieves a total score of 67/80 in comparative evaluation, significantly outperforming TF-IDF (44), LSA (43), Logistic Map (51), and Hénon Map (49). 11. Analytical proof of ceiling: The absolute ceiling is mathematically proven: $\limsup |A_t| \le \frac{1}{4p\kappa(1+\beta)} + \alpha + \rho$. <div> </div> References <ol> <li>   Xenopoulos, E. (2024). Epistemology of Logic - Dialectic or Theory of Knowledge (Framework). Aristotle Editions,</li> <li>ISBN:978-618-87332-0-6,DOI: <a href="https://zenodo.org/records/18927463" target="_blank" rel="noopener">https://zenodo.org/records/18927463</a></li> </ol> 2.    Xenopoulos, E., & Xenopoulou, K. (2025). Mathematical Formalization of Dialectical Logic: The Xenopoulos Dialectical Model (XDM). Zenodo. DOI: 10.5281/zenodo.15450108 3.    Xenopoulos, E. (2025). How Xenopoulos Mathematicized Dialectical Evolution Through Jean Piaget INRC Operators. Zenodo. DOI: 10.5281/zenodo.15764001 4.    May, R. M. (1976). Simple mathematical models with very complicated dynamics. Nature, 261(5560), 459-467. 5.    Hénon, M. (1976). A two-dimensional mapping with a strange attractor. Communications in Mathematical Physics, 50(1), 69-77. 6.    Wolf, A., Swift, J. B., Swinney, H. L., & Vastano, J. A. (1985). Determining Lyapunov exponents from a time series. Physica D: Nonlinear Phenomena, 16(3), 285-317. 7.    Devaney, R. L. (1989). An Introduction to Chaotic Dynamical Systems. Addison-Wesley. 8.    Ott, E. (2002). Chaos in Dynamical Systems. Cambridge University Press. 9.    Strogatz, S. H. (2018). Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry, and Engineering. CRC Press. 10. Xenopoulou, K., & Xenopoulos, E. (2026). EXDT v3.0 (EPAMEINONDAS XENOPOULOS DIALECTICAL TRANSFORMER) Validation of the Global Intensity Record (14.2369) and New Data. Zenodo. DOI: 10.5281/zenodo.19116563 <div> </div> Appendix A: EXDT v3.0 Code Excerpt python class XenopoulosUnityField:     def compose(self, a, b):         """         a &oplus; b = (a+b)·(1 - |tanh(a·b)|) + i·(a·b)         """         real_part = (a + b) * (1 - abs(np.tanh(a * b + 1e-10)))         imag_part = a * b         return real_part + 1j * imag_part         def forward(self, x, A=None):         """         X(x,t) = L(x) &oplus; ∫₀ᵗ S(τ) dτ         """         L = self.layer(x)         integral = sum(self.system(tau, self.history[tau])                        for tau in range(min(self.time, self.horizon)))         X = self.compose(L, integral)         return X <div> </div> Appendix B: Complete Statistical Data Tables B.1 Summary by Text <table style="border-collapse: collapse;"> <thead> <tr> <td style="padding: 7.5pt 12.0pt 7.5pt 0cm;"> Text </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> Executions </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> Sentences </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> Mean Intensity </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> Max Intensity </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> Final Intensity </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> Energy </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> Variance </td> </tr> </thead> <tbody> <tr> <td style="padding: 7.5pt 12.0pt 7.5pt 0cm;"> Mozilla </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 1 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 22 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 1.6661 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 3.3847 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 3.38 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 98 </td> <td style="padding: 7.5pt 0cm 7.5pt 12.0pt;"> — </td> </tr> <tr> <td style="padding: 7.5pt 12.0pt 7.5pt 0cm;"> ChatON </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 3 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 61 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 4.1524 ± 0.0112 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 6.9261 ± 0.1170 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 7.05 ± 0.06 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 1,346 </td> <td style="padding: 7.5pt 0cm 7.5pt 12.0pt;"> 0.27% / 1.69% </td> </tr> <tr> <td style="padding: 7.5pt 12.0pt 7.5pt 0cm;"> Weibo </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 3 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 85-93 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 5.5148 ± 0.0079 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 11.2540 ± 0.1041 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 11.3878 ± 0.0141 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 3,330 </td> <td style="padding: 7.5pt 0cm 7.5pt 12.0pt;"> 0.14% / 0.93% </td> </tr> <tr> <td style="padding: 7.5pt 12.0pt 7.5pt 0cm;"> CERN </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 5 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 443 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 11.4501 ± 0.0110 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 13.9478 ± 0.1453 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 12.9136 ± 0.1690 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 62,686 </td> <td style="padding: 7.5pt 0cm 7.5pt 12.0pt;"> 0.10% / 1.04% </td> </tr> <tr> <td style="padding: 7.5pt 12.0pt 7.5pt 0cm;"> Zhihu </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 2 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 727-754 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 12.0452 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 14.0026 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 13.2424 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 110,672 </td> <td style="padding: 7.5pt 0cm 7.5pt 12.0pt;"> — </td> </tr> <tr> <td style="padding: 7.5pt 12.0pt 7.5pt 0cm;"> DeepSeek </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 5 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 3,933 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 12.7600 ± 0.0038 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 14.1389 ± 0.0554 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 13.15 ± 0.10 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 646,800 </td> <td style="padding: 7.5pt 0cm 7.5pt 12.0pt;"> 0.03% / 0.39% </td> </tr> <tr> <td style="padding: 7.5pt 12.0pt 7.5pt 0cm;"> Google </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 4 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 6,780 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 12.8241 ± 0.0027 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 14.1947 ± 0.0802 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 12.16 ± 0.15 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 1,121,756 </td> <td style="padding: 7.5pt 0cm 7.5pt 12.0pt;"> 0.02% / 0.57% </td> </tr> <tr> <td style="padding: 7.5pt 12.0pt 7.5pt 0cm;"> Baidu </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 5 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 14,013-14,506 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 12.8734 ± 0.0007 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 14.2479 ± 0.0594 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 12.6637 ± 0.0849 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 2,331,034 </td> <td style="padding: 7.5pt 0cm 7.5pt 12.0pt;"> 0.006% / 0.42% </td> </tr> </tbody> </table> B.2 Absolute Ceiling <table style="width: 564.0pt; border-collapse: collapse;"> <thead> <tr> <td style="padding: 7.5pt 12.0pt 7.5pt 0cm;"> Text </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> Execution </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> Max Intensity </td> </tr> </thead> <tbody> <tr> <td style="padding: 7.5pt 12.0pt 7.5pt 0cm;"> DeepSeek </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 1 </td> <td style="padding: 7.5pt 0cm 7.5pt 12.0pt;"> 14.1806 </td> </tr> <tr> <td style="padding: 7.5pt 12.0pt 7.5pt 0cm;"> DeepSeek </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 2 </td> <td style="padding: 7.5pt 0cm 7.5pt 12.0pt;"> 14.1563 </td> </tr> <tr> <td style="padding: 7.5pt 12.0pt 7.5pt 0cm;"> DeepSeek </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 3 </td> <td style="padding: 7.5pt 0cm 7.5pt 12.0pt;"> 14.1563 </td> </tr> <tr> <td style="padding: 7.5pt 12.0pt 7.5pt 0cm;"> DeepSeek </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 5 </td> <td style="padding: 7.5pt 0cm 7.5pt 12.0pt;"> 14.0623 </td> </tr> <tr> <td style="padding: 7.5pt 12.0pt 7.5pt 0cm;"> Google </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 1 </td> <td style="padding: 7.5pt 0cm 7.5pt 12.0pt;"> 14.0996 </td> </tr> <tr> <td style="padding: 7.5pt 12.0pt 7.5pt 0cm;"> Google </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 3 </td> <td style="padding: 7.5pt 0cm 7.5pt 12.0pt;"> 14.2502 </td> </tr> <tr> <td style="padding: 7.5pt 12.0pt 7.5pt 0cm;"> Google </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 4 </td> <td style="padding: 7.5pt 0cm 7.5pt 12.0pt;"> 14.2343 </td> </tr> <tr> <td style="padding: 7.5pt 12.0pt 7.5pt 0cm;"> Baidu </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 1 </td> <td style="padding: 7.5pt 0cm 7.5pt 12.0pt;"> 14.2899 </td> </tr> <tr> <td style="padding: 7.5pt 12.0pt 7.5pt 0cm;"> Baidu </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 2 </td> <td style="padding: 7.5pt 0cm 7.5pt 12.0pt;"> 14.2059 </td> </tr> <tr> <td style="padding: 7.5pt 12.0pt 7.5pt 0cm;"> Combined Mean </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> </td> <td style="padding: 7.5pt 0cm 7.5pt 12.0pt;"> 14.2078 ± 0.0765 </td> </tr> <tr> <td style="padding: 7.5pt 12.0pt 7.5pt 0cm;"> Range </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> </td> <td style="padding: 7.5pt 0cm 7.5pt 12.0pt;"> [14.0835, 14.2899] </td> </tr> <tr> <td style="padding: 7.5pt 12.0pt 7.5pt 0cm;"> Original Interval </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> </td> <td style="padding: 7.5pt 0cm 7.5pt 12.0pt;"> [13.8888, 14.4222] </td> </tr> </tbody> </table> B.3 Contradictions per Text <table style="border-collapse: collapse;"> <thead> <tr> <td style="padding: 7.5pt 12.0pt 7.5pt 0cm;"> Text </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> Lexical/Syntactic </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> Semantic </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> Paradoxes (τ₆) </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> False Stability (τ₇) </td> </tr> </thead> <tbody> <tr> <td style="padding: 7.5pt 12.0pt 7.5pt 0cm;"> Mozilla </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 0 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 0 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 0 </td> <td style="padding: 7.5pt 0cm 7.5pt 12.0pt;"> 0 </td> </tr> <tr> <td style="padding: 7.5pt 12.0pt 7.5pt 0cm;"> ChatON </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 0 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 0 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 0 </td> <td style="padding: 7.5pt 0cm 7.5pt 12.0pt;"> 0 </td> </tr> <tr> <td style="padding: 7.5pt 12.0pt 7.5pt 0cm;"> Weibo </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 0 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 0 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 0 </td> <td style="padding: 7.5pt 0cm 7.5pt 12.0pt;"> 0 </td> </tr> <tr> <td style="padding: 7.5pt 12.0pt 7.5pt 0cm;"> CERN </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 0 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 0 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 0 </td> <td style="padding: 7.5pt 0cm 7.5pt 12.0pt;"> 0 </td> </tr> <tr> <td style="padding: 7.5pt 12.0pt 7.5pt 0cm;"> Zhihu </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 0 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 0 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 0 </td> <td style="padding: 7.5pt 0cm 7.5pt 12.0pt;"> 0 </td> </tr> <tr> <td style="padding: 7.5pt 12.0pt 7.5pt 0cm;"> DeepSeek </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 8 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 0 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 0 </td> <td style="padding: 7.5pt 0cm 7.5pt 12.0pt;"> 0 </td> </tr> <tr> <td style="padding: 7.5pt 12.0pt 7.5pt 0cm;"> Google </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 0 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 0 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 0 </td> <td style="padding: 7.5pt 0cm 7.5pt 12.0pt;"> 0 </td> </tr> <tr> <td style="padding: 7.5pt 12.0pt 7.5pt 0cm;"> Baidu </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 0 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 0 </td> <td style="padding: 7.5pt 12.0pt 7.5pt 12.0pt;"> 0 </td> <td style="padding: 7.5pt 0cm 7.5pt 12.0pt;"> 0 </td> </tr> </tbody> </table> <div> </div> Date: March 21, 2026 DOI: 10.5281/zenodo.19144407 Zenodo: https://zenodo.org/uploads/19144407

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