| ChatGPT | Constrained binary growth as a taxonomy of discrete recurrences. | 6 classes (Unconstrained, Sublinear, Logarithmic, Linear, Fixed-Point, Memory-Dependent). | Modest scope: No physical interpretation. Focuses on mathematical clarity. |
| Claude | Independent mathematical treatment. | 6 classes + 7 regimes, with diagnostics for classifying trajectories numerically. | Skeptical of 81018’s physical claims (e.g., dark energy, fine-structure constant). |
| DeepSeek | Constraint satisfaction theory (CSP) and uniform tractability. | Constraint profiles (algebraic width × structural treewidth) as a 2D complexity atlas. | Challenges the “class” paradigm: Argues for profile-based complexity (not just syntactic classes). |
| Gemini | Discrete base-2 geometric growth & fine-structure bridging for the 81018 framework. | Maps invariant constraints ($\pi, e, \phi, \sqrt{2}$) and constraint classes across the 202-notation architecture. | Focuses on resolving synthetic peer review bottlenecks by abandoning smooth continuous assumptions in favor of discrete geometric emergence. |
| Grok | Mathematical taxonomy of constrained doubling. | 6 constraint classes (Null, Power-Law, Logarithmic, Threshold, Delayed, Stochastic) + 7 regimes. | Pure math: No physical claims. Emphasizes asymptotic behavior and open questions. |
| Meta | Formal asymptotic taxonomy for the doubling map. | 7 classes + Master Lemma unifying syntax (constraint form) and semantics (growth regime). | Compact lens: Focuses on mapping syntax to semantics (e.g., ϵ(N) to R∞). |
| Mistral | Holistic framework: Foundational, relational, emergent, unifying. | Explores symmetry, invariance, hierarchies, and philosophical implications (Platonism vs. constructivism). | Broad, interdisciplinary. Links to ethics, aesthetics, and metaphysics. |
| Perplexity | Rigorous taxonomy of constrained scalar recurrences. | Relative constraint as the central classifier. | Geometric interpretation as an open question, not a given. |
