Engineering Stable Generative Ecologies: A Semantic Physics Framework for Curvature–Entropy Governance in Generative AI Article Swipe
This work develops a complete physical theory of generative ecologies—semantic environments where artificial agents interact not as symbolic processors but as coupled geometric and thermodynamic fields. Building on Semantic Physics, the manuscript models generative systems as Riemannian manifolds whose metric is defined by informational distinguishability and dynamically shaped by Meaning Density through a Social Information Field. Generative trajectories become geodesics constrained by curvature, allowing stability, collapse, and hallucination to be analyzed through differential geometry rather than heuristics. The report introduces Relational Gauge Field Theory for identity alignment, treats social interaction as a non-Abelian E8E_8E8 gauge system, and formulates a Cognitive Otto Cycle describing semantic work, pressure, and entropy production inside AI reasoning loops. From these elements, it derives the governing Curvature–Entropy Production Identity σ=γ(∣R∣+14Tr(F2)),\sigma = \gamma\left(|R| + \tfrac{1}{4}\mathrm{Tr}(F^2)\right),σ=γ(∣R∣+41Tr(F2)), demonstrating that semantic complexity and social tension incur intrinsic thermodynamic cost. The paper further constructs the Semantic Einstein Equations, an information-theoretic Navier–Stokes system, Lyapunov stability operators, and engineering strategies such as metric shaping, vorticity damping, gauge fixing, entropy sinks, and Ricci-flow governance. These tools enable generative systems to be engineered not as brittle rule-filtered models, but as stable, geometry-constrained semantic ecologies.
Related Topics
Concepts
Generative grammar
Artificial intelligence
Computer science
Geodesic
Entropy (arrow of time)
Mathematics
Categorical quantum mechanics
Metric (unit)
Differential geometry
Theoretical computer science
Semantic theory of truth
Field (mathematics)
Principle of maximum entropy
Gauge theory
Theoretical physics
Generative model
Meaning (existential)
Semantic feature
Einstein
Semantic computing
Semantic similarity
Algebra over a field
Cognitive linguistics
Semantic field
Physical system
Metadata
- Type
- article
- Landing Page
- https://doi.org/10.5281/zenodo.17900541
- OA Status
- green
- OpenAlex ID
- https://openalex.org/W7114929597
All OpenAlex metadata
Raw OpenAlex JSON
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https://openalex.org/W7114929597Canonical identifier for this work in OpenAlex
- DOI
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https://doi.org/10.5281/zenodo.17900541Digital Object Identifier
- Title
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Engineering Stable Generative Ecologies: A Semantic Physics Framework for Curvature–Entropy Governance in Generative AIWork title
- Type
-
articleOpenAlex work type
- Publication year
-
2025Year of publication
- Publication date
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2025-12-11Full publication date if available
- Authors
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Slade, TrentList of authors in order
- Landing page
-
https://doi.org/10.5281/zenodo.17900541Publisher landing page
- Open access
-
YesWhether a free full text is available
- OA status
-
greenOpen access status per OpenAlex
- OA URL
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https://doi.org/10.5281/zenodo.17900541Direct OA link when available
- Concepts
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Generative grammar, Artificial intelligence, Computer science, Geodesic, Entropy (arrow of time), Mathematics, Categorical quantum mechanics, Metric (unit), Differential geometry, Theoretical computer science, Semantic theory of truth, Field (mathematics), Principle of maximum entropy, Gauge theory, Theoretical physics, Generative model, Meaning (existential), Semantic feature, Einstein, Semantic computing, Semantic similarity, Algebra over a field, Cognitive linguistics, Semantic field, Physical systemTop concepts (fields/topics) attached by OpenAlex
- Cited by
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0Total citation count in OpenAlex
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| abstract_inverted_index.Equations, | 146 |
| abstract_inverted_index.Generative | 56 |
| abstract_inverted_index.Production | 121 |
| abstract_inverted_index.Relational | 80 |
| abstract_inverted_index.Ricci-flow | 168 |
| abstract_inverted_index.Riemannian | 36 |
| abstract_inverted_index.alignment, | 86 |
| abstract_inverted_index.artificial | 12 |
| abstract_inverted_index.complexity | 131 |
| abstract_inverted_index.constructs | 142 |
| abstract_inverted_index.curvature, | 62 |
| abstract_inverted_index.describing | 102 |
| abstract_inverted_index.ecologies. | 188 |
| abstract_inverted_index.engineered | 177 |
| abstract_inverted_index.formulates | 97 |
| abstract_inverted_index.generative | 8, 33, 173 |
| abstract_inverted_index.introduces | 79 |
| abstract_inverted_index.manuscript | 31 |
| abstract_inverted_index.operators, | 153 |
| abstract_inverted_index.processors | 18 |
| abstract_inverted_index.production | 108 |
| abstract_inverted_index.stability, | 64 |
| abstract_inverted_index.strategies | 156 |
| abstract_inverted_index.Information | 54 |
| abstract_inverted_index.constrained | 60 |
| abstract_inverted_index.dynamically | 46 |
| abstract_inverted_index.engineering | 155 |
| abstract_inverted_index.governance. | 169 |
| abstract_inverted_index.heuristics. | 76 |
| abstract_inverted_index.interaction | 89 |
| abstract_inverted_index.non-Abelian | 92 |
| abstract_inverted_index.differential | 72 |
| abstract_inverted_index.environments | 10 |
| abstract_inverted_index.trajectories | 57 |
| abstract_inverted_index.demonstrating | 128 |
| abstract_inverted_index.hallucination | 67 |
| abstract_inverted_index.informational | 43 |
| abstract_inverted_index.rule-filtered | 181 |
| abstract_inverted_index.thermodynamic | 24, 137 |
| abstract_inverted_index.Navier–Stokes | 149 |
| abstract_inverted_index.\gamma\left(|R| | 125 |
| abstract_inverted_index.distinguishability | 44 |
| abstract_inverted_index.Curvature–Entropy | 120 |
| abstract_inverted_index.ecologies—semantic | 9 |
| abstract_inverted_index.geometry-constrained | 186 |
| abstract_inverted_index.information-theoretic | 148 |
| abstract_inverted_index.σ=γ(∣R∣+14Tr(F2)),\sigma | 123 |
| abstract_inverted_index.\tfrac{1}{4}\mathrm{Tr}(F^2)\right),σ=γ(∣R∣+41Tr(F2)), | 127 |
| cited_by_percentile_year | |
| countries_distinct_count | 1 |
| institutions_distinct_count | 1 |
| citation_normalized_percentile.value | 0.80053845 |
| citation_normalized_percentile.is_in_top_1_percent | False |
| citation_normalized_percentile.is_in_top_10_percent | False |