navi-creative-determinant¶
Autopoietic closure as a nonlinear elliptic BVP on a compact Riemannian manifold.
A field theory of coherence and meaning, with Lean 4-verified existence conditions (15 theorems, zero sorry).
Core concepts¶
| Concept | Symbol | Role |
|---|---|---|
| Semiotic manifold | \(M\) | Space of possible meanings or interpretations |
| Presence field | \(\Phi(x)\) | Intensity of coherent presence at each point on \(M\) |
| Care | \(\kappa\) | Energetic investment sustaining the system |
| Coherence | \(\gamma\) | Structural integrity holding the system together |
| Contradiction | \(\mu\) | Generative tension driving exploration |
| Creative drive | \(a(x) = \kappa\gamma\mu\) | Gradient activity where all three fields jointly support |
| Viability potential | \(b(x) = \kappa\gamma - \lambda\mu\) | Where care-coherence support dominates contradiction cost |
| Viability threshold | \(\lambda_1(-\Delta - b;\, M) < 0\) | Nontrivial coherent configurations exist (Theorem 3.16) |
| CD condition | --- | Coherence observables correlate with Jacobian volume dynamics |
Entry ramps by background¶
PDE / analysis --- Start with Sections 2--3 of the paper (existence and nontriviality theorems) and the eigenvalue verification in the notebook (Part 1). Treat Sections 4--5 as motivation and proposed applications.
AI / interpretability --- Start with Section 5 (the CD condition and falsifiability criteria) and skim the notebook plots showing bifurcations at viability thresholds. Then read Section 3 for the spectral foundation.
Lean / formal verification --- Start with the cd-formalization subdirectory for the axiom boundary and what's proved.
Cognitive science / philosophy --- Start with Sections 1 and 4 (introduction and interpretive layer), which connect the framework to enactivism, semiotics, and phenomenology. Then see Theorem 3.16 (nontriviality) to see how "viability exceeds dissipation" is made mathematically precise.
Documentation¶
| Section | Contents |
|---|---|
| Quickstart | Install, run tests, open the notebook |
| Conceptual Primer | Gentle introduction without math |
| Author's Note | Origin story and motivation |
| Open Problems | Ten explicit theoretical gaps |
| Ethical Covenant | Voluntary ethical commitments |
| Contributing | How to participate, extend, or challenge |
| FAQ | Quick answers to common questions |
| Research Roadmap | Ten open research directions |
| Changelog | Release history |