navi-creative-determinant¶
Autopoietic closure as a nonlinear elliptic BVP on a compact Riemannian manifold.
A field theory of coherence and meaning, with a machine-checked finite-graph existence theorem and conditionally formalized continuum theorems (Lean 4, Mathlib v4.34.1).
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 | \(\lambda_1(-\Delta - b;\, M) < 0\) | A positive coherent configuration exists (Theorem 3.16); exact when \(a \equiv 0\) (Proposition 3.19) |
| 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 positive-existence 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 the zero and positive branches on either side of the viability threshold. Then read Section 3 for the spectral foundation.
Lean / formal verification --- Start with the cd_formalization directory for the assumption boundary and what is proved. CdFormal/Graph/Existence.lean holds the unconditional finite-graph theorem (exists_pos_graph); CdFormal/Theorems.lean holds the continuum theorems, which are conditional on the PDEInfra hypotheses.
Cognitive science / philosophy --- Start with Sections 1 and 4 (introduction and interpretive layer), which connect the framework to enactivism, semiotics, and phenomenology. Then read Theorem 3.16 (positive existence), which makes "viability exceeds dissipation" precise.
Documentation¶
| Section | Contents |
|---|---|
| Quickstart | Install, run tests, open the notebook |
| Conceptual Primer | Gentle introduction without math |
| The CD Stack | One diagram of how the pieces fit, with what is proved, defined, heuristic or deferred |
| Author's Note | Origin story and motivation |
| Open Problems | Eleven open theoretical questions |
| 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 |