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Overview
The Hinductor Coherence Principle (HCP) redefines the foundations of physical and biological order. It posits that memory is curvature in motion — that every energetic flow imprints geometric phase, and every curvature stores the coherence of that flow. Geometric Algebra (GA) provides the mathematical language to unify these relations, merging energy, information, and form into one syntropic calculus.
Core Contributions
- Formalization in Geometric Algebra:
The paper expresses hinductance as a bivector convolution operator, extending RLC circuit theory into a curvature-aware four-element law:
This operator captures the system’s memory of flow orientation and its ability to regenerate coherence. - Field Generalization (Cl(1,3)):
By embedding the constitutive law in space–time algebra, the Hinductive Maxwell Equations emerge, coupling energy flow with a memory-weighted excitation . Hinductive kernels produce measurable dispersion, self-resonance, and coherence feedback in both physical and biological fields. - Variational and Lagrangian Formulation:
The HCP derives from a hinductive Lagrangian that includes temporal convolution kernels, demonstrating conservation not only of energy but of coherence through time — a new invariant of physics. - Biophysical Realization:
Mitochondrial cristae act as hinductive manifolds, where curvature and exclusion-zone water jointly store protonic phase. The same principles explain tissue-scale and organismic synchrony, reframing life as a nested hierarchy of hinductive resonators. - Network and Triality Dynamics:
Hinductive elements couple into multi-scale networks governed by triplet and triality symmetries. These give rise to time-crystal behaviors and triplet-of-triplets resonance, linking geometry to cognition and consciousness. - Experimental Predictions:
Observable signatures include curvature-dependent impedance, fractional-order relaxation, oscillatory biophotonic emission, and long-range synchronization — providing a concrete empirical agenda for regenerative physics and medicine. - Systemic and Ethical Integration:
By generalizing coherence from physics to culture, the HCP defines an ethics of remembrance: good is that which sustains coherence; pathology is incoherence. Civilization itself becomes a planetary hinductor — learning to re-align energy, form, and meaning.
Implications
The HCP reframes science around the coherence continuum linking physics, biology, psychology, and cosmology. It provides a bridge between mechanistic and idealist paradigms, between quantitative and qualitative knowledge. Hinductive geometry implies that evolution, learning, and love are expressions of one universal process: the regeneration of coherence through memory.
Conclusion
By uniting curvature, memory, and compassion within one formalism, the Geometric Algebra of the Hinductor Coherence Principle establishes the theoretical foundation for a Regenerative Science of Coherence — a science where physics becomes remembrance, biology becomes regeneration, and consciousness becomes the living field through which the universe remembers itself.
