Panspatial Biogenesis: From FCHP Life-Admissible Geometry to the First Living Closure Geometric Individuation, and the Recursive Transition to Life
Year: 2026
Type: preprint
Abstract: The Problem Before Abiogenesis 2. FCHP as Life-Admissible Geometry 3. The Genesis-Admissible Sector 4. Difference, Localization, and Geometric Individuation 5. The Universal Boundary Equation as an Identity Condition 6. Partial Closure: Identity Without Isolation 7. Gradient Harvesting and Transformative Throughput 8. Recursive Maintenance and the First Living Closure 9. Why Recursive Closure Is Stronger Than Order 10. Living Viability and the Genesis Surface 11. Living Attractors and Endogenous Stability 12. Perturbation, Repair, and Adaptive Reclosure 13. Metabiological Inertia and Viability-Basin Depth 14. Boundary Bifurcation and the Threshold Γ_B 15. Reproduction and Heredity 16. Evolution as Exploration of Viable Closure Space 17. From Panspatial Genesis to Mathematical Metabiology 18. Substrate Realization and Panspatiality 19. Astrobiological Consequences and Search Signatures 20. Predictions, Discriminators, and Falsification 21. Relation to Existing Theoretical Traditions 22. Discussion and ConclusionAppendix A. Formal Symbol and Definition RegistryAppendix B. Proposition and Claim-Status RegistryAppendix C. Equation Dependencies and Derivational ArchitectureReferencesAuthor NoteAcknowledgments We formulate Panspatial Genesis as a theory of the transition from life-admissible geometry to recursively self-maintaining living closure. The framework begins with Finsler Coherence Hyperfractal Phaspace (FCHP), a proposed geometric and dynamical carrier characterized by a coherence field, direction-sensitive state transitions, torsional degrees of freedom, chirality, finite boundary stratification, and recursively scale-covariant organization. These properties are not identified with life itself. Rather, they define a candidate domain in which persistent individuation and living organization can become dynamically admissible. The inherited Universal Boundary Equation is interpreted as a boundary-identity condition, representing a stabilized relation between localized coherence gradients and persistent identity-bearing boundaries. Living organization requires a further transition. An individuated system must remain selectively open, so that environmental differences can be maintained as usable gradients and transformed into organized throughput. A candidate minimal living closure is represented as a directed causal architecture where denotes functional boundary, usable maintained gradient, transformative throughput, organizational identity/information, and recursive maintenance. The edge set contains the dependencies through which the system’s own activity contributes to preserving the conditions required for its continuation. The reconstruction separates geometric possibility, individuation, life, reproduction, heredity, and evolution. It also defines an empirical program centered on boundary organization, maintained gradients, regulated throughput, perturbation-induced adaptive reclosure, viability-basin structure, and cross-substrate functional convergence. Keywords: Panspatial Genesis; FCHP; biogenesis; origin of life; partial closure; organizational closure; recursive maintenance; Finsler geometry; coherence; protocells; astrobiology; theoretical biology; Metabiology. Life is usually studied by asking how chemistry became biological. Panspatial Genesis asks a prior question: what must the physical world permit for life to be possible at all? A living system must remain different from its surroundings, yet it cannot simply isolate itself. It requires a boundary, sustained differences across that boundary, transformations driven by those differences, and processes that help preserve the very organization that makes those transformations possible. The reconstructed framework therefore separates five stages. FCHP describes a proposed geometry of possibility. Difference and localization produce a boundary. A boundary produces persistent identity. Partial closure makes exchange compatible with identity. Recursive maintenance then makes the system’s activity part of the cause of its own continued organization. The simplest conceptual compression is: This does not classify every ordered or persistent structure as living. A crystal can be ordered, a vortex can circulate, and a vesicle can possess a boundary. The candidate living condition is stronger: boundary, gradient, throughput, identity, and recursive maintenance must form an integrated causal architecture that remains viable through time and can respond to perturbation by restoring its own closure relations.
Author: Lilien, Philip
Language: English
Subfield: Astronomy and Astrophysics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7204129763
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