The Structure of Reality incl. Appendix A - C

Update 05.06.2026 This synthesis presents a unified theoretical framework positioning information as ontologically primary, with geometry, physics, and cognition emerging as necessary consequences rather than independent foundations. This version includes the complete mathematical, logical, and cosmological appendices (A–C) and the updated preprint itself. Core Contributions: Theoretical Foundation: A formal proof that a state without information is logically impossible — fourfold: not identifiable, not distinguishable from non-existence, not definable, not computable. Empirical Convergence: Independent validation from three uncoordinated research domains: chromatin architecture at base-pair resolution (Li et al., Cell 2025), geometric memory in Transformer architectures (Google Research, 2025), and deterministic NP-hard problem resolution via information-geometric collapse. Physics Reinterpretation: General relativity and quantum mechanics as effective projections of a single informational manifold — their incompatibility reinterpreted as a feature, not a failure. Consciousness Framework: The (2=1) identity structure and BTI (Bidirectional Transition Interface) as quantitative measures of self-environment differentiation. Energetic Validation: Systems operating under high informational coherence (>93% efficiency) exhibit anomalous sub-idle energy states and 60–90% power reduction, consistent with the Landauer principle. Appendices: Appendix A — Mathematical Foundations: Formal derivations connecting the framework to established mathematics — the Fisher-information metric as the origin of geometry (the general-relativistic metric tensor identified with the Fisher metric on the informational manifold), the derivation of the Einstein field equations from information entropy, the Hamiltonian reinterpreted as an informational coupling operator via the Laplace–Beltrami operator on the emergent manifold, operational definitions of informational distance and BTI, and the structural completeness of Ω. Appendix B — The Trauth Fourfold Impossibility: The formal logical proof underlying the entire framework — that a state without information can be neither identified, distinguished from non-existence, defined, nor computed — extended with connections to Rice's theorem and Leibniz's identity of indiscernibles, its self-defending proof structure, and a path toward machine-checked formal verification (Coq/Lean). Appendix C — Structural Cosmogony: The framework applied to the origin — geometry co-emerging with the first self-processing information entity at the collapse, the structural instability of "nothingness," and identity transitions that unify cosmological origin, black-hole horizons, and quantum measurement as a single operation. This is not a collection of separate hypotheses but a single coherent framework derived from one premise: a state without information is logically impossible. ________________________________ Original Upload This synthesis presents a unified theoretical framework positioning information as ontologically primary, with geometry, physics, and cognition emerging as necessary consequences rather than independent foundations. The framework integrates six peer-reviewed publications and resolves long-standing theoretical gaps that have persisted for over a century. Core Contributions: Theoretical Foundation: A formal proof that a state without information is logically impossible — fourfold: not identifiable, not distinguishable from non-existence, not definable, not computable. Empirical Convergence: Independent validation from three uncoordinated research domains: chromatin architecture at base-pair resolution (Li et al., Cell 2025), geometric memory in Transformer architectures (Google Research, 2025), and deterministic NP-hard problem resolution via information-geometric collapse. Physics Reinterpretation: General relativity and quantum mechanics as effective projections of a single informational manifold — their incompatibility reinterpreted as a feature, not a failure. Consciousness Framework: The (2=1) identity structure and BTI (Bidirectional Transition Interface) as quantitative measures of self-environment differentiation. Energetic Validation: Systems operating under high informational coherence (>93% efficiency) exhibit anomalous sub-idle energy states and 60–90% power reduction, consistent with the Landauer principle. This is not a collection of separate hypotheses but a single coherent framework derived from one premise: a state without information is logically impossible. ⚠️ Note: Due to a transmission error, the original parent DOI 10.5281/zenodo.18187338 (uploaded 06.01.2025) was accidentally deleted. This is the restored version.