SPU Framework: Complete Navigable Document Index

This index provides direct access to all documents in the SPU framework with brief descriptions. Each filename is a clickable link to the corresponding document in the local directory.

📚 Core Framework Documents

• index.md – Main introductory document presenting the SPU framework, its foundational principles, geometric basis, and comparison with standard paradigms.

• SPU Theory Symmetry_Phase_Unification Framework.md – Comprehensive presentation of the full SPU theory, including geometric foundations, fermionic capacity, gauge unification, emergent gravity, and falsifiability conditions.

• What SPU Explains That Standard Paradigms Do Not.md – Comparative analysis highlighting SPU’s explanatory power for phenomena left unexplained by standard paradigms.

🧮 Geometric Foundations

• spu_geometric_origin_uv-1.md – Detailed derivation of the UV Lagrangian from the geometric structure $E_7/SU(8)$, explaining the origin of fermionic capacity.

• spu_fermionic_capacity_128.md – Explanation of why fermionic capacity is fixed at 128 and cannot be tuned within the SPU framework.

δ Dynamical Parameter δ

• Minimal Microscopic Toy Model Generating a Non_Zero δ under RG Flow.md – A UV-complete quantum field theory demonstrating that δ ≠ 0 necessarily emerges from renormalization group (RG) flow.

• rg_origin_of_delta.md – Proof that δ arises as an infrared fixed point of the renormalization group flow.

• derivation_of_δ_rg_and_qft_analysis.md – Technical QFT derivation of δ from one-loop effects and dynamical decoupling mechanisms.

• spu_consistency_bound_delta.md – Internal consistency bounds on δ derived from RG stability and perturbative control requirements.

• spu_refined_semi_analytic_bound.md – Refined semi-analytic bounds on δ combining asymptotic safety, unitarity, and decoupling constraints.

• spu_dynamical_origin_delta.md – Minimal dynamical origin of δ without invoking topological arguments or index theorems.

⚡ Gauge Unification

• Gauge_Unification_in_SPU.md – Explanation of dynamical gauge unification without group embedding, based on common fermionic origin.

• Weinberg_Angle_in_SPU.md – Analysis of the Weinberg angle within the SPU framework (note: content may overlap with Gauge_Unification_in_SPU.md).

• spu_appendix_b.md – Spectral normalization of the electromagnetic sector, including representation factors and η-invariant contributions.

🌌 Emergent Gravity

• Minimal Emergent Gravity in the SPU Framework.md – Semi-analytic derivation of the gravitational scale from collective suppression in the fermionic medium.

• consistency_bound_gravity_scale.md – Consistency constraints on the emergent gravitational scale from decoupling requirements and collective nature.

• rg_to_emergent_gravity.md – Connection between the RG flow of δ and the emergence of gravity at the unification scale.

• spu_gravity_predictions.md – Concrete predictions for gravitational phenomena: tensor modes, proton decay, and absence of UV quantum gravity effects.

🕰️ Early Universe and Cosmology

• Early-Universe Signatures in the SPU Framework.md – Early-universe phenomenology, including an inflation-like phase and primordial gravitational waves.

• semi_analytical_estimate_vacuum_energy.md – Semi-analytic estimate of vacuum energy with non-extensive scaling proportional to curvature.

🌠 Galactic Dynamics

• readme_1.md – Full application of SPU to galactic rotation curves, deriving the transition radius and the baryonic Tully-Fisher relation.

• spu_critical_surface_density.md – Interpretation of the critical surface density in terms of a dimensionless loading parameter and saturation of the fermionic medium.

• spu_scale_separation_vortex.md – Explanation of why vortex gravitational effects appear only on galactic scales, not on stellar scales.

🔬 Fermionic Medium and Spacetime

• spu_mezzo_fermionico.md – Ontological definition of the fermionic medium, saturated degrees of freedom, and coherence length ℓ_SP.

• spu_einstein_hilbert.md – Derivation of the Einstein-Hilbert action as the universal collective response of the fermionic medium.

• spu_limite_newtoniano.md – Recovery of the Newtonian limit from the Einstein-Hilbert action through standard approximations.

• spu_fallimento_eh.md – Conditions for the breakdown of Einstein-Hilbert at scales below ℓ_SP or in high-curvature regimes.

• spu_n3_vortex.md – Emergence of the n=3 vortex in the fermionic condensate from energetic stability arguments and capacity constraints.

🧪 Falsifiability and Consistency

• Minimal falsification conditions for SPU.md – Model-independent falsification criteria covering RG behavior, unification, gravity emergence, and tensor modes.

• spu_falsification_conditions.md – Alternative formulation of falsification conditions focused on structural predictions and RG consistency.

📖 Technical Appendices

• spu_appendix_a.md – Spectral derivation and clarification of δ’s role, separating topological structure from dynamical RG corrections.

• spu_consistency_bound.md – Document on consistency bounds focusing on general theoretical constraints within SPU.

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🔄 Logical Reading Path

For a coherent understanding of SPU, consider this reading sequence:

1. Start with: README.md → SPU Theory Symmetry_Phase_Unification Framework.md
2. Geometric foundation: spu_geometric_origin_uv-1.md
3. δ dynamics: Minimal Microscopic Toy Model Generating a Non_Zero δ under RG Flow.md → rg_origin_of_delta.md
4. Gauge unification: Gauge_Unification_in_SPU.md
5. Emergent gravity: Minimal Emergent Gravity in the SPU Framework.md → rg_to_emergent_gravity.md
6. Cosmology: Early-Universe Signatures in the SPU Framework.md
7. Galactic physics: readme_1.md
8. Medium structure: spu_mezzo_fermionico.md → spu_einstein_hilbert.md
9. Falsifiability: Minimal falsification conditions for SPU.md