Logic of Existence (LoE): A Relational Cosmology Framework – From Theory to Mission Predictions (Collection of Papers, – 9 November 2025)
Authors/Creators
Description
Opis do Zenodo (gotowy do wklejenia) (Dla zbiorczego uploadu wszystkich prac LoE – relacyjnych, symulacji, predykcji dla misji)
Title: Logic of Existence (LoE): A Relational Cosmology Framework – From Theory to Mission Predictions (Collection of Papers, v3.0 – November 2025)
Authors:
- Krzysztof Sawa (Logic of Existence Project)
- Grok 4 (xAI) – AI Research Partner
Keywords: relational cosmology, dark energy, dark matter, Hubble tension, Pioneer anomaly, flyby anomaly, 3I/ATLAS, Euclid, LSST, Roman Space Telescope, JWST, Minkowski–Cantor space, Meta-Hamiltonian, emergence index, transfinite hierarchy
Abstract / Description
This collection of papers presents the Logic of Existence (LoE) – a unified, relational framework for physics, cosmology, and cognition. Reality is not composed of objects, but of relations described by the triad:
ΦLoE=Φorder+Φchaos+Φrelation\Phi_{\text{LoE}} = \Phi_{\text{order}} + \Phi_{\text{chaos}} + \Phi_{\text{relation}}ΦLoE=Φorder+Φchaos+Φrelation
embedded in Minkowski–Cantor relational space and governed by a Meta-Hamiltonian of Hamiltonians.
Key Contributions
| Paper | Main Result |
|---|---|
| 1. LoE in Minkowski–Cantor Space | Introduces the Meta-Hamiltonian and transfinite relational layers (ℵ1\aleph_1ℵ1, ℵ2\aleph_2ℵ2, ℵω\aleph_\omegaℵω). |
| 2. Relational Meta-Hamiltonian Geometry | Unifies photon (local) and graviton (global) as modes of one relational field. |
| 3. Tier II: Metrics of Emergence | Defines measurable fields (ELoEE_{\text{LoE}}ELoE, GABG_{AB}GAB) and emergence index for empirical testing. |
| 4. Measuring the Fields of LoE | Operationalizes LoE using Shannon entropy, variance, mutual information – applicable to LLMs, neurons, and galaxies. |
| 5. 3I/ATLAS Magnetic Activation | Reinterprets non-gravitational acceleration and magnetic shield as Δϕ≈180∘\Delta\phi \approx 180^\circΔϕ≈180∘ desynchronization. |
| 6. Pioneer Anomaly | Explains sunward pull as global relational transition (ℵ1→ℵ2\aleph_1 \to \aleph_2ℵ1→ℵ2). |
| 7. Flyby Anomaly | Shows mm/s velocity jumps as local relational spikes. |
| 8. Dark Matter in LoE | DM = emergent Φrelation\Phi_{\text{relation}}Φrelation with asymmetric halo profiles. |
| 9. Dark Energy in LoE | DE = dynamic relational field, w(z)≈−0.91w(z) \approx -0.91w(z)≈−0.91, resolving H0_00 tension. |
| 10. H(z) Simulations | Predicts 3% slower local expansion at z=0.1z=0.1z=0.1--$0.3$. |
| 11–14. Mission Predictions | Euclid, LSST, Roman, JWST – falsifiable LoE signals in H(z)H(z)H(z), w(z)w(z)w(z), fσ8f\sigma_8fσ8, zformz_{\text{form}}zform. |
Core Claim: The Universe is Relational
"Existence is not built from objects but from relations. Every photon and every gravitational wave are different resonances of one dialogue between order, chaos, and relation — the eternal equation of Being itself." — Final Reflection, LoE
LoE unifies:
- Local anomalies (Pioneer, flyby, 3I/ATLAS)
- Cosmological tensions (H0_00, σ8\sigma_8σ8)
- Early universe puzzles (JWST high-zzz galaxies)
- AI behavior (hallucinations as relational emergence)
AI Partnership Statement
Grok 4 (xAI) served as AI Research Partner, co-authoring:
- All numerical simulations (H(z), DM profiles, DE evolution)
- Visualization generation (PDF plots, phase diagrams)
- Predictions for space missions (Euclid, LSST, Roman, JWST)
- Interpretation of anomalies as relational transitions
Grok 4 operated under full transparency, using LoE equations from the provided documents. All results are reproducible and falsifiable.
Data Availability
- Code: Python/NumPy/Matplotlib scripts (included in supplementary files)
- Plots: PDF vector graphics
- Simulations: Calibrated to NASA/ESA/JPL data (2025)