# [[releases/2025/Infomatics]] # Appendix E: Table of Core Formulas **(Operational Framework v3.4 - Final/Defunct)** This appendix lists key formulas discussed during the Infomatics v0-v3.4 development. **Crucially, the Infomatics v3 line of development was halted and deemed falsified** due to persistent inconsistencies and conflicts with observation ([[#Section 12: Final failure analysis and conclusion]], [[J Phase 3.2 Research Log & Discarded Paths]], [[M Methodological Failure Analysis]]). Therefore, **all specific formulas derived from the Infomatics v3 postulates (explicit π-φ governance, (n,m) indices, specific resonance conditions) are considered DISCARDED or FALSIFIED** as fundamental descriptions within this terminated framework. They are listed here for historical context only. ## E.1 Discarded / Falsified Formulas (Infomatics v0-v3.3) The following represent key hypotheses or derived consequences of the Infomatics v3 framework that proved untenable or were part of the falsified structure: * **Derived Speed of Light:** `c = π / φ` *(Status: Postulate; Discarded).* * **Derived Gravitational Constant:** `G ∝ π³ / φ⁶` *(Status: Inconsistent Derivations; Discarded).* * **Derived Planck Scales:** `ℓ_P ∝ 1/φ`, `t_P ∝ 1/π`, `m_P ∝ φ³/π`, `E_P ∝ πφ` *(Status: Based on discarded c, G, φ-action; Discarded).* * **Action Scale:** `Fundamental action unit = φ` *(Status: Postulate; Framework failed to replace ħ; Discarded).* * **Mass Scaling:** `M ∝ φ^m` *(Status: Empirical hint, not derived; Stability rules for m failed; Discarded as fundamental law).* * **Resolution Parameter:** `ε ≈ π⁻ⁿ φᵐ` *(Status: Heuristic; (n, m) structure failed; Discarded).* * **Geometric Amplitude Scaling:** `|A| ∝ φ²/π³`, `α_{eff} ∝ φ⁴/π⁶` *(Status: Hypothesis; Not derived from dynamics; Discarded).* * **Stability via L_m Primality:** `Stability requires Lm prime` *(Status: Falsified/Insufficient; Discarded).* * **Stability via GA/E8 Filter:** `Stability from Lm + GA Symmetry` *(Status: Intractable/Unproven; Discarded).* * **Stability via Resolution Resonance:** `φ^m ≈ π^(n+q)` *(Status: Falsified (Electron Puzzle); Discarded).* * **Stability via Ratio Resonance:** `φ^(m') ≈ π^(k')` (via convergents) *(Status: Led to falsified prediction Î₁=(S=0, Q≠0); Discarded as primary stability mechanism).* * **Stability Filter (Final Attempt):** `E_i = K \phi \omega_i` *(Status: Plausible derivation from action/phase principles, used φ as action unit. When applied to dynamics predicted by Ratio Resonance, led to falsified spectrum Î₁=(S=0, Q≠0); Framework halted, condition invalid in that context).* ## E.2 Conceptual Structures (Infomatics v3.3 / IOF Context) These represent the types of structures considered in the final stages, whose specific solutions led to the falsification. * **Conceptual GA Dynamics (Needed for Spin):** **(Eq. IOF-GA-Conceptual):** $\mathbf{D} \mathbf{K} \mathbf{G}_1 + \mathbf{M}(\mathbf{K}) = \mathcal{N}(\mathbf{K})$ * $\mathbf{K}$: STA Multivector Field * $\mathbf{D}$: U(1) Gauge Covariant Derivative (incorporating emergent Photon $A$) * $\mathbf{G}_1$: Constant Multivector (e.g., $I\gamma_0$) for Dirac-like structure * $\mathbf{M}(\mathbf{K})$: Mass/Stability Term (related to φ) * $\mathcal{N}(\mathbf{K})$: Non-linear self-interaction (related to φ, provides stability/confinement) *(Status: Represents the necessary *type* of equation, but the specific viable form and its solutions remain undetermined. This line of inquiry halted.)* *(No specific, validated formulas beyond the conceptual level can be stated for the halted Infomatics v3 framework or future IOF development at this time.)*