# RST Python Vault Index > **Epistemic labels:** See [[../../expanded theory applied/Implementation status and problems#Epistemic status glossary|Implementation status — Epistemic status glossary]] for definitions (Derived, Calibrated, Illustrative, External consistency, Hypothesis / audit). ## The Sovereign Chain (Paper 2 Core) These are the definitive scripts that implement the complete derivation. | Script | Role | Key output | Epistemic note | |:---|:---|:---|:---| | `rst_engine/core.py` | Central library: `mu_rst`, `volume_ln_ball` | Fidelity function, L^n geometry | **Derived** (definitions in code) | | `rst_hardware.py` (in Substrate Hardware/) | Physical constants: `surface_area_ln_3d`, `perimeter_ln_2d`, alpha scan, mass scan | alpha, m_p/m_e, alpha_G | **Derived** (chain inputs) | | **`rst_complete_chain.py`** | **THE CAPSTONE.** Recursive render: n → everything | All 10 SM quantities from n≈1.24 | **Derived** (given input \(n\)) | | **`rst_minimal_proof.py`** | **NAPKIN SCRIPT.** Standalone, zero vault deps, <50 lines | Same 5 quantities; reviewer-readable in 60 seconds | **Derived** (same chain, minimal) | | **`rst_unfolding.py`** | **Level-2 saturation masses** | Z boson (N=d*) and Top quark (N=18) from alpha^-2 unfolding | **Derived** (given \(\alpha\), \(d^*\)) | | `rst_self_consistency.py` | Self-consistency loop: n → sin^2 → d* → alpha | Chain closes within stated residual tolerances | **Derived** (closure check) | | `rst_sovereign_chain_geometry.py` | Geometry visualizations | L^{1.25} ball mapping, star vs box, unified diagram | **Illustrative** | | `rst_action_complete.py` | Consolidated verification of listed constraints | Constraint table PASS/FAIL vs targets | **Derived** (internal consistency checks) | ## Sector-Specific Derivations (Paper 2 Supporting) Each script targets one sector of the theory. | Script | Sector | Status | Key result | |:---|:---|:---|:---| | `rst_generalized_aether.py` | Tensor (GW speed) | **External consistency** | \(c_\mathrm{gw} = c\) in the Skordis–Zlosnik parameterization | | `rst_disformal_derivation.py` | Lensing (B(q)) | **External consistency** | \(B(q) = (1-\mu^2)/\mu^2\); Cassini-scale benchmark | | `rst_gate3.py` | Alpha drift (Gate 3) | **Derived** | \(\kappa_n = d(\ln\alpha)/dn\) at \(n=1.25\) | | `rst_connes_koide.py` | EW + Leptons | **Hypothesis / audit** | Structural identities (e.g. \(\sin^2\theta\), Koide); not a standalone SM proof | | `rst_kigami_spectrum.py` | Mass hierarchy audit | **Hypothesis / audit** | Feasibility of decimation schemes; not a full hierarchy theorem | | `rst_n_shannon.py` | n-scaling law | **Derived** (fit) | Regression \(n = 1 + \log_2(1+M)\), \(R^2 = 0.985\) | ## Historical / Superseded These scripts were intermediate steps. Their results are incorporated into the capstone. | Script | Superseded By | Notes | |:---|:---|:---| | `rst_weinberg_derivation.py` | `rst_connes_koide.py` | Early Weinberg angle candidates | | `rst_dstar_gauge.py` | `rst_self_consistency.py` | d* = 9 + theta_W identification | | `rst_n_scaling.py` | `rst_n_shannon.py` | Early n-scaling (naive DoF, R^2=0.15) | | `rst_closure_audit.py` | `rst_final_closure.py` | Intermediate closure tests | | `rst_final_closure.py` | `rst_complete_chain.py` | Honest residual analysis | | `rst_perturbations.py` | `rst_generalized_aether.py` | Simple Einstein-Aether (failed GW170817) | | `rst_param_audit.py` | `rst_action_complete.py` | Early parameter audit | ## The Complete Derivation Chain (Paper 2 Narrative) ``` n = 1.25 (SPARC galaxy rotation curves — calibrated anchor; see SPARC evaluation notes) │ ├─ Connes NCG: sin²θ_W = (3n/16)(1 - απ(2-n)²) → 0.058% │ ├─ Gauge count: d* = 9 + θ_W → 0.002% │ ├─ Volume deficit: α = V_d*(1.25) / V_d*(2) → 0.022% │ ├─ Phase space: m_μ/m_e = (D/2α)(1 + α(2-n)) → 0.021% │ ├─ A-O trace: m_τ/m_e via Koide Q = d_s/2 = 2/3 → 0.013% │ ├─ Topology: m_p/m_e = α⁻¹·d*·SA₃/P₂·(1-αs/π) → 0.038% │ └─ Unfolding: m_Z/m_e = d*·α⁻² → 0.035% m_t/m_e = 18·α⁻² → 0.066% ``` All errors < 0.07%. One free parameter. 9 derived quantities.