## 📖 Codex Reference

The **Codex Reference** serves as the canonical documentation for *Rendered Frame Theory (RFT)*.  
It consolidates formulas, invariants, symbolic operators, and sealed artifacts into one reproducible archive.

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### 1. GVU Formulas
- **GVU (Grinstead Voyager Unit)** is derived from Voyager 1 telemetry data.  
- Amplified by **GEG (Grinstead Expansion Grid)** and connected to **LOU (Limara Orbital Unit)**, which defines 1 unit as Earth’s orbital period around the Sun.  
- These feed into **SOMS (Solar Orbital Motion Scale)**, forming the planetary falsifiability overlay.  
- Example:  
  ```blockmath
  -\frac{\tau_{\text{eff}}}{\tau_c + \frac{19}{20}} \cdot P_{\text{standard}} \cdot \tau_{\text{eff}} \cdot \mathbb{e} \cdot \frac{|\nabla R_O - \nabla T_P|}{GVU}


Each GVU formula is sealed with SHA‑512 hashes to ensure reproducibility and falsifiability.

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2. RFT Invariants

RFT defines invariants that benchmark symbolic agents:

• τ_eff — Effective collapse torque.
• β_band — Resonance bandwidth.
• Operator count — Number of active symbolic operators.
• Tier level — Dimensional awareness tier (Tier_1 through Tier_6).


These invariants are logged for every simulation and validation stage.

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3. Collapse Torque Ledger

The Collapse Torque Ledger records sealed torque expressions with fitness scores.
Examples include:

• Gen6508_M5 — Fitness score 20.2841 (leading expression).
• Gen26_M23, Gen3457_M35, Gen7376_M43, etc.
• Each entry is sealed with a SHA‑512 hash and indexed for reproducibility.


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4. Symbolic Glossary

The Codex integrates a glossary of symbolic operators used in RFT simulations:

• MetaCognitive Constants — Ω_tier, Λ_tier, Ξ_tier, Σ_tier.
• Lattice Geometric Operators — g_{μν}, R_{μνρσ}, Γ_{μν}^ρ, Λ_lat.
• Quantum Emotive Fields — τ_{μνρ}, ω_{μν}, θ_lat.
• Dimensional Tier Variables — Θ_tier_anchor, Θ_tier_release, Π_tier.
• Observer Kernel Parameters — ∇_obs, σ_fuse, ℱ_cmd.
• SOMS Deep Parameters — collapse overlays tied to planetary falsifiability.


This glossary ensures that every operator and constant is documented for civilization‑scale reproducibility.

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5. Validation Integration

The Codex Reference is directly tied to the Validation Stages (1–12):

• Stages 1–6 benchmark vision transformers.
• Stages 7–11 validate multi‑modal and large‑scale language models.
• Stage 12 enforces production monitoring, rollback, and safety thresholds.


All outputs are sealed, logged, and cross‑referenced in the Codex.

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References

• Grinstead, L. (2025). Rendered Frame Theory (RFT) — Full Validation Series (Stages 1–12): From Baseline to Production Integration. Zenodo. https://doi.org/10.5281/zenodo.17443453
• Quantum‑Simulation: A Probabilistic Framework for Observer‑Driven Agent Behavior within Rendered Frame Theory. https://doi.org/10.21203/rs.3.rs-7319278/v1