codex_reference.md

📖 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:

  -\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