# R&D Memorandum: Non-Forced Applications of Fibonacci and Golden Ratio Dynamics in the CORE Substrate

**Status**: Proposed (Exploratory R&D / Theoretical Blueprint)  
**Date**: 2026-07-13  
**Authors**: Multi-model R&D + Joshua Shay  
**Traceability**: Drive memo `1wcuxwfxk6AW6du4SgKe4AuRxMaE5tipxG2VbrXeWM6c`  
**Related**: ADR-0003, ADR-0006, ADR-0238, ADR-0239, ADR-0241, ADR-0242, `core/physics/energy.py`, `core/physics/fibonacci_search.py`, `core/physics/atlas_packing.py`  
**Canonical path**: `docs/analysis/fibonacci_applications_in_core_substrate.md`

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## 1. Introduction

In natural systems, the Fibonacci sequence \(F_n = F_{n-1}+F_{n-2}\) and Golden Ratio \(\varphi = (1+\sqrt{5})/2\) appear in optimal packing and multi-scale structure. CORE does **not** force sacred geometry. Operators land only where they provide deterministic, reconstructible, evidence-gated advantage (ADR-0242 sovereignty invariant).

## 2. Four integration vectors (memo) ↔ ADR-0242 five vectors

| Memo § | Topic | ADR-0242 vector | Landing status |
|--------|-------|-----------------|----------------|
| 2.1 | Hyperbolic golden-spiral mode packing | V3 | 🟢 `atlas_packing.py` |
| 2.2 | Fibonacci anyons / braid holonomy | V5 | 🔴 research only |
| 2.3 | Fibonacci-section search | V1 | 🟢 cert-gated `fibonacci_search.py` |
| §4 | Multi-scale \(\tau_n = F_n\tau_0\) energy | V2 | 🟡 table in `wave_energy_boundary`; not production default |
| (Drive add) | Fibonacci-word observability schedule | V4 | 🔴 staged |

### 2.1 Optimal spectral mode packing (V3)

Place mode centroids via Golden Angle / phyllotaxis and lift to Cl(4,1) null points. Separation pin \(d_{\min}\) uses CGA null-point distance (honest Euclidean readout). See ADR-0242 V3.

### 2.2 Fibonacci anyons (V5 — research)

Fusion \(\tau\otimes\tau = \mathbf{1}\oplus\tau\) as a topological composition research program. **Blocked from production** until algebraic + numerical proofs exist. Do not wire into serve, vault COHERENT, or FFI.

### 2.3 Fibonacci-section search (V1)

Fixed-budget unimodal search for κ / residual brackets. Public API returns `FibonacciSearchCertificate | OptimizationFailure` only. κ failure → baseline 1.0.

### 2.4 Multi-scale temporal windows (V2)

\[
\tau_n = F_n\cdot\tau_0
\quad\Rightarrow\quad
\{1,1,2,3,5,8,13,\ldots\}\tau_0
\]

Progressive landing: constants schedule + band index. Production `FieldEnergyOperator` multi-band \(E_n(t)\) requires comparative evidence vs dyadic bases (ADR-0242 Phase 2).

## 3. Engineering guidelines

- **No force-fitting** — elegance is not acceptance.  
- **Evidence gate** — certificates / failures, not silent floats.  
- **Off-serve** — fibonacci / packing / energy-boundary modules quarantined from `chat/runtime.py`.  
- **Reconstruction-over-storage** for packing layout identity.  

## 4. Cross-links

- ADR-0242 (authoritative five-vector decision record)  
- ADR-0241 wave-field substrate  
- Cohesion master plan entity traces  
- Fidelity ledger §12  
