📖 Ch.5 — phi-distance and Fibonacci-Lucas seeds (500w · 🟢 P2 · I — FOUNDATIONS)

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Ch.5 — phi-distance and Fibonacci-Lucas seeds

Master: trios#380 · Part: I — FOUNDATIONS
Scope: software-only (Rust/Zig), no hardware/FPGA/KOSCHEI
Words: 500 · Priority: 🟢 P2 · Owner: GoldenSunWeaver

🎯 Scope (FROZEN, v2.1 SOFTWARE-ONLY)

φ-distance metric definition. Why Fibonacci F_n / Lucas L_n seeds (deterministic, sanctioned, audit trail). Sealed seeds for OSF preregistration.

🔑 Key claims / formulas

• phi_distance(e,m) = |e/m - 1/φ|
• F₁₇=1597, F₁₈=2584, F₁₉=4181, F₂₀=6765, F₂₁=10946
• L₇=29, L₈=47 (Lucas extras)
• Why Fibonacci/Lucas: closure under multiplication by φ

📦 Deliverables

• paper/sections/5_phidistance_and_fibonaccilucas_seeds.tex

✅ Definition of Done (v2.1)

• Word count 500 ±10%
• All claims cited (primary literature)
• No woody-shop / KOSCHEI / FPGA references
• Compiles in main.tex via tectonic
• L1 (no .sh) · L3 · L4 · L8

🤖 ONE-SHOT directive (when operator types ONE SHOT Ch.5)

A: take Markdown draft from §"Draft", convert to LaTeX, place in
paper/sections/5_<slug>.tex, ensure compile, open PR with Closes #<this>.

phi^2 + phi^-2 = 3 · TRINITY · NEVER STOP