Author notes — full detail, auditor-facing

The cipher framework originally extended a single Fibonacci-based formula across ALL dimensional cycles. The c-ladder (the per-dimension speed-of-light scaling that comes out of the cipher engine) was computed as c_d = Budget(d) × v_write, where Budget(d) was the Fibonacci-derived count of independent geometric modes packable into one frame, and v_write = c/8.

This gave a clean ladder:

• 1D: c₁ = 2/8 = 0.25c
• 2D: c₂ = 5/8 = 0.625c
• 3D: c₃ = 8/8 = 1.0c (speed of light)
• 4D: c₄ = 13/8 = 1.625c
• 5D: c₅ = 21/8 = 2.625c
• 6D: c₆ = 34/8 = 4.25c

The framework adopted this and used it for predictions through cipher v9, v10, and v11.

In April 2026, working through 5D and 6D ratio derivations, the structural insight landed: dimensional cycles aren't governed by one universal formula. Each cycle has its OWN recurrence engine, and the recurrence orders themselves follow Fibonacci.

• Cycle 1 (dims 1-3): 2-term Fibonacci — binary recurrence, peak at φ
• Cycle 2 (dims 4-6): 3-term Tribonacci — trinary recurrence, peak at τ ≈ 1.839
• Cycle 3 (dims 7-9): 5-term Pentanacci — peak at ≈1.966
• Cycle 4 (dims 10-12): 8-term Octanacci — peak at ≈1.996

The cycle orders (2, 3, 5, 8, 13) are themselves Fibonacci. This is the unifying branch: Fibonacci operates self-similarly at two levels — within each cycle, AND across cycles.

What this meant concretely: the c-ladder values for dims 4-6 in cipher v9 (1.625, 2.625, 4.25) were extending Fibonacci/8 across the cycle-1 → cycle-2 boundary, which is exactly the kind of universal-formula-extrapolation the cycle-specific framework rejects. The correct cycle-2 values use Tribonacci-derived ratios:

• 4D: r = 1 + sin(45°) = 1.707 (cycle-2 substrate, 24-cell geometry)
• 5D: r = 7/4 = 1.750 (early Tribonacci ratio T₆/T₅)
• 6D: r = τ ≈ 1.839 (Tribonacci limit, root of x³=x²+x+1)

Three significant downstream effects:

1. Unifying the magic numbers. The 5D interference produces a √7 structural factor. The 7-fold is the first frustration overtone in the cycle-2 {5,7,9,11,13} set. The nuclear magic numbers 28, 50, 82, 126 emerge from the {7,9,11,13} intruders — and now we know WHY {7} appears first: it's the structural factor of cycle-2 interference. The cycle framework gives a geometric mechanism for the magic numbers, not just a numerical match.

2. Stale references to clean up. Cipher v9 §III, v10, v11, and tlt notes/theory/dimensional_formulas_extrapolated.txt all use the Fibonacci-only ladder. These are flagged as stale in /CORRECTIONS_2026-05-11_c_ladder_and_dim_ladders.md with forward pointers to the cycle-specific derivation source. The historical docs are preserved (not rewritten) as the audit trail of how thinking evolved.

3. The Hubble-tension analysis sharpens. When evaluating whether TLT's staging-quadratic framework predicts the observed H₀ discrepancy (67.4 km/s/Mpc CMB vs 73.0 SH0ES), the relevant cosmic-epoch range maps to d_CMB ≈ 2.95 — still in cycle 1 — so the c-ladder correction doesn't affect that headline calculation. But ANY analysis touching d≥4 (UHECRs as d=5 events, 120-cell as 4D-projected, plasma confinement) now uses the corrected ladder.

This is the textbook example of what the framework calls a refinement rather than a correction. The mechanism changed (one universal formula → cycle-specific recurrence engines). The framework absorbed the change cleanly. No smoothing terms added; the underlying physical insight is sharper now.