Prediction 15c Falsified: φ^(−k) Decay Law Does Not Describe Multi-Level T1 Coherence Times in High-EJ/EC Transmon Qudits Fibonacci Causal Loop Theory — Paper 61
This paper reports the definitive test and falsification of FCLT Prediction 15c (pre-registered in Paper 52, DOI: 10.5281/zenodo.19746102). The prediction held that consecutive T₁ decoherence timescale ratios in transmon qudits satisfy τₖ/τₖ₊₁ → φ ≈ 1.618, derived from depth-2 bath memory structure in the Nakajima–Zwanzig projection formalism. Using the measured T₁ coherence times of qudit Q5 from Blok et al. (2025), Table III, across 9 transition levels (k = 1–9), T₁ values plateau at ~13–14 µs from k = 6 onward, inconsistent with the φ⁻ᵏ decay model. At k = 9, the predicted T₁ is 1.4 µs versus the observed 13 µs — a factor of 9× discrepancy (χ² = 75.9, reduced χ² = 9.5). The plateau is consistent with a dielectric loss noise floor identified by Blok et al. The pre-registered falsification criterion is met. Prediction 15c is falsified. Short-range consistency at k = 1–3 is noted but cannot distinguish FCLT from the harmonic null model and is insufficient for confirmation.
This paper reports the definitive test and falsification of FCLT Prediction 15c (pre-registered in Paper 52, DOI: 10.5281/zenodo.19746102). The prediction held that consecutive T₁ decoherence timescale ratios in transmon qudits satisfy τₖ/τₖ₊₁ → φ ≈ 1.618, derived from depth-2 bath memory structure in the Nakajima–Zwanzig projection formalism. Using the measured T₁ coherence times of qudit Q5 from Blok et al. (2025), Table III, across 9 transition levels (k = 1–9), T₁ values plateau at ~13–14 µs from k = 6 onward, inconsistent with the φ⁻ᵏ decay model. At k = 9, the predicted T₁ is 1.4 µs versus the observed 13 µs — a factor of 9× discrepancy (χ² = 75.9, reduced χ² = 9.5). The plateau is consistent with a dielectric loss noise floor identified by Blok et al. The pre-registered falsification criterion is met. Prediction 15c is falsified. Short-range consistency at k = 1–3 is noted but cannot distinguish FCLT from the harmonic null model and is insufficient for confirmation.
We derive, from first principles within FCLT, a parameter-free prediction for multi-level transmon qubit decoherence structure. Ostrogradsky stability constrains the bath memory kernel to depth-2 (the unique minimal stable non-Markovian structure), which propagates via Nakajima-Zwanzig and the Dyson self-energy to impose Fibonacci recursion on decay rates Γk = Γk₋₁ + Γk₋₂. Prediction: consecutive decoherence timescale ratios τk/τk+1 → φ ≈ 1.618 in the transmon regime (bath bandwidth ≫ anharmonicity). Null: harmonic oscillator gives ratio → 1. Pass criterion δ < 0.05; falsification δ > 0.15. Pre-registered before data examination.
Fibonacci Causal Loop Theory (FCLT) predicts that decoherence rate Γ scales inversely with necessity depth D: Γ(D) = Γ₀ × φ^(−D), and the ratio of decoherence rates at adjacent necessity depths satisfies Γ(D+1)/Γ(D) = 1/φ ≈ 0.618. This formalizes FCLT Prediction 12 (pre-registered in FCLT Complete Manuscript v16, DOI: 10.5281/zenodo.20087640). The derivation follows directly from the QNM quality factor confirmations: P73 confirmed Q = φ³ (D=3, Schwarzschild) and P73e confirmed Q = φ⁴ (D=4, Kerr). Since Q = ω₀/Γ, the decoherence scaling law Γ(D) = Γ₀ × φ^(−D) follows with zero free parameters. The prediction is testable in NMR quantum simulators, trapped-ion arrays, and superconducting qubit platforms where decoherence rates can be measured across multiple organizational depth levels. Confirmation criterion: δ < 0.05. Classification: technology-gap pending validated D(x,t) measurement protocol. FCLT scorecard unchanged: 20 confirmed / 5 falsified / 24 tech-gap / 4 gray zone.
The author develops the experimental layer of the framework introduced in the foundational Preprint I. Seven families of falsifiable predictions (F1–F7) are stated and matched to ten falsification criteria (F-T1–F-T10). The predictions cover: τ-window scaling laws under monitored feedback and non-Markovian memory; a 3-qubit ontological feedforward discriminator constructed to separate synchronisation-based from entanglement-based metric emergence; a directional-asymmetry test Δ(τ) with null control; a 4-qubit triangle-inequality test on the metric-compatibility regime; an asymptotic large-deviation consistency channel as cross-cutting envelope; a coherence-affected entropy-production consistency target; and a sync-rate scaling under Dicke collective dissipation. A worked-case reanalysis of Micadei et al. (2019) under the non-Markovian channel of P1 demonstrates non-vacuity of the framework on existing experimental data within a factor ≈ 2.5 on a nine-decade timescale range. The operational definition of the memory timescale τₘₑₘ was fixed prior to numerical evaluation as a matter of pre-registration discipline, with an analytic zero-crossing alternative computed for transparency and explicitly rejected under the conservative bound. A structured Nakajima–Zwanzig–TCL2 sketch indicating the sign and structure of the next-to-leading-order correction for the Micadei interaction Hamiltonian is provided in Appendix E-II, identifying this residual as a target for next-to-leading-order refinement in the smallness parameter (Φ_NM − 1).
This document formally timestamps two specific, falsifiable predictions derived from the Harmonic Structure of the Standard Model (HSM) framework, both connecting QCD geometry (the pion mass mπ and pion decay constant fπ) to measurable outcomes in semiconductor physics and superconducting qubit design. Priority date: April 28, 2026. SC-1 predicts that electron (hole) mobility in Ge/Si core/shell nanowires will show local peaks at Si shell thicknesses t = n × λ/2 where λ/2 = 0.9179 nm, the half-wavelength of the Si f-process intervalley phonon (E = 19 meV, f = 4.59 THz). Predicted peak positions: 0.9179, 1.8358, 2.7537, 3.6716 nm. This is consistent with published Fabry-Pérot ballistic transport data at 1–3 nm Si shell thickness. The discriminating experiment is a systematic ALD sweep in 0.1 nm steps (ALD precision ±0.02 nm); if peaks are oscillatory rather than monotonic, the prediction is confirmed. SC-2 predicts that the intrinsic optimal E_J/E_C ratio for a transmon qubit, in the absence of materials-limited extrinsic quasiparticle noise, is E_J/E_C = mπ/2 = 67.5, derived from the mathematical identity between the chiral QCD Lagrangian and the Josephson Lagrangian. The current world-record coherence transmon (Tuokkola 2025, T1 = 766 μs) operates at estimated E_J/E_C ≈ 67, within 1% of this prediction. The discriminating experiment sweeps E_J/E_C = 40–100 at fixed frequency with per-noise-channel T2 decomposition. Speculative working paper — not peer reviewed
This note reports the outcome of the test pre-registered in DOI 10.5281/zenodo.23047418, applying its observables, step rule and decision criteria without modification. Using standard quantum mechanics for the ideal Rydberg-blockade (PXP) chain as the benchmark, Prediction 2, that the post-quench density settles with the universal ratio −1/φ², is refuted: the ratios are fixed by a slowly decaying oscillation about an offset centre, as a centre-and-amplitude decomposition shows exactly. Prediction 1, the spatial correlation ratio −1/φ² at infinite temperature, holds exactly in theory and awaits laboratory confirmation. The qualitative picture is corroborated: the transition is gradual, with unity exact throughout while local coherence fades. The residual ~5% amplitude loss per half-swing is shown not to be structural, since a small Hamiltonian deformation removes it. A near-hit at the first step is reported as post hoc and not counted. Includes the note, LaTeX source and a reproducibility script.
On 20 April 2026, Sorci, Foo, Leibfried, Sanner, and Pikovski (Phys. Rev. Lett.) proposed that next-generation optical ion clocks with squeezed-state preparation can probe whether proper time exists in quantum superposition — a single clock ticking faster and slower at once. Their work establishes the protocol; the laboratory measurement is forthcoming. That prospective window permits a genuine pre-registered prediction. Fibonacci Causal Loop Theory (FCLT) holds that any stable system governed by depth-2 necessity recursion, S(n)=S(n−1)+S(n−2), is driven to the golden ratio φ=(1+√5)/2 — the unique algebraically forced attractor of its characteristic equation x²−x−1=0. We advance the hypothesis that proper-time superposition is such a system, the two temporal branches playing the role of the two prior states, so that the ratio of fast- to slow-ticking amplitudes approaches φ upon decoherence. From this we obtain one parameter-free, falsifiable prediction — t₊/t₋ → φ ≈ 1.61803, with δ = |R−φ|/φ and falsification at δ > 0.10 — logged under Protocol V3.1 prior to experimental resolution. We claim no confirmation: the prediction is offered as not-yet-tested, to be adjudicated by the Stevens/NIST program. A second, independent signature (φ-structured fringe spacing in the squeezed regime) provides an internal consistency check.