Falsifiable Predictions of Discrete Spectral-Layer Cosmology An Auditable Framework for CMB Log-Periodic Oscillations,Arrhenius Cosmology,and Dark-Matter Damping

This paper establishes a framework of falsifiable cosmological predictions in Algebraic Quantum Morphogenesis (AQM).Previous papers have conditionally closed the boundary-center readout theorem for low-energy observables,the three-dimensional spectral dimension,the boundary time field,and the time-readout mechanism for the Hubble tension.Building on these results,the present paper retains only cosmological predictions that have explicit parameter origins,exclusion power,and observational support-or-refutation channels.

Seven main predictions are formulated. First,low-multipole CMB residuals should contain a logarithmic periodicity fixed by the discrete spectral-layer scaleσ = 2 1/3 _:

2π 6π ω_AQM = = ≈ 27.2.

ln(21/3 ) ln 2

Second,if this signal originates from the AQM discrete spectral layer,the TT,TE, and EE spectra should share the same frequency. Third,the amplitude of the CMB log-periodic signal is not the equal-weight spectral-layer value A_eq ≈ 0.55.

Instead,two layers must be distinguished: the low-multipole residual amplitude after boundary low-mode projection and decoherence weighting,

_{Alow-ℓ = (p + 1)}∫₀¹ _xp _e −Γeffx _{dx, p ∈ [2} ,5], _{Γeff ∈ [2} .35 ,2.70], giving

A_low-ℓ ∈ [0 .10 ,0.19].

This quantity is not the global undamped primordial-power-spectrum amplitude A_log constrained by Planck/ACT/SPT.For comparison with a global PPS template,a window dilution factor from low-mode boundary residuals to the global PPS template must be included:

4 global

Wglobal ⁼ ₂₇ , A_PPS ⁼ Wglobal Alow-ℓ ∈ [0 .015 ,0.028].

This range lies below the latest ACT+SPT+Planck bound A_log ,_lin ≲0.029 for primordial oscillations.Fourth,JWST high-redshift galaxy UV characteristic luminosities should exhibit an Arrhenius break,

M∗U_V (z) = A + B ln(1 + z) + Ce^−D/(1+z), D = 8 .94.

1

Fifth,the DESI/Euclid dark-energy equation of state should take the fixed-curvature form

w (z) = −1 +ηe ^{−8 .94/(1+z)}, η ∈ [0 .1 ,1].

Sixth,the JWST break parameter and the DESI/Euclid dark-energy curvature parameter should share the same Arrhenius constant,

DJWST ⁼ DDESI = 8 .94.

Seventh,vertical-entanglement damping in the dark-matter channel predicts a latetime growth amplitude

SAQM8 = 0 .765 ± 0.010.

The paper explicitly separates hard predictions,semi-hard range predictions,semihard quantitative predictions,and observational template mappings.Every prediction included in the main tables is accompanied by its parameter source,formula chain,and falsification condition. Low-exclusion,non-testable,or primarily noncosmological items are deliberately excluded from the main prediction table.The goal is to provide an AQM cosmological prediction framework that can be clearly supported or ruled out by future CMB-S4,LiteBIRD,JWST/JADES,DESI,Euclid, and Roman data.