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Zenodo
2025
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| Online-Zugang: | https://doi.org/10.5281/zenodo.17695821 |
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Inhaltsangabe:
- In previous ``computational universe'' framework, universe axiomatized as discrete object U_{comp} = (X,T,C,I), upon which constructed discrete complexity geometry, discrete information geometry, control manifold (M,G) induced by unified time scale, task information manifold (S_Q,g_Q), and time--information--complexity joint variational principle. Unified time scale given by scattering master scale $ \kappa(\omega) = \varphi'(\omega)/\pi = \rho_{rel}(\omega) = (2\pi)^{-1}\tr Q(\omega) unifying phase derivative, spectral shift density, and Wigner--Smith group delay trace as single scale. However, this framework still remains mainly at ``theoretical geometry'' level, has not systematically given how to metrologically measure and calibrate unified time scale and computational universe structure in actual experiments. This paper, on basis of computational universe--unified time scale--spectral windowing readout, constructs cross-platform metrology paradigm using ``phase--frequency'' as sole observable, implementing it on two representative testbeds: cosmological-distance Fast Radio Burst propagation (FRB) and laboratory-scale \delta-ring--Aharonov--Bohm (AB) flux scattering. Core idea: from computational universe perspective, all observables realized through phase--frequency readout under unified time scale; FRB and \delta-ring scattering respectively provide cosmic-scale and laboratory-scale ``homologous readouts'', viewable as implementations of same metrology paradigm at different scales under unified time scale and complexity geometry. Main results of this paper: enumerate \item Under framework of categorical equivalence between computational--physical universes, introduce ``phase--frequency readout functor'' PhFr, sending any physically realizable computational universe object to metrology object containing only phase--frequency data. Prove PhFr compatible with unified time scale master scale: under traceable perturbation and wave operator completeness, PhFr output completely determined by \kappa(\omega) and finite spectral--scattering invariants. \item For FRB, construct ``vacuum polarization windowing upper limit'' model: window FRB frequency-domain phase using PSWF/DPSS type window functions, prove under fixed complexity budget and cosmological distance constraints, any unified time scale variation \delta \kappa(\omega) contribution to FRB phase residual can be bounded by strict upper bound; if observed residual below this bound, obtain unified time scale type upper limit on vacuum polarization or other new physics. \item For \delta-ring--AB flux scattering, restate equivalence between spectral quantization equation f(k,\alpha_\delta,\theta) = \cos(kL) + (\alpha_\delta/k)\sin(kL) - \cos\theta = 0 and ``amplitude-corrected phase closure'' \cos\gamma(k) = |t(k)|\cos\theta and prove under computational universe--control manifold perspective: under spectral observation \{k_n(\theta)\} at fixed (L,\theta), \delta--coupling strength \alpha_\delta and AB flux \theta are identifiable in non-pathological domain (Jacobian full rank), usable as ``laboratory ruler'' for unified time scale--phase metrology. \item Under unified time scale--spectral windowing readout framework, embed FRB and \delta-ring scattering in same ``phase--frequency metrology universe'', prove existence of ``cross-platform scale unification condition'': when FRB phase residual and \delta-ring scattering spectral shift both explained by same \kappa(\omega) model, their windowed readouts belong to same equivalence class on appropriate PSWF/DPSS space, thus can calibrate and consistency-test unified time scale through joint fitting. \item Embed above phase--frequency metrology structure into time--information--complexity variational principle, formalize ``choosing FRB/\delta-ring window functions and control parameters'' as variational problem on joint manifold, give variational conditions for ``simultaneously using cosmic-scale and laboratory-scale phase--frequency readouts to maximize unified time scale identifiability under finite complexity budget''. enumerate This paper thus completes experimental implementation design of ``phase--frequency unified metrology'' within computational universe framework: FRB and \delta$-ring scattering become two-end testbeds of unified time scale and complexity geometry, PSWF/DPSS window functions become natural tools for error control, both jointly constructing cross-scale, cross-platform, yet completely unified phase--frequency metrology system under computational universe perspective.