Scope (minimal thesis): The record contains (i) the main preprint (PDF), (ii) LaTeX source (fully reproducible), and (iii) an extended “explainer” PDF (intuition-first, minimal prerequisites, with figures and tables). Key idea: effective degradation of geometric regularity—defined without smooth curvature—can act as a temporal bottleneck, increasing measurable quantum time delays. Operational proxies: (1) volume-growth/ball-measure deficit proxy , and (2) spectral/heat-kernel descriptors including spectral dimension . Mechanism anchor: geometry-induced spectral modifications can shift scattering phase through spectral shift theory (Kreĭn / Birman–Yafaev viewpoint), hence modifying EWS delays. Test program: controlled families where a geometric scale is varied at fixed probe conditions; fit versus and apply falsifiability Types I–III. Non-claims: no new gravity, no QM violation, no “free energy”, no universal constant assumed a priori. Reproducibility: theoretical/conceptual; no proprietary data required.
Scope (minimal thesis): The record contains (i) the main preprint (PDF), (ii) LaTeX source (fully reproducible), and (iii) an extended “explainer” PDF (intuition-first, minimal prerequisites, with figures and tables). Key idea: effective degradation of geometric regularity—defined without smooth curvature—can act as a temporal bottleneck, increasing measurable quantum time delays. Operational proxies: (1) volume-growth/ball-measure deficit proxy , and (2) spectral/heat-kernel descriptors including spectral dimension . Mechanism anchor: geometry-induced spectral modifications can shift scattering phase through spectral shift theory (Kreĭn / Birman–Yafaev viewpoint), hence modifying EWS delays. Test program: controlled families where a geometric scale is varied at fixed probe conditions; fit versus and apply falsifiability Types I–III. Non-claims: no new gravity, no QM violation, no “free energy”, no universal constant assumed a priori. Reproducibility: theoretical/conceptual; no proprietary data required.
This work introduces an operational geometric framework for analyzing Eisenbud–Wigner–Smith (EWS) time delay in non-smooth quantum regimes. Without modifying standard quantum mechanics, we define scale-dependent geometric proxies compatible with non-smooth metric-measure structures and connect them to spectral shift mechanisms via Krein theory. Two scaling regimes are distinguished and expressed through a falsifiable law τ(E;ℓ) ∝ (1 + X(ℓ))^γ. The framework explicitly preserves unitarity, no-signaling, and relativistic causality. Concrete falsifiability criteria (Types I–III) are formulated. Order-of-magnitude comparison with attosecond chronoscopy suggests compatibility with observed delay enhancements in reduced-dimensional systems. The work introduces no new fundamental fields; it reframes time-delay observables in terms of coarse-grained geometric descriptors.
Using the de Branges--Kreĭn (DBK) canonical system and weighted Mellin space as carriers, we explicitly incorporate the finite bandwidth/time window of real instruments into spectral measures, forming a windowed readout framework; we characterize ``commit (collapse/commit)'' through KL/Bregman information geometry; use scattering phase--spectral density--Wigner--Smith delay as energy scale; close non-asymptotic errors via Nyquist--Poisson--Euler--Maclaurin (three-term decomposition); ensure realizability and stability through variational optimization of frame/sampling density and window/kernel. The core unified formula is $ \,\varphi'(E)=-\pi\,\rho_{\mathrm{rel}(E)=1{2}trQ(E)\,}\quad(a.e.) $ unifying (single/multi-channel) scattering phase derivative, relative local density of states (LDOS) and Wigner--Smith delay; under information geometry we obtain Born probability = minimal-KL projection (I-projection), and ``pointer basis'' is spectral minimum of windowed readout operator. Above criteria consistent with Herglotz--Weyl, Birman--Kreĭn, Wigner--Smith, Ky Fan, Poisson/EM and other standard results, directly interchangeable and implementable.
This record presents a short, time-stamped research note proposing a clean control experiment aimed at clarifying the physical origin of recently observed quantum-metric-induced trajectory bending in quantum materials. While such effects are commonly interpreted as arising from geometric structure in Hilbert space, an open question remains as to whether an effective temporal or phase-delay contribution may act as the underlying generator of the observed metric. The proposed protocol isolates temporal phase modulation from spatial geometry by keeping particle trajectories and external forces fixed while varying only the effective phase, delay, or frequency associated with the quantum state. The experiment constitutes a null test: a positive outcome would indicate a temporal contribution to the effective metric, while a null result would strengthen a purely geometric interpretation. The proposal requires no new instrumentation and is compatible with existing solid-state platforms (such as oxide-interface two-dimensional electron gases), topological or quantum Hall interferometers, and cold-atom interferometric systems. This note is intended as a conceptual and experimental guide rather than a report of new data.
We construct a unified framework of Windowed Scattering--Information Geometry (WSIG) centered on the ``operator--measure--function'' triple: observation is operationalized through Toeplitz/Berezin compression Kw,h=ΠwMhΠw, reducing all readouts to linear functionals on spectral measures. The trinity scale identity φ′(E)/π=ρrel(E)=(2π)−1trQ(E)=−ξ′(E) unifies phase, relative density of states, and Wigner--Smith group delay as master scales. For observer filter chains {Kθ}θ∈Θ, we define an information action S and induce an information metric via the Hessian gμν=∂μ∂νS, interpreting connection and curvature as second-order non-commutative responses of readouts to observation parameters. Under the ``double-time separation'' postulate---where causal partial order is uniquely defined by frontier time t∗ while windowed group delay Tγ[w,h] serves only as operational scale---variation of the action A=(2κ)−1∫(R−2Λ)∣g∣dnθ+∫(Linfo+λμν[gμν−∂μ∂νSloc])∣g∣dnθ yields Einstein-type equations Gμν+Λgμν=κTμν. The right-hand stress-energy tensor Tμν arises from spectral responses of Kθ. Under band-limited and Nyquist--Poisson--finite-order Euler--Maclaurin (NPE) discipline, we achieve error closure with ``non-increasing singularity: poles = master scales''. Within the same geometric framework, we unify quantum measurement: superposition = convex superposition of compatible components in static blocks; collapse = anchor switching and π-semantic collapse; entanglement = inseparable information correlations in causal networks. Continuous monitoring satisfies GKSL dynamics and Spohn entropy production monotonicity, with Belavkin filtering providing conditional state updates. Core criteria and required external theorems are provided, along with one-dimensional potential scattering examples and complete proof chains.
Version 4.0 public record for “A Nuisance-Aware Residual-Test Framework for Geometry-Induced Quantum Potentials in Curved Constrained Platforms”. Version 4.0 is a substantive revision of the public record. It updates the title and scientific framing, clarifies the established Jensen–Koppe–da Costa geometric-potential anchor versus the new nuisance-aware residual-test methodology, adds an explicit finite-width/disorder/spin-orbit/electrostatic validity envelope, strengthens the minimum experimental-design protocol, improves figure readability, and synchronizes the journal and Zenodo packages. The work is framed as a conservative methodological and design-level residual-test framework for geometry-induced quantum potentials in curved constrained platforms. The manuscript is anchored to the established Jensen–Koppe–da Costa geometry-induced potential for scalar particles constrained to smooth curves. The standard constrained-curve prediction is represented by the fixed coefficient −1/4, while the residual parameter delta-lambda is defined as a falsifiable null-test quantity. Standard constrained quantum mechanics predicts delta-lambda = 0. The manuscript emphasizes that any nonzero residual should first be treated as a platform anomaly unless it survives curvature scaling, nuisance projection, matched-reference controls, blind residual extraction, and cross-geometry replication. No experimental detection is claimed. The included simulations and prospective bounds remain design-level estimates. The package contains the manuscript, supplementary information, figures, reproducibility code, generated CSV/JSON data, metadata files, and public technical materials sufficient to regenerate the numerical validation tables, platform-specific energy-scale estimates, residual sensitivity plots, and figures.