arXiv subjects

Christoph Kirsch

Publications and source records attributed to Christoph Kirsch.

5 recordsLinked to original sources

arXiv2026

Untrusted Authors, Trusted Answers: A Calculus of Fidelity-Graded Translations

To answer a question about a program, move the program to where the question is decidable. Every such move is a translation, and every translation is a place to be wrong. We study translation as a graph -- many languages, a few reasoning targets, independently built routes of honestly different trustworthiness -- and give it a calculus: pairs of languages close commuting squares that are directional (exactness is the identity-embedding special case of over-approximation), checkable per program, and composable, a route's contract being the componentwise meet of its hops' contracts -- assurance class, direction, kept observables, measured cost. One asymmetry organizes trust: witness-carrying answers are self-certifying by replay at the source; universal answers are where grades, independent branches, and re-checked certificates earn their cost. The compositional core, lax telescope included, is mechanized in Lean 4. hurdy-gurdy implements the calculus as two planes meeting in one registry. The use plane reads declarations and produces evidence-carrying answers; its builders and its intended player are both LLMs, untrusted by construction. The evolution plane grows the graph: unmet questions are recorded as demand, pairs are recommended by evidence and registered by humans, and a ratchet keeps every prior verdict standing. Answers never write; growth never answers. Run indefinitely, the loop converges on every reducibly decidable question, at fidelity that only rises. We measure the July 2026 snapshot -- per-construct conjoined coverage, dual-route branch agreement for two ISAs, source-level witness replay, certified unreachability re-validated by a formally verified checker, escape rates for the gate itself -- and report the defects the architecture caught in its own authors' work.

cs.PL↗

arXiv2025

Bridging Atomistic and Mesoscale Lithium Transport via Machine-Learned Force Fields and Markov State Models

Lithium diffusion in solid-state battery anodes occurs through thermally activated hops between metastable sites often separated by large energy barriers, making such events rare on ab initio molecular dynamics (AIMD) timescales. Here, we present a bottom-up multiscale workflow that integrates AIMD, machine-learned force fields (MLFFs), and Markov state models (MSMs) to establish a quantitatively consistent link between atomistic hopping mechanisms and mesoscale transport. MLFFs fine-tuned on AIMD reference data retain near-DFT accuracy while enabling large-scale molecular dynamics simulations extending to tens of nanoseconds. These extended trajectories remove the strong finite-size bias present in AIMD and yield diffusion coefficients in excellent agreement with experiment. Furthermore, from these long MLFF trajectories, we obtain statistically converged lithium jump networks and construct MSMs that remain Markovian across more than two orders of magnitude in the lag times used for their construction. The resulting MSMs faithfully reproduce mean-square displacements and recover rare diffusion processes that do not occur on AIMD timescales. In addition to propagating lithium distributions, the MSM transition matrices provide mechanistic insight: their eigenvalues and eigenvectors encode characteristic relaxation timescales and dominant transport pathways. Although demonstrated for defect-free crystalline Li$_x$Si$_y$ phases, the AIMD$\rightarrow$MLFF$\rightarrow$MSM framework is general and provides a transferable approach for describing lithium transport in amorphous materials, defect-mediated diffusion, and next-generation solid-state anodes.

physics.chem-ph↗

arXiv2021

Auditory-visual scenes for hearing research

While experimentation with synthetic stimuli in abstracted listening situations has a long standing and successful history in hearing research, an increased interest exists on closing the remaining gap towards real-life listening by replicating situations with high ecological validity in the lab. This is important for understanding the underlying auditory mechanisms and their relevance in real-life situations as well as for developing and evaluating increasingly sophisticated algorithms for hearing assistance. A range of 'classical' stimuli and paradigms have evolved to de-facto standards in psychoacoustics, which are simplistic and can be easily reproduced across laboratories. While they ideally allow for across laboratory comparisons and reproducible research, they, however, lack the acoustic stimulus complexity and the availability of visual information as observed in everyday life communication and listening situations. This contribution aims to provide and establish an extendable set of complex auditory-visual scenes for hearing research that allow for ecologically valid testing in realistic scenes while also supporting reproducibility and comparability of scientific results. Three virtual environments are provided (underground station, pub, living room), consisting of a detailed visual model, an acoustic geometry model with acoustic surface properties as well as a set of acoustic measurements in the respective real-world environments. The current data set enables i) audio-visual research in a reproducible set of environments, ii) comparison of room acoustic simulation methods with "ground truth" acoustic measurements, iii) a condensation point for future extensions and contributions for developments towards standardized test cases for ecologically valid hearing research in complex scenes.

physics.med-ph↗

arXiv2021

Spatial resolution of late reverberation in virtual acoustic environments

Late reverberation involves the superposition of many sound reflections resulting in a diffuse sound field. Since the spatially resolved perception of individual diffuse reflections is impossible, simplifications can potentially be made for modelling late reverberation in room acoustics simulations with reduced spatial resolution. Such simplifications are desired for interactive, real-time virtual acoustic environments with applications in hearing research and for the evaluation of hearing supportive devices. In this context, the number and spatial arrangement of loudspeakers used for playback additionally affect spatial resolution. The current study assessed the minimum number of spatially evenly distributed virtual late reverberation sources required to perceptually approximate spatially highly resolved isotropic and anisotropic late reverberation and to technically approximate a spherically isotropic diffuse sound field. The spatial resolution of the rendering was systematically reduced by using subsets of the loudspeakers of an 86-channel spherical loudspeaker array in an anechoic chamber. It was tested whether listeners can distinguish lower spatial resolutions for the rendering of late reverberation from the highest achievable spatial resolution in different simulated rooms. Rendering of early reflections was kept fixed. The coherence of the sound field across a pair of microphones at ear and behind-the-ear hearing device distance was assessed to separate the effects of number of virtual sources and loudspeaker array geometry. Results show that between 12 and 24 reverberation sources are required.

eess.AS↗

arXiv2021

Computationally efficient spatial rendering of late reverberation in virtual acoustic environments

For 6-DOF (degrees of freedom) interactive virtual acoustic environments (VAEs), the spatial rendering of diffuse late reverberation in addition to early (specular) reflections is important. In the interest of computational efficiency, the acoustic simulation of the late reverberation can be simplified by using a limited number of spatially distributed virtual reverb sources (VRS) each radiating incoherent signals. A sufficient number of VRS is needed to approximate spatially anisotropic late reverberation, e.g., in a room with inhomogeneous distribution of absorption at the boundaries. Here, a highly efficient and perceptually plausible method to generate and spatially render late reverberation is suggested, extending the room acoustics simulator RAZR [Wendt et al., J. Audio Eng. Soc., 62, 11 (2014)]. The room dimensions and frequency-dependent absorption coefficients at the wall boundaries are used to determine the parameters of a physically-based feedback delay network (FDN) to generate the incoherent VRS signals. The VRS are spatially distributed around the listener with weighting factors representing the spatially subsampled distribution of absorption coefficients on the wall boundaries. The minimum number of VRS required to be perceptually distinguishable from the maximum (reference) number of 96 VRS was assessed in a listening test conducted with a spherical loudspeaker array within an anechoic room. For the resulting low numbers of VRS suited for spatial rendering, optimal physically-based parameter choices for the FDN are discussed.

eess.AS↗