Mathematical Materiality: Relational Foundations, Physical Bridges and a Programme of Verification

Mathematical Materiality addresses four foundational problems within a common relational perspective: the stability of physical laws across space and time, dark matter, dark energy and an ontological explanation of quantum mechanics. The volume organises mathematical contributions that can be examined: the algebra of nexuses and registers, matter-field dynamics, gravitational bridges involving a clock and memory, a distal hypothesis with a bounded cosmological comparison, and a statistical pre-geometric candidate. It states results, conditions and further developments for each area. Effective bridges disclose their imported physical structures; the pre-geometric candidate does not yet derive gravity, Lorentz invariance or dimensionality 3+1. The historical R29 comparison has a standard equivalent; the new B18 comparison also remains compatible with standard alternatives and does not identify an exclusively MM origin. Audit B20 internally reproduces the B17-B18 chain through a distinct implementation, without constituting external review. The programme provides structured proposals and checks for an initial expert assessment, with different levels of maturity across the four areas and global unification and validation still open. Ugo Lanciano conceived the foundational ontological architecture; the physical-mathematical architecture in the phase assembled in the dossier is attributed to GPT-6 Astra, in dialogue directed by the author. This declared division of contributions documents the method and provenance of the work, not its scientific validity. This standalone documentary report presents the English edition of volume 0.19 and its selected annexes. It references, but does not replace, Mathematical Materiality: a status report, version 2.27 (DOI 10.5281/zenodo.22667516). It does not reproduce every historical MM development or redistribute the preceding executable research package. Scientific code, observational catalogues and execution environments are not included. The English translation was produced with AI assistance, parallel translation agents and a unified final editorial review. Translation and layout checks do not constitute a new scientific audit.