Quantum Sphaera Companion: A Structure-First Mathematical Unfolding
Year: 2026
Type: preprint
Abstract: Description Quantum Sphaera Companion v2.27.0 is a structure-first mathematical unfolding of the Quantum Sphaera / Sphaera-Cascade framework. The Companion serves as the extended mathematical, semantic, tensorial, and proof-structural support layer of the main paper. It preserves the normalized release chronology while continuing the long-form development of projector logic, closure structure, compensator-guided admissibility, and the internal proof architecture of the framework. This release completes the mathematics-first consolidation cycle that followed the earlier computational opening. In particular, v2.27.0 strengthens the mathematical dependency spine running from ground condition and collapse picture through Heisenberg-compensator emergence, closure, projector stabilization, admissible transport, Millennium-matrix realization, and trace/branch continuation. Several local hardening steps have been integrated into this release, including explicit dependency-spine lemmas and invariance-style propositions for projected transport, admissible matrix-sector action, and admissible trace/branch persistence. As a result, the first major A-priority block is now no longer treated merely as roadmap material, but as mathematically release-supporting. The Companion therefore shifts from pure steering logic toward a more explicit local closure status: the first core dependency chain is structurally closed for now, even if some parts remain only medium-density in proof expansion and may be unfolded further in later versions. The computational chapter remains present, visible, and intentionally preserved, but it is not the primary driver of this release. MML, MMA, MCP, the co-processor view, proof-as-program templates, certificates, normalization, execution, and host-export ideas remain in place as a teaser and reserved architecture, while mathematical closure and dependency stabilization take precedence. v2.27.0 should therefore be read as a mathematics-first release: it does not claim a finished standalone proof engine, compiler, runtime, or proof kernel, but it does provide a more stable mathematical backbone on which such later work could rest more safely. Concept DOI: 10.5281/zenodo.19210728Version DOI: 10.5281/zenodo.19266666
Author: Brendecke, Marc
Language: English
Subfield: Astronomy and Astrophysics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7140888203
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