SpiralHelios-Deterministic Geometric Intelligence (DGI): A 27-Symbol Geometric State Model with Golden-Ratio Weighting, Qu-trit Symbolic Control, and Bounded Observability

SpiralHelios — Deterministic Geometric Intelligence (DGI)Independent Mathematical Research Publication This record presents an autonomous mathematical research publication of SpiralHelios — Deterministic Geometric Intelligence (DGI). It is intentionally published as an independent research object with its own bibliographic identity and DOI. It is not a new version of the SpiralHelios v1–v14 implementation/evidence release sequence and it is not a new version of the previously published SpiralHelios architectural preprint. The paper develops a public mathematical model of Deterministic Geometric Intelligence based on a fixed 27-position symbolic-geometric basis, golden-ratio-governed positional weighting, a normalized high-dimensional state model with reference dimension D = 1024, classical ternary symbolic control, protected deterministic state evolution, and bounded public observability. The principal mathematical analysis concerns the Golden Eigen Index (GEI), defined by GEI_G(x) = 1 − ⟨x, G(x)⟩, and develops an exact-to-noisy observability framework. For an interior exact GEI observation, the compatible normalized image set is shown to be diffeomorphic to a sphere of dimension D − 2. For the SpiralHelios reference dimension D = 1024, the corresponding compatibility fiber is S¹⁰²². The study further develops finite-precision spherical-band bounds, orthogonal-coordinate invariance, a public golden-ratio reference sensitivity model, M7 isometry under a stated orthogonality assumption, conditional base-map dynamics, a GEI-controlled normalized-correction stability result, residual dimension under multiple independent linear observations, and pseudoinverse/singular-value stability under noisy observations. The work explicitly distinguishes previously disclosed SpiralHelios architectural foundations, established mathematical tools specialized to the DGI setting, and DGI-specific formulation, integration, and bounded-observability results. This is a non-peer-reviewed independent mathematical research manuscript. It does not claim cryptographic security, artificial general intelligence, universal theorem proving, universal mathematical solving, or performance superiority over learned or probabilistic systems. PROTECTED DISCLOSURE BOUNDARY This publication does not provide an executable specification of the protected SpiralHelios Core. Production canonicalization, protected state construction, internal coordinates, control derivation, operator internals, private constants, serialization, source code, and other reconstruction-enabling implementation details remain undisclosed. The mathematical propositions can be independently examined from the definitions, assumptions, and constructions stated in the paper. Mathematical theorem verification and reconstruction of the protected production implementation are deliberately treated as separate tasks. AUTHOR AND RESEARCH IDENTITY Christos BaltasORCID: https://orcid.org/0009-0000-9743-3678 Zenodo Community:The Spiral Code & Energy Sciencehttps://zenodo.org/communities/spiral-code-energy/ RELATED PUBLIC SPIRALHELIOS RECORDS The following persistent identifiers are provided for provenance and research navigation only. The present mathematical publication is autonomous and is not a new version of these records. SpiralHelios v1:https://doi.org/10.5281/zenodo.18449312 SpiralHelios v2:https://doi.org/10.5281/zenodo.18475449 SpiralHelios v3:https://doi.org/10.5281/zenodo.18523349 SpiralHelios v4:https://doi.org/10.5281/zenodo.18645299 SpiralHelios v5:https://doi.org/10.5281/zenodo.18868454 SpiralHelios v6:https://doi.org/10.5281/zenodo.18917561 SpiralHelios v7:https://doi.org/10.5281/zenodo.19119985 SpiralHelios v8:https://doi.org/10.5281/zenodo.19421308 SpiralHelios v9:https://doi.org/10.5281/zenodo.19803050 SpiralHelios v10:https://doi.org/10.5281/zenodo.20639008 SpiralHelios v11:https://doi.org/10.5281/zenodo.20689308 SpiralHelios v12:https://doi.org/10.5281/zenodo.20772098 SpiralHelios v13:https://doi.org/10.5281/zenodo.20969765 SpiralHelios v14:https://doi.org/10.5281/zenodo.21363006 Related SpiralHelios Architectural Preprint:https://doi.org/10.5281/zenodo.22214397 The DOI records above provide persistent provenance and public research navigation. Their existence should not by itself be interpreted as independent peer-reviewed validation of the scientific claims of the corresponding records.