SpiralHelios — Deterministic Geometric Intelligence (DGI): Math Solver v0.5 Patch002–Patch100 Deterministic Execution Evidence Archive, External Graph Laplacian / QASM Bell Boundary, and Post-Patch100 Scientific Extension Roadmap

This Zenodo release presents SpiralHelios Math Solver v0.5 as a public-safe deterministic execution evidence archive. The release documents the full Patch002–Patch100 execution chain of SpiralHelios Math Solver v0.5 through one main paper and ninety-nine supplementary evidence PDFs. The main paper provides the architectural framing, public-safe boundary, execution model, patch roadmap, selected screenshot anchors, File15B post-Patch100 roadmap, legal notice, and anti-reconstruction disclosure boundary. The supplementary evidence archive contains: S001 = Patch002S002 = Patch003S003 = Patch004...S099 = Patch100 Each supplementary file corresponds to one patch execution record and preserves screenshot-based terminal evidence, query outputs, classification fields, verification status fields, proof-binding fields, result digests, checkpoint references, hash records, passed records, and public-safe runtime indicators where available. This release does not disclose the protected SpiralHelios Core, raw vectors, internal operators, hidden transforms, private state dumps, reconstruction-enabling constants, or implementation material that would allow copying or replication of the protected mechanism. The purpose of this release is to document operation, not to transfer implementation. The Patch002–Patch100 chain covers a broad mathematical and applied-mathematical range, including arithmetic, algebra, symbolic transformations, geometry, trigonometry, complex numbers, number theory, inequalities, exponential/logarithmic forms, sequences and series, rational functions, limits, conics, set theory, logic, predicate logic, proof templates, parser/AST foundations, calculus, multivariable polynomial systems, optimization, ODE recognition, derivative rules, integral rules, Taylor/Maclaurin series, linear algebra, vector spaces, eigenvalue layers, diagonalization, Gram-Schmidt, least squares, QR/LU/Cholesky decompositions, quadratic forms, Rayleigh quotient, condition number, matrix powers, Cayley-Hamilton, minimal polynomial, Jordan form, linear transformations, Riemann sums, vector calculus, Fourier methods, PDE residual verification, infinite series, zeta/Dirichlet recognition, Riemann Hypothesis safe statement handling, prime counting safe approximation, state-space systems, discrete dynamics, controllability/observability, stability criteria, Kalman predict/update, LQR/Riccati recognition, linear inequalities, linear programming, simplex tableau, LP infeasible/unbounded gates, LP duality, convex quadratic optimization, graph representation, BFS/DFS/connectivity, tree/spanning-tree checks, weighted shortest paths, network max flow, network min cut, and Graph Laplacian extended binding. The main paper includes direct screenshot evidence for three architectural boundary anchors: Patch003 — External Graph Laplacian LayerPatch004 — External QASM Bell SerializerPatch100 — Graph Laplacian Extended Binding Layer These three patches are highlighted because they define the boundary between the protected SpiralHelios Core and the external-derived Graph Laplacian / QASM / Spectral extension layers. Patch003 documents early external Graph Laplacian behavior. Patch004 documents deterministic QASM Bell serialization as symbolic external-derived output, without quantum hardware execution, without stochastic measurement sampling, and without cloud quantum backend claims. Patch100 closes the Patch002–Patch100 execution chain by formalizing Graph Laplacian Extended Binding through the Core Adapter external-derived path. File15B is included as the post-Patch100 roadmap boundary. It defines the controlled future path for Spectral Graph, Laplacian, QASM, graph-state, stabilizer, diffusion, topological quantum error-correction primitives, and scientific/engineering extension layers. All post-Patch100 extensions remain external-derived, adapter-bound, non-core-canonical, deterministic, public-safe, and governed by strict no-Core-mutation and no-ROM-mutation rules. This release explicitly does not claim: open-source disclosure full Core reproducibility quantum hardware execution stochastic simulation machine-learning training cloud inference universal mathematical omnipotence proof of the Riemann Hypothesis general spectral eigensolver behavior commercial license technology transfer The release claims a narrower and auditable milestone: SpiralHelios Math Solver v0.5 reached a public-safe deterministic execution milestone from Patch002 to Patch100. The evidence is operational.The execution archive is structured.The supplementary proof chain is preserved.The protected Core remains undisclosed.The external-derived boundary is preserved. Author: Christos Baltas (PH-GAIOS)Architect – Creator – Systems DesignerSpiralEnergy-SystemsAthens, GreeceEmail: info@spiral-code.comORCID: https://orcid.org/0009-0000-9743-3678Zenodo Community: https://zenodo.org/communities/spiral-code-energy/ License / Rights Notice: This release is governed by the custom rights notice titled:“All Rights Reserved – No Implementation, No Derivatives, No AI Training, No Commercial Use.” Full rights terms are included in the license notice attached to this Zenodo record and in the legal section of the main paper.