This deposit contains version v10. 1-CONJECTUREFIX-0805e-FULLREPRO of the Prime Positioning Model (PPM), a structural and empirical framework for studying the sequence of prime numbers through consecutive quadruples, modular states, structural cells, finite-state transition dynamics, and segment-wise predictive validation. The central magnitude of the model is Kₙ = (pₙ - p₍-₃) /2. From this quantity, the model defines families, classes, blocks, segments, modular states, and the complete structural coordinate (S, B, c, e; i). The main manuscript develops the static architecture of the model, the induced 64-state transition dynamics modulo 30, predictive validations between consecutive segments, robustness checks against boundary effects, residual and directional energy analyses, gap-prediction experiments, reliability and reversibility tests, and comparisons with conditioned Cramér and naive Hardy–Littlewood reference models. This FULLREPRO version extends the computational material through complete segment S14. It includes compact but complete computational data for the extended segments, including prime values, K-values, classes, blocks, state identifiers, and modular residues. These data allow the reconstruction of p₍-₃ through p₍-₃ = pₙ - 2Kₙ, and support independent recomputation of transition matrices, class tables, block tables, state tables, validation summaries, and extended-segment analyses. The deposit includes manuscript PDFs in English and Spanish, LaTeX sources, figure files, spreadsheets, transition matrices, compact NPZ data files, Python reproducibility scripts, HTML analysis reports, predictive-validation outputs, robustness checks, supplementary manifests, SHA256 verification files, and download/extraction instructions. This version also includes six independent addenda. Addendum I studies the relationship between the Ulam spiral and the PPM coordinate system, quantifying the mutual information between Ulam diagonal families and PPM classes and states. Addendum II develops PPM210 as a high-resolution modular refinement of PPM30, including the modular-refinement theorem, the relationship between PPM30 and PPM210 structural coordinates, mixed PPM30-scale / PPM210-state analysis through S14, robustness controls, order-2 residual memory tests, and conjectures on marginal modular uniformization and modular dissipation of residual memory. Addendum III explores possible connections between the PPM framework, Riemann-type prime-counting fluctuations, residue-class decompositions, Dirichlet-type L-functions modulo 30, and Hardy–Littlewood-style reference models. Addendum IV examines the sensitivity of the PPM construction to the order of the transition window, evaluating how changes in the structural transition order affect classes, states, transition matrices, and predictive dynamics. Addendum V analyzes Sophie Germain primes inside the PPM coordinate system, including their exact modular restrictions, their induced subgeometry of states and classes, and their segment-wise density and occupation patterns through S14. Addendum VI studies prime constellations and prime quadruplet-type structures within the PPM framework, including rigid gap patterns, their embedding in PPM classes, states, blocks and segments, their comparison with Hardy–Littlewood heuristics, and their empirical distribution across the extended S1–S14 range. This version is a preprint / research manuscript and has not undergone peer review. The empirical results, conjectures, and proposed structural interpretations should therefore be read as research-stage material intended for inspection, reproduction, and further development. For convenience, the main manuscript and the six addenda are also provided as standalone PDF files in English and Spanish. The corresponding reproducibility packs contain the LaTeX sources, figures, computational outputs, scripts, data files, manifests, and SHA256 checksums. The six addenda included in this deposit should be understood as working research drafts rather than final standalone papers. They are intended to document exploratory extensions, empirical checks, computational experiments, and emerging conjectures derived from the main PPM framework. Their purpose is to open lines of investigation, provide reproducible evidence, and make intermediate results available for scrutiny and future development, not to present closed or peer-reviewed conclusions. AI-use disclosure: Large language model assistants were used as auxiliary tools in the preparation of this manuscript, addenda, and supplementary materials. The assistance included exploratory computation, statistical summarization, comparison of transition matrices, organization and interpretation of empirical results, English translation, editorial revision, LaTeX formatting, figure text translation, document assembly, and preparation of the Zenodo deposit package. AI tools are not listed as authors and do not bear responsibility for the scientific content. All scientific claims, interpretations, and decisions remain the responsibility of the human author.
Celestino SAN ROMAN RODRIGUEZ (Sun,) studied this question.