Grammatical Horizons in Nuclear Physics: From Coordinate Dissolution to Pure Transition

Grammatical Horizons in Nuclear Physics From Coordinate Dissolution to Pure Transition Version 2.0 Version 2.0 completes the pilgrimage by extending the grammatical analysis from the coordinate horizon at Ra to the pure transition horizon at ³H. Author Takayuki TakagiIndependent Researcher, Higashimatsuyama, Saitama, JapanORCID: 0009-0003-5188-2314Email: lemissio@gmail.com Abstract Nuclear physics employs distinct descriptive frameworks—collective coordinates, statistical distributions, resonance conditions, transition probabilities—each with its own domain of validity. This work identifies and classifies the boundaries between these domains, termed grammatical horizons. We trace a sequence of four horizons: Coordinate horizon (Ra): Where collective shape variables cease to organize nuclear behavior Distribution horizon (Fe peak): Where thermal statistical equilibrium freezes Resonance horizon (¹²C): Where neither structural nor transitional description alone suffices Pure transition horizon (³H): Where all grammar has departed, leaving only transition probability The ordering Ra → Fe → ¹²C → ³H represents a sequence of diminishing grammatical adequacy, not a physical reaction chain. File Contents Main Document File Description grammatical_horizons_main.tex Complete LaTeX source (revtex4-2 format) inscription.pdf Standalone inscription page inscription.tex LaTeX source for inscription Figures File Description figure_pilgrimage_route.pdf Fig. 1: The pilgrimage route overview figure_y1_nse_freezeout.pdf Fig. 2: NSE freeze-out schematic figure_z1_hoyle_resonance.pdf Fig. 3: Hoyle resonance window Supplementary Materials File Description appendix_odd_number_universality_v3.md Appendix X: Odd-number universality hypothesis Compilation Instructions bash pdflatex grammatical_horizons_main.tex pdflatex grammatical_horizons_main.tex # Run twice for references Required packages: revtex4-2, amsmath, amssymb, graphicx, hyperref Related Works This work extends the coordinate horizon analysis presented in: Takagi, T. (2026). Appendix D: Extension to Ra — Grammar Shift at the Boundary of Fission. Zenodo. DOI: 10.5281/zenodo.18181402 Keywords grammatical horizons; nuclear structure; nucleosynthesis; Hoyle state; formal causation; descriptive limits; iron peak; tritium; coordinate horizon; distribution horizon License CC-BY 4.0 International Citation If you use this work, please cite: Takagi, T. (2026). Grammatical Horizons in Nuclear Physics: From Coordinate Dissolution to Pure Transition (Version 2.0). Zenodo. DOI: 10.5281/zenodo.18184166 Version History v2.0 (2026-01-08): Pilgrimage Complete Extended grammatical analysis from Ra (coordinate horizon) to ³H (pure transition horizon) Added distribution horizon (Fe peak) and resonance horizon (¹²C / Hoyle state) Introduced unified pilgrimage route: Ra → Fe/Co → ¹²C → ³H Added inscription marking the closure of the pilgrimage Consolidated Discussion with formal causation implications Added Appendix X: Odd-number universality hypothesis v1.7 (2026-01-08): Ra Coordinate Horizon Initial coordinate horizon analysis at Ra Grammar shift at the boundary of fission See DOI: 10.5281/zenodo.18181402 Inscription This work traces a descent through nuclear description. At Ra, coordinate grammar fails.At the Fe peak, statistical grammar freezes.At the Hoyle state, structure and transition coexist.At ³H, grammar falls silent. What remains is not form, nor distribution, but transition itself. The silence of β here is not absence, but confirmation:it acts only on boundaries, never on existence itself.