Appendix D: Extension to Ra — Grammar Shift at the Boundary of Fission

Isotope-Independent Geometric Invariants in Fermium Fission Version 1.7 — Ra: Grammar Shift Author: Takayuki TakagiORCID: 0009-0003-5188-2314Date: January 2026Extends: v1.6 (DOI pending) What's New in v1.7 Added: Appendix D — Extension to Ra (Grammar Shift) The measurement network established in Fm and extended through Cf/No/Pu/U is now tested at its boundary: the Ra isotopes (Z=88), where fission gives way to α-decay and the ground state exhibits octupole (pear-shaped) deformation. Key Findings Three-point structure identified: Onset (²²²Ra, N=134): Ground-state reflection symmetry breaks Maximum (²²⁴Ra, N=136): β₃ ≈ 0.13, B(E3) = 42±3 W.u. Closure (²³⁰Ra, N=142): Return to reflection symmetry Grammar shift documented: Coordinate system changes: Q₂₀ [b] → β₂ [dimensionless] Bifurcation marker survives but meaning changes Pairing and scission markers become undefined Philosophical conclusion: The measurement network does not "break" at Ra; rather, it reveals its own domain of validity. Files Included Core Documents File Description Appendix_D_Ra.tex LaTeX source for Appendix D v17_extract_sheet.csv Complete extract sheet (Fm through Ra) README.md This file Figures File Description Pilgrimage_Sigil.svg Main figure: Complete pilgrimage route (Fm → n-star) Fig_D1_grammar_shift.svg Marker survival/loss diagram Fig_D2_octupole_island.svg β₂-β₃ plane with three-point structure Fig_D3_pilgrimage_route.svg Measurement network overview Stone_Tablet.svg Minimal version for stone tablet Minimal_Sigil.svg Wordless version for journal Extract Sheet Summary (v1.7) Nucleus Z Q₂,Δ Q₂,bif Q₂,sc Status ²⁵⁶Fm 100 30 b 50 b 100 b Definition ²⁵²Cf 98 35 b 65 b 130 b A-lite ²⁵⁸No 102 35 b 75 b 140 b A-lite ²⁴⁰Pu 94 54 b 110 b 295–340 b Phase 2 ²²²Ra 88 — β₂≈0.15 — Onset ²²⁴Ra 88 — — — Maximum ²³⁰Ra 88 — β₂≈0.25 — Closure Measurement Network Structure Fm (Z=100) ─── Definition ─────────────────────┐ │ │ Cf/No ─── Cross-element validation │ │ │ Q₂₀ [b] Pu (Z=94) ─── Scaling + definition dependence │ coordinate │ │ U (Z=92) ─── Stress test │ │ ┘ ├─────────── GRAMMAR SHIFT ───────────────── │ ┐ Ra (Z=88) ─── Boundary (octupole island) │ β₂ │ onset / maximum / closure │ coordinate ↓ ┘ [Beyond: Fe → C → ³H → n-star] Citation If using this work, please cite: Takagi, T. (2026). Isotope-Independent Geometric Invariants in Fermium Fission: Evidence from Pairing and Neck Systematics (v1.7 — Ra: Grammar Shift). Zenodo. https://doi.org/10.5281/zenodo.18181402 Sources for Ra Data Agbemava et al. (2016) PRC 93, 044304 — CDFT calculations for Ra chain Gaffney (2012) PhD Thesis, Liverpool — B(E3) experimental values Gaffney et al. (2013) Nature 497, 199 — Static octupole in ²²⁴Ra License CC-BY 4.0 Contact Takayuki TakagiHigashimatsuyama Baptist Church / Independent ResearcherEmail: lemissio@gmail.com