Isotope-Independent Geometric Invariants in Fermium Fission: Evidence from Pairing and Neck Systematics

Isotope-Independent Geometric Invariants in Fermium Fission: Evidence from Pairing and Neck Systematics Version v1.6 — January 8, 2026 Extends v1.5: DOI 10.5281/zenodo.18174265 What's New in v1.6 Added Appendix C: Extension to ²³⁶U (uranium closure) Key finding: Measurement network closed across actinides (Fm → Cf/No → Pu → U) Bifurcation meaning shift: From sym/asym separation to intra-asymmetric (S1/S2) splitting Scission as shallow band: Zhou et al. (2023) demonstrates "estuary" structure Prediction row: ²³⁸U with testable consequences Figure C1: 4-panel comparison across measurement network Table C1: Complete extract sheet (8 nuclei) Total pages: 12 (was 9 in v1.5) Overview This work identifies isotope-independent critical deformations in fermium fission using Gogny D1S calculations from the literature. The analysis spans three fermium isotopes (²⁵⁴Fm, ²⁵⁶Fm, ²⁵⁸Fm), two neighboring actinides (²⁵²Cf, ²⁵⁸No), a lighter actinide (²⁴⁰Pu), and now extends to the uranium region (²³⁶U), with predictions for ²³⁸U. Key Results 1. Early marker (Q₂,Δ ≈ 30 b for Fm): Functionally preserved across all nuclei Fm: 30 b → Cf/No: 35 b → Pu: 54 b → U: β₂≈0.30 Preservation = functional correspondence, not numerical equality 2. Channel bifurcation: Systematic scaling with Z, then meaning shift Fm: ~50 b → Pu: ~110 b (×2.2 factor) U: Meaning shifts from sym/asym to S1/S2 internal splitting 3. Scission: Definition-dependent scaling, culminating in shallow band Fm: ~100 b → Pu: ~295–340 b (×3 factor) A/B proxy gap (45 b) quantifies definition dependence U: Scission is not a line but a "shallow estuary" Conclusion The Fermium ruler survives extension to uranium not as a rigid numerical scale, but as a hierarchy of operationally defined markers: an early pairing-related marker that is functionally preserved, followed by later markers that undergo systematic, nucleus-dependent rescaling and semantic evolution. The measurement network is closed. The definitions are complete. What remains is application. Package Contents File Description v16_fermium_invariants.pdf Main manuscript (12 pages) v16_fermium_invariants.tex LaTeX source v16_appendix_C.tex Appendix C source (Uranium closure) v13_fermium_triangle.png Figure 1: Fermium systematics A_lite_final.png Figure A1: Cf/No comparison Figure_B1_Pu240.png Figure B1: ²⁴⁰Pu extension Figure_C1_FINAL.png Figure C1: 4-nucleus comparison (NEW) 254Fm_final.csv ²⁵⁴Fm pairing data 258Fm_QN_CF.csv ²⁵⁸Fm neck data v13_254_256_comparison.csv Isotope comparison data Pu240_extract.csv ²⁴⁰Pu extracted values U236_extract.csv ²³⁶U extracted values (NEW) Keywords nuclear fission · fermium isotopes · geometric invariants · pairing correlations · neck parameter · Gogny D1S · formal causation · californium · nobelium · plutonium-240 · uranium-236 · operational definitions · measurement network · scission band License Creative Commons Attribution 4.0 International (CC BY 4.0) Citation @misc{takagi2026fermium_v16, author = {Takagi, Takayuki}, title = {{Isotope-Independent Geometric Invariants in Fermium Fission: Evidence from Pairing and Neck Systematics}}, year = {2026}, month = jan, version = {1.6}, publisher = {Zenodo}, doi = {10.5281/zenodo.XXXXXXXX}, note = {Uranium closure: measurement network complete} } Version History Version Date Scope Key Addition v1.0 Jan 4, 2026 $^{256}$Fm Initial framework v1.1 Jan 5, 2026 $^{254-258}$Fm Isotope chain v1.2 Jan 6, 2026 Fm + literature Cross-validation v1.3 Jan 7, 2026 Fm + Cf/No A-lite extension v1.4 Jan 7, 2026 + methodology SI structure v1.5 Jan 7, 2026 + ²⁴⁰Pu Functional correspondence v1.6 Jan 8, 2026 + ²³⁶U, ²³⁸U Uranium closure Closure Note The measurement network is closed across actinides. What persists: Functional correspondence (not numerical equality) What changes: The meaning of bifurcation and the topology of scission What emerges: Scission as a definition-dependent band, not a line Beyond uranium, the same markers would require redefinition rather than extension. Transition Note The same operational philosophy invites a transition from deformation space to configuration space in β-dominated nuclei. Author: Takayuki TakagiORCID: 0009-0003-5188-2314Contact: lemissio@gmail.com