The Causal Spine of Discrete Spacetime: A Spectral Fingerprint of Causal Structure in Causal Dynamical Triangulations (GRU v2.1.2, with eps-scan K=256 and CDT-real Percolation)

The Causal Spine of Discrete Spacetime: A Spectral Fingerprint of Causal Structure in Causal Dynamical Triangulations GRU Research Program — v2.1.2 (eps-scan K=256 + CDT-real percolation) This version adds two completed pendientes to the v2.1.1 addendum: (1) the eps-scan extended to K=256 (previously only K=4,16,64-partial), and (2) the percolation stress-test repeated on 9 real CDT geometries (T=20,40,80) instead of the synthetic toy spine used in Section 6. eps-scan K=256: ds grows monotonically with eps (0.97→1.88 for eps=2..32), saturating toward 2 without reaching it. eps=1 (ds=0.58) is documented as a numerical artifact, not a physical result -- the near-disconnected graph (N=10,240, single coupling edge per spine pair) produces degenerate near-zero Laplacian eigenvalues with no clean power-law window for the heat-kernel fit. This is confirmed by the abrupt, non-physical jump from eps=1 to eps=2 (0.58→0.97). Percolation on real CDT geometries: ds(p=0)≈1.0 confirmed across 9/9 real CDT geometries (T=20,40,80, mixed published/new seeds), validating the Section 6 finding (spine degrades faster than connectivity) on real geometries, not only the synthetic spine. New finding: the percolation peak position and height depend only on T (geometric), not on the specific CDT realization or seed. Author: Alfredo Flores Cornejo, Independent Researcher, Zapopan, Jalisco, México (dr.alfredo.fc@gmail.com) Related: Concept DOI: 10.5281/zenodo.20352929. Previous version (v2.1.1): 10.5281/zenodo.20751161.