The Causal Spine of Discrete Spacetime: A Spectral Fingerprint of Causal Structure in Causal Dynamical Triangulations (GRU v2.1)

The Causal Spine of Discrete Spacetime: A Spectral Fingerprint of Causal Structure in Causal Dynamical Triangulations GRU (Geometría Radial Unitaria / Radial Unitary Geometry) Research Program — v2. 1 This deposit contains the formal v2. 1 paper, together with the scripts, numerical results, and configuration files needed to verify its central claims. v2. 1 supersedes the technical dossier format of v1. 9. x–v2. 0 with a single, self-contained paper (Abstract, Sections 1–9, Appendices A–E, 9 references) written for a CDT/discrete-quantum-gravity audience. Central claim: a one-dimensional "causal spine" extracted from Causal Dynamical Triangulations (CDT) — via breadth-first-search collapse into a closed cycle — has spectral dimension ds (spine) ≈ 1, measured via heat-kernel random-walk methods, precisely when the underlying discrete geometry satisfies three structural conditions: temporal foliation, causal locality, and bounded connectivity. This is established across real two-dimensional CDT (60 geometries, ds = 1. 019 ± 0. 015, separated from the full graph by 15. 8σ), real three-dimensional CDT (multiseed, ds = 1. 039 ± 0. 040), and a toy four-dimensional model (ds = 1. 0428 ± 0. 0157, a pre-registered blind prediction). What is new in v2. 1 relative to v2. 0: Full formal paper structure (Abstract + 9 sections + 5 appendices), replacing the technical-dossier format of earlier versions Explicit scope-discipline statements (Sections 1. 3, 4. 2) distinguishing established results from open questions, including an explicit statement that no real four-dimensional CDT validation exists yet (the single most important open question for this program) Five independent anti-triviality controls plus a systematic graph-family elimination experiment (Erdős–Rényi, Watts–Strogatz, causal sets, 3-regular spin networks) identifying the three necessary conditions for the central result (Section 5) A percolation-based stress test showing the spine observable degrades ~17% under a perturbation that reduces standard giant-component connectivity by only ~3. 5% (Section 6) Validated (not yet exploited) observational infrastructure: a complete Cobaya+CAMB+Planck ΛCDM MCMC run (R−1 = 0. 029, χ² consistent with Planck 2018) and a gravitational-wave waveform pipeline (bbhx/LISA), including documentation of an upstream packaging bug found and fixed during this work (Appendix C. 2) One explicitly conceptual, falsifiable open question connecting the central result to the existing CMB low-ℓ power anomaly (Section 7. 3, Appendix D), with an external falsifiability criterion (LiteBIRD, 2028 onward) An explicit falsifiability statement (Section 8. 4) and a dedicated statistical-honesty appendix (Appendix E) documenting a retracted internal claim and known unresolved methodological limitations Contents of this deposit: paper/ — the paper itself (HTML and PDF) scripts/ — Python scripts for the core numerical results (spine extraction, T-scan, k3-scan, eps-scan, percolation, elimination-experiment graph families) data/ — JSON files with the numerical results tabulated in Appendix B, including the LISA orbit file used in Appendix C. 2 (data/lisafiles/) config/ — Cobaya/CAMB configuration and MCMC chains for the cosmological pipeline (Appendix C. 1) figures/ — supporting figure (s) docs/ — background technical notes documenting some results' development history README. md — full file structure and a table mapping each paper claim to its corresponding script/data file Author: Alfredo Flores Cornejo, Independent Researcher, Zapopan, Jalisco, México (dr. alfredo. fc@gmail. com) Related identifiers: Concept DOI (all versions): 10. 5281/zenodo. 20352929. Previous version (v2. 0): 10. 5281/zenodo. 20708589. Companion work on anisotropic loop quantum cosmology: 10. 5281/zenodo. 20360870.