Appendix C: Comparison with Other Quantum Gravity Programs

Appendix C: Comparison with Other Quantum Gravity Programs

Feature String Theory LQG Causal Sets Ultrametric / Distinction Tree (This Work)
Fundamental entity Strings (1D objects) Spin networks (graphs) Causal relations (partial orders) Distinctions — Spencer-Brown marks arranged in trees
Geometry Emergent from CFT on worldsheet Quantum geometry (area/volume operators) Discrete causal set Hierarchical distinction tree $T_{N,q}$
Dimensions 10/11 (compactified) 4 4 Emergent 4 from tree automorphisms
UV finiteness Finite (perturbative) Finite (kinematical) Finite (discrete) Finite (tree depth — finite distinction hierarchy)
Time Background or emergent Emergent (relational) Fundamental (causal) Emergent — tree navigation through distinction levels
Holography AdS/CFT Area spectrum Implicit Rigorous on trees (boundary DOF < bulk DOF)
Standard Model String phenomenology (landscape) Matter as defects To be developed Geometric — branching types at different distinction depths
CC problem Landscape anthropics Unresolved Unresolved Adelic cancellation — distinction frameworks cancel across primes
Testability Planck-suppressed Planck-suppressed Discrete imprints CMB log-periodic oscillations, HEP anomalies, 18 protocols
Foundational principle Worldsheet dynamics Canonical quantization of GR Causal set growth The act of drawing a distinction