The DDT/FDM Stage-1 Framework: A Unified Approach to Fundamental Physics V1.1

𝗪𝗲 𝗽𝗿𝗲𝘀𝗲𝗻𝘁 𝘁𝗵𝗲 𝗰𝗼𝗺𝗽𝗹𝗲𝘁𝗲, 𝘀𝗲𝗹𝗳-𝗰𝗼𝗻𝘁𝗮𝗶𝗻𝗲𝗱 𝗳𝗿𝗮𝗺𝗲𝘄𝗼𝗿𝗸 𝗼𝗳 𝗗𝗶𝗺𝗲𝗻𝘀𝗶𝗼𝗻𝗮𝗹 𝗗𝗲𝗽𝗹𝗼𝘆𝗺𝗲𝗻𝘁 𝗧𝗵𝗲𝗼𝗿𝘆 (𝗗𝗗𝗧), 𝘄𝗶𝘁𝗵 𝗮𝗹𝗹 𝗱𝗲𝗿𝗶𝘃𝗮𝘁𝗶𝗼𝗻𝘀 𝗳𝗿𝗼𝗺 𝗳𝗶𝗿𝘀𝘁 𝗽𝗿𝗶𝗻𝗰𝗶𝗽𝗹𝗲𝘀 V1. 1. Observable 3+1-dimensional physics—spacetime geometry, 𝘜 (1) gauge fields, topologically quantized matter, and quantum-mechanical behavior—emerges from a single dynamical scalar field 𝒳² on a 2+1-dimensional Lorentzian substrate (ℳ³, 𝘨ₐᵦ). The framework rests on one ontological commitment (the dimensionality of space is deployed, not given) and one derived constant (𝒳²ᵥₐ𝒸 = 𝗹𝗻 𝟮, forced by bidirectional consistency). From these, four sectors of physics emerge: (𝗜) 𝗖𝗼𝘀𝗺𝗼𝗹𝗼𝗴𝗶𝗰𝗮𝗹 𝘀𝗽𝗮𝗰𝗲𝘁𝗶𝗺𝗲 with propagating fronts and a universal −8. 98% lensing reduction (boundary-regime: ℛ (𝘣𝘰𝘶𝘯𝘥𝘢𝘳𝘺) /ℱ ≈ 0. 9102) ; (𝗜𝗜) 𝗔 𝘜 (1) 𝗴𝗮𝘂𝗴𝗲 𝘀𝗲𝗰𝘁𝗼𝗿 with coupling 𝘨²_ₑ𝘧𝘧 = μ∗ (𝗹𝗻 𝟮) ²; (𝗜𝗜𝗜) 𝗧𝗼𝗽𝗼𝗹𝗼𝗴𝗶𝗰𝗮𝗹𝗹𝘆 𝗾𝘂𝗮𝗻𝘁𝗶𝘇𝗲𝗱 𝗺𝗮𝘁𝘁𝗲𝗿 with gap mass ℳ∞ = (𝗹𝗻 𝟮) √ (λ/μ∗) ; (𝗜𝗩) 𝗘𝗳𝗳𝗲𝗰𝘁𝗶𝘃𝗲 𝗦𝗰𝗵𝗿𝗼̈𝗱𝗶𝗻𝗴𝗲𝗿 𝗱𝘆𝗻𝗮𝗺𝗶𝗰𝘀 with the Born rule 𝒫 = |ψ|². Every theorem is proved within this document. Every admissibility condition is stated with explicit gates. Every prediction carries a falsification criterion with precommitted thresholds. No external reference is required to verify any claim. The framework introduces three free parameters (β, μ∗, κ𝘨) plus one extension parameter (λ) ; all physical scales in all four sectors are determined by these parameters and the derived vacuum 𝗹𝗻 𝟮. An appendix of worked examples demonstrates operational reproducibility: a single parameter set produces numerical predictions across all four sectors with cross-sector consistency verified to four significant figures. 𝗣𝗔𝗖𝗦 𝗻𝘂𝗺𝗯𝗲𝗿𝘀: 04. 60. -m, 98. 80. -k, 11. 15. -q, 03. 65. Ta, 11. 25. -w 𝗞𝗲𝘆𝘄𝗼𝗿𝗱𝘀: Dimensional deployment, substrate cosmology, emergent gauge theory, emergent quantum mechanics, operational calculus, informational foundations