A Unified Description via the Triadic Structure: Quantum Theory and General Relativity as a Single Structure

This paper gives a unified description of quantum theory and relativity as readings of different axes of a single triadic structure (Δ, Λ, Ψ), presupposing the preceding paper "The Triadic Structure (Δ, Λ, Ψ): Foundations in Orientation, Relation, and Dimension" (DOI: 10.5281/zenodo.20986811). The unification claimed is a unification of description, not of dynamics: no new dynamics are introduced, and "unification" here does not refer to gauge grand unification (GUT). The central new result: the light-cone coordinates of the 1+1-dimensional Minkowski plane form the standard two-dimensional triad as they stand (Proposition 1.1). The two poles V₊, V₋ are the two null directions; parity is P = Ψ; time reversal is T = −Ψ; the total spacetime inversion is PT = −id = Δ²; the boost of rapidity s is exp(sσ) = diag(eˢ, e⁻ˢ); and a boost composed with parity is the scaled exchange Ψ_λ (λ = e⁻ˢ). Under boosts the interval x₊x₋ is invariant while only the ratio x₊/x₋ moves (Proposition 2.1): the invariance of the interval is "a fixed product with a free ratio" — the same structure as the uncertainty relation (the fixed product ℏ with a free ratio). On the quantum side the identifications of the preceding paper are inherited: the complex unit i as the generator Δ (in the sense of right multiplication), the spinor's 2π as Δ², and the KMS antiperiodicity as a conditional reading. A dictionary maps the basic objects of both theories onto the elements and axes of one triad, and the junction identity −id = Δ² = PT ties them to one and the same half-period residue (Theorem 4.1). Gravity is placed as follows: by axiom T2 of the preceding paper, the scale cannot be fixed from inside the structure; the metric field is read as the field that supplies this externally required calibration at each point. The Einstein equations, the gauge content, and the values of the constants are external inputs and are not derived. A demarcation table states the status of every claim (theorem / citation / identification / reading / conditional / unconstructed), and criteria of attainment (U1–U3) for a unification of dynamics are defined, with a self-assessment of this paper against them. Files: Triadic_Unified_Description.pdf (the paper, Draft v2); Triadic_Unified_Description_verification_scripts.zip (three verification scripts — verify_lightcone_triad.py 12/12, verify_interval_product.py 8/8, verify_reversal_T.py 7/7 — with README; dependencies: numpy, scipy). Related: the foundations paper (DOI: 10.5281/zenodo.20986811); the axiomatic proposal for a non-orientable spacetime (DOI: 10.5281/zenodo.20678390).