An Arithmetic Stratification of Polynomial Continued Fractions — v2.0 (Modular-Discriminant Framing)

This is the v2.0 revision of the SIARC umbrella program statement. It is a program statement, not a results paper: it organises the SIARC series of companion records, fixes unified notation, and tabulates the role and current status of each companion paper. v1 (April 2026, concept DOI 10.5281/zenodo.19885550) anchored the program in PSL_2(Z) and the degree pair (2,1). v2.0 promotes the framing to a cross-degree organisational principle built on the invariant triple PCF(1, b) ↦ ( Δ_d(b), ‖Δ‖_Pet(τ_b), ξ_0(b) ), namely the polynomial discriminant of the denominator polynomial b (the discriminant axis), the Petersson-normalised modular discriminant ‖Δ‖_Pet(τ) = |Δ(τ)|·(Im τ)^6 evaluated at the period τ_b of the…