M9: ξ0 Affine-Reindexing Covariance for Polynomial Continued Fractions — an In-Repo Symbolic-in-d Discharge of the Newton-Edge Lemma

This record deposits the M9 ξ₀-covariance results for polynomial continued fractions (PCFs) b(n)=β_d n^d+…, with the SIARC four-way epistemic discipline made explicit. M9.0 (object level). Each deposited family admits the invariant triple (Δ_d, ‖Δ‖_Pet, ξ₀) with Borel-singularity radius ξ₀(b)=d/β_d1/d; a map of objects, no morphism action asserted. M9.1 (ξ₀ affine-reindexing covariance). For φ(n)=αn+γ, ξ₀(b∘φ)=α⁻¹·ξ₀(b), shift-invariant; grounded on the β_d-only slope-1/d Newton-polygon edge and numerically VERIFIED for the computed pairs d∈{2,3,4}, α∈{2,3}, γ∈{0,1}. All-d lift M9.1⁺. The algebraic core is symbolically derived (d-free) for all d≥2 — the edge polynomial χ_d(c)=1+(−1)ᵈ⁺¹(β_d/d^d)c^d (only β_d on the edge) and the α⁻¹ covariance — carried by a symbolic-in-d leading-symbol lemma (not the d≤6 numerics, which only corroborate). “Symbolically derived” is a grade strictly weaker than the corpus's machine-checked PROVEN (a Lean axiom cone {propext, Classical.choice, Quot.sound}, zero sorry): there is no Lean formalization here, and the lemma's general-k step is a hand induction (k=0..8 machine-checked in sympy). The analytic edge⇒Borel-radius step references standard asymptotics literature (Wasow §19 sectorial-existence theory; Birkhoff–Trjitzinsky Borel-summability) and remains cited-conditional — it is NOT discharged here. \"VERIFIED\" is restricted to the computed (d,β_d,φ); no d≥7 claim. Artifacts: a symbolic+numeric derivation script (lemma31_edge_derivation.py), its raw output and results JSON, a derivation note, and an AEAL provenance ledger.