A Certified Bound and a Conditional Lean Theorem for a Bounded-Height Algebraicity Exclusion for Khinchin's Constant

We deposit two complementary artifacts concerning Khinchin's constant K_0 ≈ 2.6854520010…: 1. **A certified Hermite/LLL bound `M_certified`** (578-digit integer; SHA-256 of decimal-string form `c51099378e8c199c70d4543fb6b69f4de80986af34b628f6d9619f2181f6ab8e`) emitted by an interval-arithmetic verification chain (FLINT/Arb) anchored against OEIS A002210 via the BBC (Bailey–Borwein–Crandall, 1997) series identity at precision 8663 decimal places (M1 top rung P_bits = 28712). 2. **A formally-verified `conditional` Lean 4 / Mathlib v4.14.0 theorem** (`no_euclidean_relation_conditional`) that, under three explicit hypotheses matching the certified-bound + GS-lower-bound supplied numerically by the bound emission chain, **rules out** any nonzero integer relation of squared Euclidean norm ≤ M_sq among the committed 15-element basis `B_D(C) = {1, K_0, K_0^2, …, K_0^6, log K_0, K_0·π, K_0·e, K_0·ln2, K_0·γ, K_0·ζ(2), K_0·ζ(3), K_0·G}`. A companion lemma (`c1_from_c2_zero_extension`, this session's R-0 deliverable) extends this to the degree-≤6 pure-power sub-block at the same bound, via a norm-preserving zero-extension.