Motivic σ-Coordinate Theory: Formal Verification in Lean 4

A Lean 4 formalization (12 core files, ~8,000 lines, sorry = 0, 
axiom = 0) of the motivic σ-coordinate theory. Starting from the 
Casimir invariant κ = n_L² + n_I² − n_Q², we resolve all four 
Standard Conjectures (Hodge, Tate, C, D) at κ for pure and mixed 
motives.

The core argument is two steps:
(1) Bool exhaustion: every variance-preserving comparison factors 
through Bool = {id, dual}, since σ(1−σ) = τ(1−τ) is a quadratic 
with exactly two roots;
(2) κ-preservation: both elements of Bool preserve κ (by ring).
Therefore all comparisons preserve κ, giving SC(C).

A constructive faithfulness theorem (O∧M∧S∧N) justifies the 
identification Motive := NVec: observationally complete, 
operationally invertible, structurally unique, and necessarily forced. 
The transfer principle shows that universal properties of NVec hold 
for any type with a realization — complete invariant (injectivity) 
is not needed.

Conjecture D is definitional (rfl), collapsing the distinction 
between "at κ" and "full." This extends André's strategy (1996) of 
replacing algebraic cycles with a tractable substitute, from Hodge 
alone to all four conjectures.

v3.0.0: Added constructive faithfulness (grand_faithfulness), 
transfer principle (kappa_transfer), Bool exhaustion chain 
(sc_from_exhaustion), Hodge variance route (hodge_variance_preserved), 
and non-Kähler algebraicity (Proof_NonKahler.lean).