diff --git a/crates/aprender-core/src/format/lb_001_006.rs b/crates/aprender-core/src/format/lb_001_006.rs
new file mode 100644
index 000000000..ad5b21787
--- /dev/null
+++ b/crates/aprender-core/src/format/lb_001_006.rs
@@ -0,0 +1,370 @@
+// `lbfgs-kernel-v1` algorithm-level PARTIAL discharge for
+// FALSIFY-LB-001..006.
+//
+// Contract: `contracts/lbfgs-kernel-v1.yaml`.
+//
+// LB-001: descent direction — g^T * direction < 0 for non-zero gradient
+// LB-002: curvature condition — y^T * s > 0 for accepted (s, y) pairs
+// LB-003: history length bounded by m
+// LB-004: objective decrease on Rosenbrock — f(x_{k+1}) < f(x_k)
+// LB-005: SIMD vs scalar within 8 ULP
+// LB-006: empty history → direction == -g (steepest descent)
+
+/// LB-005 SIMD vs scalar tolerance (8 ULP * EPSILON).
+pub const AC_LB_SIMD_ULP_BUDGET: u32 = 8;
+
+#[derive(Debug, Clone, Copy, PartialEq, Eq)]
+pub enum LbVerdict {
+    Pass,
+    Fail,
+}
+
+/// Reference dot product (returns NaN on length mismatch / non-finite).
+#[must_use]
+pub fn dot(a: &[f32], b: &[f32]) -> f32 {
+    if a.is_empty() || a.len() != b.len() {
+        return f32::NAN;
+    }
+    let mut sum = 0.0_f32;
+    for (x, y) in a.iter().zip(b.iter()) {
+        if !x.is_finite() || !y.is_finite() {
+            return f32::NAN;
+        }
+        sum += x * y;
+    }
+    sum
+}
+
+/// LB-001: g^T * direction < 0 strictly (descent direction).
+#[must_use]
+pub fn verdict_from_descent_direction(grad: &[f32], direction: &[f32]) -> LbVerdict {
+    let prod = dot(grad, direction);
+    if !prod.is_finite() {
+        return LbVerdict::Fail;
+    }
+    // Skip if grad is effectively zero (gate doesn't apply).
+    let g_norm_sq = dot(grad, grad);
+    if g_norm_sq <= 0.0 || !g_norm_sq.is_finite() {
+        return LbVerdict::Fail;
+    }
+    if prod < 0.0 {
+        LbVerdict::Pass
+    } else {
+        LbVerdict::Fail
+    }
+}
+
+/// LB-002: y^T * s > 0 for every accepted (s, y) pair.
+#[must_use]
+pub fn verdict_from_curvature(s_y_pairs: &[(&[f32], &[f32])]) -> LbVerdict {
+    if s_y_pairs.is_empty() {
+        return LbVerdict::Fail;
+    }
+    for (s, y) in s_y_pairs {
+        let p = dot(s, y);
+        if !p.is_finite() || p <= 0.0 {
+            return LbVerdict::Fail;
+        }
+    }
+    LbVerdict::Pass
+}
+
+/// LB-003: history length ≤ m.
+#[must_use]
+pub fn verdict_from_history_bound(history_len: usize, m: usize) -> LbVerdict {
+    if m == 0 {
+        return LbVerdict::Fail;
+    }
+    if history_len <= m {
+        LbVerdict::Pass
+    } else {
+        LbVerdict::Fail
+    }
+}
+
+/// LB-004: f(x_{k+1}) < f(x_k) (objective strictly decreased).
+#[must_use]
+pub fn verdict_from_objective_decrease(f_k: f32, f_k_plus_1: f32) -> LbVerdict {
+    if !f_k.is_finite() || !f_k_plus_1.is_finite() {
+        return LbVerdict::Fail;
+    }
+    if f_k_plus_1 < f_k {
+        LbVerdict::Pass
+    } else {
+        LbVerdict::Fail
+    }
+}
+
+/// LB-005: SIMD vs scalar within `AC_LB_SIMD_ULP_BUDGET * EPSILON`.
+#[must_use]
+pub fn verdict_from_simd_scalar_parity(
+    simd_direction: &[f32],
+    scalar_direction: &[f32],
+) -> LbVerdict {
+    if simd_direction.is_empty() || simd_direction.len() != scalar_direction.len() {
+        return LbVerdict::Fail;
+    }
+    let bound = (AC_LB_SIMD_ULP_BUDGET as f32) * f32::EPSILON;
+    for (a, b) in simd_direction.iter().zip(scalar_direction.iter()) {
+        if !a.is_finite() || !b.is_finite() {
+            return LbVerdict::Fail;
+        }
+        let scale = a.abs().max(b.abs()).max(1.0);
+        if (a - b).abs() > bound * scale {
+            return LbVerdict::Fail;
+        }
+    }
+    LbVerdict::Pass
+}
+
+/// LB-006: empty history → direction == -gradient (steepest descent).
+#[must_use]
+pub fn verdict_from_empty_history_steepest(grad: &[f32], direction: &[f32]) -> LbVerdict {
+    if grad.is_empty() || grad.len() != direction.len() {
+        return LbVerdict::Fail;
+    }
+    for (g, d) in grad.iter().zip(direction.iter()) {
+        if !g.is_finite() || !d.is_finite() {
+            return LbVerdict::Fail;
+        }
+        if (-g).to_bits() != d.to_bits() {
+            return LbVerdict::Fail;
+        }
+    }
+    LbVerdict::Pass
+}
+
+#[cfg(test)]
+mod tests {
+    use super::*;
+
+    // -----------------------------------------------------------------
+    // Section 1: Provenance pin.
+    // -----------------------------------------------------------------
+    #[test]
+    fn provenance_simd_ulp_budget_8() {
+        assert_eq!(AC_LB_SIMD_ULP_BUDGET, 8);
+    }
+
+    // -----------------------------------------------------------------
+    // Section 2: LB-001 descent direction.
+    // -----------------------------------------------------------------
+    #[test]
+    fn flb001_pass_descent() {
+        let g = vec![1.0_f32, 2.0];
+        let d = vec![-1.0_f32, -2.0];
+        let v = verdict_from_descent_direction(&g, &d);
+        assert_eq!(v, LbVerdict::Pass);
+    }
+
+    #[test]
+    fn flb001_fail_ascent() {
+        let g = vec![1.0_f32, 2.0];
+        let d = vec![1.0_f32, 2.0]; // same direction as grad
+        let v = verdict_from_descent_direction(&g, &d);
+        assert_eq!(v, LbVerdict::Fail);
+    }
+
+    #[test]
+    fn flb001_fail_orthogonal() {
+        let g = vec![1.0_f32, 0.0];
+        let d = vec![0.0_f32, 1.0];
+        let v = verdict_from_descent_direction(&g, &d);
+        assert_eq!(v, LbVerdict::Fail);
+    }
+
+    // -----------------------------------------------------------------
+    // Section 3: LB-002 curvature.
+    // -----------------------------------------------------------------
+    #[test]
+    fn flb002_pass_positive_inner() {
+        let s = vec![1.0_f32];
+        let y = vec![2.0_f32];
+        let pairs: &[(&[f32], &[f32])] = &[(&s, &y)];
+        let v = verdict_from_curvature(pairs);
+        assert_eq!(v, LbVerdict::Pass);
+    }
+
+    #[test]
+    fn flb002_fail_zero_inner() {
+        let s = vec![1.0_f32, 1.0];
+        let y = vec![1.0_f32, -1.0]; // dot = 0
+        let pairs: &[(&[f32], &[f32])] = &[(&s, &y)];
+        let v = verdict_from_curvature(pairs);
+        assert_eq!(v, LbVerdict::Fail);
+    }
+
+    #[test]
+    fn flb002_fail_negative_inner() {
+        let s = vec![1.0_f32];
+        let y = vec![-1.0_f32];
+        let pairs: &[(&[f32], &[f32])] = &[(&s, &y)];
+        let v = verdict_from_curvature(pairs);
+        assert_eq!(v, LbVerdict::Fail);
+    }
+
+    #[test]
+    fn flb002_fail_empty() {
+        let pairs: &[(&[f32], &[f32])] = &[];
+        let v = verdict_from_curvature(pairs);
+        assert_eq!(v, LbVerdict::Fail);
+    }
+
+    // -----------------------------------------------------------------
+    // Section 4: LB-003 history bound.
+    // -----------------------------------------------------------------
+    #[test]
+    fn flb003_pass_at_capacity() {
+        let v = verdict_from_history_bound(5, 5);
+        assert_eq!(v, LbVerdict::Pass);
+    }
+
+    #[test]
+    fn flb003_pass_under_capacity() {
+        let v = verdict_from_history_bound(3, 5);
+        assert_eq!(v, LbVerdict::Pass);
+    }
+
+    #[test]
+    fn flb003_fail_over_capacity() {
+        let v = verdict_from_history_bound(6, 5);
+        assert_eq!(v, LbVerdict::Fail);
+    }
+
+    #[test]
+    fn flb003_fail_zero_m() {
+        let v = verdict_from_history_bound(0, 0);
+        assert_eq!(v, LbVerdict::Fail);
+    }
+
+    // -----------------------------------------------------------------
+    // Section 5: LB-004..005.
+    // -----------------------------------------------------------------
+    #[test]
+    fn flb004_pass_decreased() {
+        let v = verdict_from_objective_decrease(10.0, 5.0);
+        assert_eq!(v, LbVerdict::Pass);
+    }
+
+    #[test]
+    fn flb004_fail_increased() {
+        let v = verdict_from_objective_decrease(5.0, 10.0);
+        assert_eq!(v, LbVerdict::Fail);
+    }
+
+    #[test]
+    fn flb004_fail_unchanged() {
+        let v = verdict_from_objective_decrease(5.0, 5.0);
+        assert_eq!(v, LbVerdict::Fail);
+    }
+
+    #[test]
+    fn flb005_pass_within_ulp_budget() {
+        let simd = vec![1.0_f32, 2.0, 3.0];
+        let scalar = vec![1.0_f32, 2.0, 3.0];
+        let v = verdict_from_simd_scalar_parity(&simd, &scalar);
+        assert_eq!(v, LbVerdict::Pass);
+    }
+
+    #[test]
+    fn flb005_fail_far_drift() {
+        let simd = vec![1.0_f32];
+        let scalar = vec![1.5_f32];
+        let v = verdict_from_simd_scalar_parity(&simd, &scalar);
+        assert_eq!(v, LbVerdict::Fail);
+    }
+
+    #[test]
+    fn flb005_pass_8_ulp() {
+        // 8 ULPs at 1.0 = 8 * f32::EPSILON ~= 9.5e-7
+        let simd = vec![1.0_f32];
+        let bumped = f32::from_bits(1.0_f32.to_bits() + 7);
+        let scalar = vec![bumped];
+        let v = verdict_from_simd_scalar_parity(&simd, &scalar);
+        assert_eq!(v, LbVerdict::Pass);
+    }
+
+    // -----------------------------------------------------------------
+    // Section 6: LB-006 steepest descent.
+    // -----------------------------------------------------------------
+    #[test]
+    fn flb006_pass_neg_gradient() {
+        let g = vec![1.0_f32, -2.0, 3.0];
+        let d = vec![-1.0_f32, 2.0, -3.0];
+        let v = verdict_from_empty_history_steepest(&g, &d);
+        assert_eq!(v, LbVerdict::Pass);
+    }
+
+    #[test]
+    fn flb006_fail_not_negated() {
+        let g = vec![1.0_f32, -2.0];
+        let d = vec![1.0_f32, -2.0]; // same as g, not -g
+        let v = verdict_from_empty_history_steepest(&g, &d);
+        assert_eq!(v, LbVerdict::Fail);
+    }
+
+    #[test]
+    fn flb006_fail_one_ulp_drift() {
+        let g = vec![1.0_f32];
+        let bumped = f32::from_bits((-1.0_f32).to_bits() + 1);
+        let d = vec![bumped];
+        let v = verdict_from_empty_history_steepest(&g, &d);
+        assert_eq!(v, LbVerdict::Fail);
+    }
+
+    // -----------------------------------------------------------------
+    // Section 7: Mutation surveys + realistic.
+    // -----------------------------------------------------------------
+    #[test]
+    fn mutation_survey_lb003_history_band() {
+        for m in [1_usize, 5, 10, 100] {
+            for h in 0..=2 * m {
+                let v = verdict_from_history_bound(h, m);
+                let want = if h <= m {
+                    LbVerdict::Pass
+                } else {
+                    LbVerdict::Fail
+                };
+                assert_eq!(v, want, "m={m} h={h}");
+            }
+        }
+    }
+
+    #[test]
+    fn realistic_healthy_passes_all_6() {
+        let g = vec![1.0_f32, -2.0];
+        let d_descent = vec![-1.0_f32, 2.0];
+        let v1 = verdict_from_descent_direction(&g, &d_descent);
+        let s = vec![1.0_f32, 1.0];
+        let y = vec![2.0_f32, 3.0];
+        let v2 = verdict_from_curvature(&[(&s, &y)]);
+        let v3 = verdict_from_history_bound(3, 5);
+        let v4 = verdict_from_objective_decrease(100.0, 50.0);
+        let simd = vec![1.0_f32, 2.0];
+        let scalar = vec![1.0_f32, 2.0];
+        let v5 = verdict_from_simd_scalar_parity(&simd, &scalar);
+        let v6 = verdict_from_empty_history_steepest(&g, &d_descent);
+        for v in [v1, v2, v3, v4, v5, v6] {
+            assert_eq!(v, LbVerdict::Pass);
+        }
+    }
+
+    #[test]
+    fn realistic_pre_fix_all_6_failures() {
+        let g = vec![1.0_f32];
+        let d_ascent = vec![1.0_f32]; // wrong sign (LB-001 sign error)
+        let v1 = verdict_from_descent_direction(&g, &d_ascent);
+        let s = vec![1.0_f32];
+        let y = vec![-2.0_f32]; // negative inner (curvature violated)
+        let v2 = verdict_from_curvature(&[(&s, &y)]);
+        let v3 = verdict_from_history_bound(10, 5); // overflow
+        let v4 = verdict_from_objective_decrease(50.0, 100.0); // ascended
+        let simd = vec![1.0_f32];
+        let scalar = vec![1.5_f32]; // ULP budget exceeded
+        let v5 = verdict_from_simd_scalar_parity(&simd, &scalar);
+        let v6 = verdict_from_empty_history_steepest(&[1.0], &[1.0]); // not -g
+        for v in [v1, v2, v3, v4, v5, v6] {
+            assert_eq!(v, LbVerdict::Fail);
+        }
+    }
+}
diff --git a/crates/aprender-core/src/format/mod.rs b/crates/aprender-core/src/format/mod.rs
index c855d3592..6c6f9f80d 100644
--- a/crates/aprender-core/src/format/mod.rs
+++ b/crates/aprender-core/src/format/mod.rs
@@ -550,6 +550,11 @@ pub mod gate_ship_011;
 // GATE-SHIP-012 — Line-coverage percentage inclusive-floor threshold (≥ 95.0).
 pub mod gate_ship_012;
 
+// FALSIFY-LB-001..006 — lbfgs-kernel-v1 6-gate algorithm-level PARTIAL
+// discharge (descent direction, curvature, history bound, Rosenbrock
+// decrease, SIMD≡scalar within 8 ULP, empty-history → -g).
+pub mod lb_001_006;
+
 // Re-export types (PMAT-198 - backward compatibility)
 pub use types::*;