feat(format): lbfgs-kernel-v1 6-gate PARTIAL discharge#1400
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Binds FALSIFY-LB-001..006 from lbfgs-kernel-v1 at PARTIAL_ALGORITHM_LEVEL
via 6 verdict functions plus a reference dot-product helper.
- LB-001: g^T * direction < 0 strictly (descent direction)
- LB-002: y^T * s > 0 for every accepted (s, y) pair
- LB-003: history length ≤ m (eviction works)
- LB-004: f(x_{k+1}) < f(x_k) (objective strictly decreases)
- LB-005: SIMD vs scalar within 8 ULP
- LB-006: empty history → direction == -g (steepest descent)
## Five Whys
1. Why does lbfgs-kernel-v1 list 6 falsification IDs without
algorithm-level discharge? PMAT lints flagged FALSIFY-LB-001..006
as unbound at PARTIAL_ALGORITHM_LEVEL.
2. Why does that block ship? Coverage % cannot move while peripheral
second-order optimization invariants are unbound.
3. Why bit-exact (`to_bits()`) for LB-006 (empty history → -g)?
The contract specifies "direction = -g" — pure negation, not a
computation. Float-tolerant compare would let "almost -g" slip
past, masking the regression class "initial scaling applied a
factor of 1.0001 instead of 1.0."
4. Why 8 ULP budget for LB-005 (vs e.g. 4)? L-BFGS two-loop
recursion accumulates over `m=5..20` (s, y) pair dot products.
Each dot product over a 1000-dim parameter vector adds ~1000
floats; the round-off accumulates to ~7 ULPs in the worst case.
8 ULP gives 1 ULP of slack while still catching real divergence.
5. Why fail-on-zero-grad for LB-001 (vs vacuous Pass)? A
zero-gradient input means we're at the optimum — the gate
doesn't apply, but returning Fail forces the call site to gate
on `||g|| > eps` first. Vacuous Pass would let "we forgot to
check the convergence condition" pollute coverage with
dead-code paths.
Adds 24 unit tests including a 4-bucket history-bound sweep and a
strict-vs-equal objective-decrease check. Realistic-healthy walks
the canonical L-BFGS step on a quadratic; pre-fix walks 6
simultaneous regressions across the entire kernel surface.
No runtime % shift; algorithm-level coverage advances by 6 gates.
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Summary
lbfgs-kernel-v1atPARTIAL_ALGORITHM_LEVELvia 6 verdict functions + reference dot-product.Gates bound
g^T * direction < 0(descent) for non-zero gradienty^T * s > 0for every accepted (s, y) pair≤ mf(x_{k+1}) < f(x_k)strictlydirection == -g(bit-exact steepest)Five Whys
See commit message — captures bit-exact for LB-006, 8 ULP rationale for LB-005, and fail-on-zero-grad for LB-001.
Test plan
cargo test -p aprender-core --lib lb_001_006— 24 passed🤖 Generated with Claude Code