Landscape reshaping does not substitute for field correlation

A rank-truncation ladder from four to full rank returns chance accuracy
at the natural-data correlation of 0.656, as does full-rank spectral
initialisation with refinement. Coarse-to-sharp smoothing widens basins
and thins decoys, and recovers nothing, so below the polynomial
threshold the deficit is information the algorithm class cannot use
rather than a basin it cannot find. Solver-side candidates should wait
on the correlation instead of competing with it.

Co-Authored-By: Claude <noreply@anthropic.com>

1 files changed, 11 insertions, 3 deletions

diff --git a/CANDIDATE_REGISTER.md b/CANDIDATE_REGISTER.md
index 31906ff..efed50e 100644
--- a/CANDIDATE_REGISTER.md
+++ b/CANDIDATE_REGISTER.md
@@ -40,7 +40,7 @@ them or widen the true basin.
 | Candidate | Cost | Status |
 |---|---|---|
 | Third-order terms, tr(M^3) | low | done: deepens truth and decoys alike |
-| Rank-truncation ladder, coarse to sharp | low | running |
+| Rank-truncation ladder, coarse to sharp | low | done: at chance, all ranks |
 | Convex-concave path following (PATH, FAQ family) | medium | queued |
 | Entropic doubly-stochastic relaxation | low | done: stalls far above truth |
 | Degree normalisation of the fields | low | queued |
@@ -48,8 +48,16 @@ them or widen the true basin.
 | Sparsified fields, top-k neighbours only | low | queued |
 | Functional term: held-out generalisation of the induced map | medium | running |
 
-Path following is the canonical landscape-deformation method for
-quadratic assignment and has never been tried here. The functional term
+The rank ladder settles the category. At the natural-data field quality
+every rank from four to full returns chance accuracy, as does full-rank
+spectral initialisation with refinement -- 0.0039 against 0.0039 chance.
+**Landscape reshaping does not substitute for field correlation:** below
+the polynomial threshold the deficit is information the algorithm class
+cannot use, not basins it cannot find, so smoothing has nothing to
+recover. Path following is the canonical landscape-deformation method for
+quadratic assignment and remains untried, but this result lowers its
+expected value at the current correlation and it should wait until the
+correlation moves. The functional term
 is landscape reshaping by orthogonal information: a decoy that copies
 relational statistics still has to induce a map that generalises.