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>

2 files changed, 33 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.
 
diff --git a/LAB_NOTES.md b/LAB_NOTES.md
index 8c0e9d5..e6aa208 100644
--- a/LAB_NOTES.md
+++ b/LAB_NOTES.md
@@ -562,6 +562,28 @@ orbit lever is unavailable on this corpus.
 
 See `NATURAL_RESULTS.md`.
 
+## 2026-08-01: landscape reshaping does not substitute for correlation
+
+At the natural-data field quality of 0.656, every solver returns chance.
+Full-rank spectral initialisation gives 0.0039 against 0.0039 chance,
+refinement 0.0078, and a rank-truncation ladder from four to full rank
+stays at or below chance throughout. Coarse-to-sharp smoothing is the
+standard way to widen basins and thin decoys, and it recovers nothing
+here.
+
+The reading is categorical rather than about this one method. Below the
+polynomial threshold the deficit is information the algorithm class
+cannot exploit, not a basin it fails to locate, so reshaping has nothing
+to work with. Solver-side candidates should therefore wait on the
+correlation rather than compete with it, and the only non-correlation
+lever still open is population size, since the phase boundary is joint
+in the two.
+
+Compute note: NCSA Delta A40 was brought in for the correlation-raising
+battery -- larger backbones and finer segmentation over the same corpus
+-- with three array tasks starting immediately against a queue of 810,
+9,624 GPU-hours remaining on the account.
+
 ## Current experimental gate
 
 The node-level ordering-and-basin gate is passed on VG by content-projected