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+# Candidate register
+
+The obstruction on natural data decomposes into five factors, and every
+candidate attacks exactly one of them. Field correlation stands at 0.656
+against the 0.9 that polynomial recovery needs, so the register is
+ordered by expected movement per unit of effort rather than by elegance.
+
+Status is one of: **done** (measured, number recorded), **running**,
+**queued** (specified, not started), **open** (idea, not specified).
+
+## A. Raise the field correlation
+
+The binding constraint. Everything else is worth less than a tenth of
+what this is worth if it moves.
+
+| Candidate | Cost | Status |
+|---|---|---|
+| Continuous states instead of class codes | low | done: 0.166 to 0.489 |
+| Content projection, between-scene over within-scene | low | done: 0.489 to 0.656 |
+| Augmentation orbits, four views | medium | done: no gain, 0.6559 either way |
+| Larger vision backbone (DINOv2-large, -giant) | medium | queued |
+| Multi-scale patch features, several receptive fields | medium | queued |
+| Corpus-trained text encoder instead of PPMI vectors | medium | queued |
+| Structured phrase encoding: head and modifiers apart | low | queued |
+| Intervention responses: occlude a region, re-encode, use the change | high | queued |
+| Native multi-view corpora: product photographs, video frames | high | queued |
+| Nonlinear content projection (kernel discriminant) | low | open |
+| Adaptive segment count with quality filtering | low | open |
+
+The intervention row is the one the closed world argued for hardest and
+the one never run on natural data. It needs real forward passes -- masked
+re-encoding on both sides -- not cached-feature algebra, which is a
+tautology.
+
+## B. Reshape the landscape
+
+Decoys exist because they match second-order statistics. Either raise
+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 |
+| 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 |
+| Hubness correction (CSLS) on field similarities | low | queued |
+| 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
+is landscape reshaping by orthogonal information: a decoy that copies
+relational statistics still has to induce a map that generalises.
+
+## C. Search harder
+
+| Candidate | Cost | Status |
+|---|---|---|
+| Spectral initialisation plus exact refinement | low | done: 53.5% to 95.3% composed |
+| Parallel tempering with exact swap deltas | medium | done: equilibrates into the decoy shelf |
+| Multiple spectral inits over eta, keep best by energy | low | queued |
+| Seeded expansion from high-confidence pairs | medium | queued |
+| Belief propagation on the assignment factor graph | high | queued |
+| Cluster moves: swap blocks rather than single pairs | low | queued |
+| Path relinking and crossover over permutations | medium | open |
+| Branch and bound, exact on small blocks | medium | open |
+| Sum-of-squares or low-degree hierarchies | high | open |
+
+Accepting exponential cost does not rescue the hard phase at fixed size:
+tempering already is exponential-time and fails by equilibrating, not by
+running out of budget. Exponential methods pay only where the block is
+small enough to finish, which is why C and D are the same programme seen
+from two sides.
+
+## D. Shrink the problem
+
+The phase boundary is joint in correlation and population size, so a
+corpus need not be matched at once.
+
+| Candidate | Cost | Status |
+|---|---|---|
+| Largest recoverable N at the natural field quality | low | running |
+| Diversity-selected bootstrap subset instead of random | low | queued |
+| Hierarchical: cluster first, match within cluster | medium | queued |
+| Many small blocks, merge by consistency voting | medium | queued |
+
+Diversity selection is the cheapest idea in the register and possibly
+the best value: decoys arise from scenes that resemble each other, and
+choosing a mutually dissimilar bootstrap set thins them at no
+algorithmic cost. It composes with small blocks by construction, since
+if only a few hundred pairs are needed they should be the most
+distinguishable few hundred.
+
+## E. Add orthogonal signal
+
+| Candidate | Cost | Status |
+|---|---|---|
+| Held-out generalisation of the induced map | medium | running |
+| Intervention response consistency | high | queued |
+| Counting and cardinality, gauge-free by construction | low | queued |
+| Higher-order joint tables (colour by shape by count) | low | queued |
+| Temporal or sequential structure where corpora carry it | high | open |
+
+## F. Change the formulation
+
+Real corpora are not in bijection, so the permutation formulation is a
+scaffold that has to be replaced eventually regardless of performance.
+
+| Candidate | Cost | Status |
+|---|---|---|
+| Unbalanced coupling: partial mass, unmatched items allowed | medium | queued |
+| Many-to-many soft assignment | medium | open |
+| Part-level matching across the corpus rather than scene-level | medium | open |
+| Joint factor-level and scene-level, alternating | medium | open |
+
+## Order of attempt
+
+Cheap and untried first, because the register's value is in eliminating
+branches quickly: diversity selection, degree normalisation, hubness
+correction, sparsified fields, multiple spectral inits, structured phrase
+encoding, higher-order joint tables. Then the medium tier led by path
+following and the functional term. The two expensive rows worth pre-
+committing to are intervention responses and a natively multi-view
+corpus, because the closed world named both as protocol requirements
+rather than optimisations.