# Candidate register

*Reordered 2026-08-01 after the rank experiment. See `RANK_RESULTS.md`.*

The register used to be ordered by how much each candidate was expected to
raise the field correlation, because correlation was the go/no-go statistic.
That statistic has been shown not to govern recovery: a synthetic field
truncated to rank 8 correlates at 0.906 and recovers 13%, while the same field
at rank 16 recovers 96%. **The target is now a pair — the correlation and the
width of the shared spectrum — and candidates are ordered by which one they
move.**

Status is one of: **done** (measured, number recorded), **running**,
**queued** (specified, not started), **open** (idea, not specified),
**closed** (measured and eliminated).

Current position: correlation 0.716, shared directions 15, against a
recovering synthetic reference at 0.928 and 26.

## A. Widen the shared spectrum

The binding constraint, and the one only identified today. Both modalities are
individually rich — vision effective rank 40, text 48 — and agree on 15
directions. Candidates here are judged on the shared count, not the
correlation.

| Candidate | Cost | Status |
|---|---|---|
| Eigenvalue-weighted projection, wide basis | low | done: shared 10 to 15, ρ 0.656 to 0.692 |
| Text vector dimension | low | done: shared 10 to 17, saturates; ρ peaks 0.716 at 128 |
| More segments per scene (6 to 16) | low | closed: shared 15 to 14 |
| Annotated boxes instead of segmentation (oracle) | low | closed: shared 15, buys one direction |
| More scenes (256 to 1024) | low | closed: shared 23 to 19 at matched width |
| Augmentation orbits, four views | medium | closed: no gain, ρ 0.6559 either way |
| Larger vision backbone (DINOv2-large) | medium | running: predicted useless, see below |
| Third-order moments in the set kernel | low | queued |
| Corpora with naturally wide overlap | high | queued |
| Intervention responses: occlude, re-encode, use the change | high | queued |
| Corpus-trained text encoder instead of PPMI vectors | medium | queued |
| Structured phrase encoding: head and modifiers apart | low | queued |
| Nonlinear content projection (kernel discriminant) | low | closed: 0.62 against 0.69 linear |

The backbone row is a live prediction test rather than a hope. The shared count
does not move when segmentation is replaced by ground-truth boxes, when
segments are nearly tripled, or when the vision field's own effective rank
doubles, so a larger backbone is predicted to leave it unchanged. The run is
finishing anyway because the project's rule is to measure the bound rather than
infer it, and a cheap refutation of my own prediction is worth more than the
GPU time.

**Corpora with naturally wide overlap is the row today's result argues for and
the one never attempted.** The synthetic world reaches 26 shared directions
because its captions state exactly the world state; Visual Genome reaches 15
because a region description and a patch descriptor overlap on about that many
aspects of a photograph. If the ceiling is a property of what the two corpora
are about, the lever is corpus choice: dense descriptions, product listings
carrying photographs and full specifications, screenshots paired with
accessibility trees, scientific figures with their captions.

## B. Raise the correlation

Still necessary — 18 shared directions at ρ = 0.508 also fails — but no longer
sufficient, and no longer the thing to optimise alone.

| 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 |
| Eigenvalue weighting plus wider text vectors | low | done: 0.656 to 0.716 |
| Degree-residual fields | low | done: +0.015, keep, composes freely |
| Hubness inflation of the statistic | low | closed: refuted, degree model is 1-5% of variance |
| Multi-scale patch features, several receptive fields | medium | queued |
| Adaptive segment count with quality filtering | low | open |

## C. Reshape the landscape — closed

| Candidate | Cost | Status |
|---|---|---|
| Third-order terms, tr(M³) | low | done: deepens truth and decoys alike |
| Rank-truncation ladder, coarse to sharp | low | closed: at chance, all ranks |
| Entropic doubly-stochastic relaxation | low | closed: stalls far above truth |
| Convex-concave path following (PATH, FAQ family) | medium | closed by inference |

Below the recoverable region the deficit is information the algorithm class
cannot use, not basins it cannot find, so smoothing has nothing to recover.
Path following remains the canonical landscape-deformation method for quadratic
assignment and remains untried, but it should not be tried until the shared
spectrum moves.

## D. Shrink the problem — closed, and the reasoning was backwards

| Candidate | Cost | Status |
|---|---|---|
| Largest recoverable N at natural field quality | low | closed: none, 16 through 256 |
| Diversity-selected bootstrap subset | low | closed by the above, and not protocol-legal |
| Hierarchical: cluster first, match within cluster | medium | closed |
| Many small blocks, merge by consistency voting | medium | closed |

The premise was that the hard phase is joint in correlation and population
size, so small blocks would need less correlation. The sign is the other way:
ρ_IT ≈ √(4 log N / N) **rises** as N falls — 0.29 at 256 scenes, 0.51 at 64,
0.83 at 16 — so small blocks need *more* correlation, not less. The gate
confirms it directly: at N = 16, 24, 32, 48 and 64, the best state a strong
searcher reaches is deeper than the truth in three replicates of three. When
the truth is not the optimum the algorithm class is irrelevant, which is also
why accepting exponential cost buys nothing.

Diversity selection additionally turns out not to be protocol-legal as
imagined: choosing dissimilar images and dissimilar captions independently
yields two sets that are not in bijection, so the selection cannot be realised
without the pairing it is meant to discover. It survives only inside the
unbalanced formulation in F.

## E. Add orthogonal signal

Unaffected by today's result and now relatively more attractive, because
information that does not pass through the relation field is not subject to the
shared-spectrum ceiling.

| 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. Today's
closure of D makes this more urgent, since the unbalanced formulation is now
the only home for selection-based ideas.

| Candidate | Cost | Status |
|---|---|---|
| Unbalanced coupling: partial mass, unmatched items allowed | medium | queued |
| Diversity selection inside the unbalanced formulation | 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

Third-order moments first: it is the cheapest untried thing that raises field
rank by construction, since a set kernel carrying third moments spans more
directions than one carrying two. Then structured phrase encoding and the
corpus-trained text encoder, because the text side is the one that moved the
shared count at all. Then the two rows worth pre-committing to regardless of
cost — intervention responses, and a corpus chosen for naturally wide overlap —
the second of which is now the register's central bet rather than one candidate
among many.