Butlin HOT-4: demote generic sparsity/smoothness proxy and qualify a real quality space

Finding

The current HOT-4 evidence path is too strong for the construct it actually measures.

measure_hot4_sparse_smooth_coding() currently measures:

1. generic output sparsity — fraction of cognitive-loop output dimensions below 5% of the output's own maximum magnitude;
2. generic local continuity — whether output cosine dissimilarity grows roughly monotonically as an arbitrary ContinuousHV is mixed with increasing random noise.

indicators.rs then treats the resulting value as a special case that directly earns SupportTier::Observed.

Repository search did not identify a production mechanism explicitly implementing or learning a perceptual quality space whose geometry is independently meaningful. Generic sparsity + continuity is useful representation diagnostics, but it is not sufficient to establish HOT-4's stronger quality-space property.

Immediate epistemic correction

Until a construct-valid quality-space theorem exists:

• retain hot4_sparsity and hot4_smoothness as diagnostics;
• annotate them as a proxy / generic representation property;
• do not allow this probe alone to mint Observed HOT-4 evidence;
• default HOT-4 to ArchitecturalOnly unless stronger independently bound evidence is supplied;
• preserve the current raw metrics for regression/history rather than deleting them.

Objective

Build and qualify a production quality-space representation with sparse, smooth coding whose geometry corresponds to independently specified perceptual/representational relations.

Proposed minimum theorem

Use at least one domain with an externally defined continuous structure (for example a controlled visual/color continuum, spatial orientation, pitch/timbre continuum, or another sensor domain already represented in Symthaea).

Required properties:

• sparsity: bounded active-code fraction under a preregistered definition;
• local smoothness: nearby stimuli map nearby and small perturbations produce small representational changes;
• global geometry: independently known neighborhoods/orderings are preserved better than shuffled controls;
• interpolation: intermediate stimuli land between endpoint representations rather than merely changing monotonically in norm;
• disentanglement / selective axes: changing one known quality dimension preferentially moves the representation along a stable direction while controlled nuisance variation does not dominate;
• held-out generalization: geometry holds for stimuli excluded from fitting/calibration;
• causal use: the learned geometry supports a downstream discrimination/generalization task and targeted disruption selectively degrades it.

Controls

• shuffled stimulus labels / geometry;
• random HDC projection with matched dimensionality and sparsity;
• magnitude-only and norm-only baselines;
• unrelated latent-dimension mask sham;
• targeted quality-space disruption;
• reconstruction/rescue from independently supplied quality coordinates where possible.

Fail-closed constraints

• Random high-dimensional continuity is not sufficient.
• A smooth response to random-vector interpolation is not sufficient.
• Near-zero coordinates alone are not sufficient evidence of sparse coding in the HOT-4 sense.
• The benchmark must not define the target geometry from the same representation it evaluates.
• Thresholds and neighborhood relations must be frozen before target outputs are inspected.
• If the representation has no independently meaningful geometry, classify the result as proxy evidence rather than HOT-4 observation.

Exit condition

A provenance-bound, held-out experiment shows that a production Symthaea representation forms a sparse, smooth quality space with independently grounded geometry, survives sham controls, degrades under targeted disruption, and supports a downstream task.

No consciousness claim is implied.

Start in indicators.rs and trace the measure_hot4_sparse_smooth_coding() evidence path, noting where hot4_sparsity and hot4_smoothness are classified. Preserve the raw metrics while preventing this probe alone from producing Observed HOT-4 evidence. Done requires a provenance-bound, held-out quality-space experiment with the listed geometry, sham controls, targeted disruption, and downstream-task checks.