Butlin HOT-3: prove metacognitive state causally guides belief updating and action

Finding

The current HOT-3 Butlin probe is not construct-specific enough.

Today the live signal resolves HOT-3 from actual_effective_lr > 0, and the ablation uses enable_online_learning=false. That establishes that online learning exists and can be disabled. It does not establish the stronger HOT-3 relation we should require: higher-order/metacognitive state causally guides belief formation or action.

Symthaea already has a promising production path: the cognitive loop's metacognitive layer computes self-model accuracy, and sufficiently high accuracy modulates the subsystem learning-rate factor. That relation should be tested directly.

Objective

Demonstrate:

metacognitive state
      ↓
precision / learning / belief update policy
      ↓
belief or action consequence

while holding first-order task evidence fixed.

Required experiment

Prefer to reuse the typed confidence/self-model intervention infrastructure being developed for HOT-2 (#1910), but keep HOT-3's outcome and evidence classification distinct.

Required arms:

• calibrated/high-reliability metacognitive state;
• deliberately degraded or corrupted metacognitive state under identical first-order evidence;
• metacognition-disabled arm;
• unrelated sham intervention;
• rescue restoring trustworthy metacognitive information without overwriting the final belief/action.

Required measurements

• independent proof of metacognitive intervention;
• first-order evidence/task input equality across arms;
• metacognitive accuracy/confidence before policy consequence;
• actual learning/precision factor selected by the production loop;
• belief update magnitude and/or action choice;
• downstream task consequence;
• exact source/config/stimulus/seed/intervention identity;
• multi-seed and alternate-task replication.

Fail-closed constraints

• actual_effective_lr > 0 alone is not HOT-3 evidence.
• Turning off all online learning is too broad to prove metacognitive guidance.
• Do not use the same scalar both as intervention verification and outcome.
• If confidence corruption changes first-order correctness/evidence, the trial is invalid for this theorem.
• Evidence reused from HOT-2 must be annotated as a shared intervention/dependency rather than counted as an independent replication.
• A learning-rate change without a belief/action consequence remains mechanistic evidence, not functional support.

Exit condition

A provenance-bound runner shows that changing only Symthaea's higher-order/metacognitive assessment changes how identical first-order evidence is incorporated into beliefs or actions, with sham specificity and rescue.

No consciousness claim is implied.

Start by reading the HOT-2 confidence/self-model intervention infrastructure from issue #1910 and the cognitive loop's metacognitive layer, including the actual_effective_lr and enable_online_learning paths. Define the required arms and provenance-bound measurements before implementing the runner. Done means identical first-order evidence produces a metacognition-specific belief or action consequence with sham, rescue, and multi-seed replication.