PCM v5 — an exploratory laboratory

Three ways to use the PCM chamber

• Learn presents focused experiments with the relevant controls. Each lesson follows Question → Predict → Try → Observe → Interpret → Limit, with an action goal and a concrete hint. You can skip without claiming completion.
• Full PCM v5 makes the full chamber available for controlled changes, display-layer choices, and comparisons. Use Open full PCM v5 beside the lesson picker to continue with the same experiment.
• Methods explains formulas, units, sampling windows, evidence, and reproducibility. Numerical tables matter even when the 3-D scene is available; a picture is not a measurement definition.

Five chapters, eleven lessons

1. Orient yourself

1. How to watch a model. Pause, Step once, then select Slow ×0.05. Step advances one fixed solver tick, not a rendered frame. Pause stops observation time; slow playback changes tick scheduling, not the equations.

2. Waves and coordination

2. A travelling pattern. Take wave speed to at least 5, then back to 1 or less. Speed changes temporal motion, not the chosen wavelengths.
3. A point of view, with a clamp. Start at zero projective strength and try 0.05. Inspect the unclamped region before exploring stronger projection.
4. Twelve clocks, measured alignment. Lower coupling and observe R below 0.4, then raise coupling and observe R above 0.7. Allow model time for both responses.
5. A slow phase modulates a fast rhythm. Increase PAC from zero to at least 0.8 while holding manual amplitudes fixed.

3. Prediction and updating

6. Observations cross an explicit boundary. Raise leak to at least 0.3 and return it exactly to zero. The conditional-dependence estimate is a limited proxy, not a proof.
7. One stimulus, two branches. Introduce one stimulus and observe its error and direct wave responses. No repeated button-spamming or score target is needed.
8. Observe beliefs, not just a falling score. Stimulate with updating rate lr = 0 and observe fixed beliefs for at least 13 ticks; then set lr ≥ 0.3, stimulate again, and observe actual belief change.

4. Boundaries and action

9. A dual gate for a model commitment. Lower both gamA ≤ 0.35 and gamP ≤ 0.5, then observe a fresh commitment. R alone is not the gate.

5. Patterns and the full signal map

10. Pattern persistence and the quench analogy. Apply tilt at least +0.3, observe actual field change, return tilt to zero, Quench, and observe settling. Quench changes scientific parameters; Slow does not.
11. Follow the loop and its separate branches. Introduce a stimulus, observe a fresh commitment, then tilt, release to zero, Quench, and observe settling.

The actual wiring is world → sensors → inference → policy/active state → world, with a separate stimulus → wave/viewpoint branch and driven pattern fields. It is not one serial belief-to-wave-to-memory chain. Event indicators report model activity, not proof of a complete causal theory.

Read measurements, not health scores

Oscillator synchrony R

R = |Σ exp(iθ)| / 12, between 0 and 1. Circular variance is 1 − R. The twelve oscillators are separate from the adjustable Fourier wave-band count. R is not PCI.

Weighted-error + KL score F

F = ½Σ πε² + KL(q || uniform). This is an executed proxy score, not subjective surprise or a fully derived variational-free-energy model. pBase is sensory-error precision, not prior precision.

Prediction-error norm ‖ε‖

The Euclidean magnitude of o − Lq, in model observation units. It can change because the world and sensors change, even with beliefs fixed.

Pattern change rate

RMS field change divided by elapsed model time, in model field units per model second. This is not cognitive flexibility, memory quality, or clinical recovery. Domain-wall count and recent consolidation ratio are separate diagnostics; a rolling-window expiration is not renewed learning.

Overview medians use 3 model seconds for R, 5 for F and error norm, and 1 for pattern change rate. Allow the sampling windows to fill. Model reference ranges are not healthy bands: they describe seeded model runs under stated settings, not people. Check the engine revision, calibration metadata, changed parameters, and retained interval. Plot spans are not clinical thresholds and can be exceeded.

Seeded baselines and reproducible experiments

Entering each lesson explicitly creates core defaults plus that lesson’s preset and seed. Welcome begins at model time zero; other lessons are prepared for 2 model seconds before your actions. Prior slider changes do not silently carry into the next lesson. The displayed seed and preset identify the setup, not its biological validity.

• Restart this experiment returns to its saved start state, including the seeded lesson baseline when studying a lesson.
• Restore defaults creates default parameters and initial state with the current seed; it is different from returning to a lesson preset.
• New random seed creates a different initialization with the current parameters. For a controlled comparison, keep the seed fixed instead.
• Save/load local JSON preserves a resumable checkpoint, including numerical and random state, parameters, solver settings, and retained history. Loading validates the file. A seed or a screenshot alone cannot reproduce an evolved run.
• Export CSV saves the retained measurement series with model-time/tick information. CSV is for analysis, not checkpoint restoration; inspect the retained interval rather than assuming a full-from-origin recording.
• Pin reference run / Compare overlays a controlled rerun. Pin a run, restart from the same setup, change one factor, and repeat actions at matching model ticks. Inspect seed, parameter, and interval differences before attributing an effect. Matching revisions and solver settings matter; revised engines need not reproduce older trajectories.

Optional hypothesis case studies

These are mechanism-first questions, not simulated diagnoses or treatment instructions.

• Reduced coupling — coma and covert-awareness context. Lower oscillator coupling and inspect the available response routes separately.
• Strong locking — seizure-dynamics context. Increase coupling and remove phase noise; strong phase alignment is not a seizure diagnosis.
• Biased patterns — craving and incentive-salience context. Bias one field sign and strengthen the potential; the field has no reward semantics.
• Slow updating — rumination context. Slow belief updates and increase sensory-error weighting, without confusing that weighting with prior precision.
• Volatility with limited updating — psychosis and voice-hearing context. Increase volatility, slow updates, and add leak; the model does not generate hallucinated speech.
• Reversible coupling change — anesthesia context. Reduce coupling, then restore its parameter value; this is not a drug-dose or emergence model.

Each case starts from an explicit seeded default-model baseline. Apply intervention changes the listed parameters. Restore parameters removes those changes without rewinding the evolving state. Return to experiment resumes the saved prior run. No restore promises a score band, an identical trajectory, or clinical recovery.

Mechanisms overlap: the coma and anesthesia topics deliberately share a coupling intervention; rumination and voices share limited updating; biased patterns reuse the ordinary persistence mechanism. The model does not distinguish these clinical conditions or calculate PCI.

Methods and evidence boundaries

In the instrument, Methods separates local mathematical claims from whole-model hypotheses:

• The HD gradient holds its sharpened target fixed within each update, including the posterior-gain factor. This is not global moving-target descent.
• Allen–Cahn energy descent requires fixed coefficients, no external injection, and a suitable stable discretization. A quench changes the parameters and can change the energy function itself.
• Policy scores are heuristics, not a complete expected-free-energy planner. Changing their weights need not change the selected policy label.
• The conditional-dependence estimator is scalar and linear-Gaussian, conditioned on current sensors/actions and previous internal state. It cannot prove full-state conditional independence.
• Finite Fourier synthesis is valid without an FFT. The perspective denominator clamp, however, prevents a global homography claim.

Measured labels a particular empirical finding; Theory labels a theoretical account or an explicitly identified review; Model labels an authored model claim. Sources retain their limitations and review articles are identified as reviews.

For example, Zhang and colleagues’ travelling-wave recordings support a wave ingredient, not this combined simulation. Rudrauf and colleagues’ projective framework supplies theoretical provenance, while Casali and colleagues’ PCI study uses a TMS–EEG complexity protocol that PCM v5 does not implement.

Worden’s wave ideas, Rudrauf’s projective framework, and ACFM’s pattern formalism are provenance, not an endorsement or clinical validation of this implementation. Evidence for ingredients is not validation of their combination. Any mistakes found in this implementation are mine alone, not theirs.