Chapter 10: The Brain on the Wire — GIGI Builds exercises

Eleven verbs the brain speaks over the wire — that's the surface area this chapter drew. Each exercise puts pressure on one seam of the polymorphic path so the receipts I shipped stay honest under new load.

Run it live — GQL console

Point at the public read-only instance (no key needed) or your own engine (start it with GIGI_CORS_ORIGIN=* for browser access — dev only).

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E10.1Reproduce the dream wander

Build

Re-run examples/brain_tour_demo.rs §4 on the 40-record BLD-CH10-BUNDLE, sweeping \(T \in {1, 2, 4, 8}\) with the SAMPLE/DREAM Langevin walker (1500 burn-in, \(dt=0.01\), seed 42), and tabulate max wander distance from \(\mu\) per temperature.

Receipt

At \(T=4\) you must hit BLD-CH10-DREAM's \(15.64\); the \(T=1\) column reproduces the SAMPLE spread; the four-row table is committed to theory/brain_primitives/dream_temperature_sweep.txt with the seed printed in the header.

Bonus

Fit \(\sqrt{T}\) scaling to your four rows; report the residual and whether it widens at \(T=8\) as the walker leaves the typical set.

done

E10.2Stress CONFIDENCE on the 184-OOM gap

Build

Run examples/predictive_coding_demo.rs (the 80-patient PK cohort) and binary-search the weight axis between 78\,kg and 300\,kg for the patient mass at which normalized drops below Marcella's refuse-gate threshold (\(10^{-2}\) in the demo).

Receipt

A single number \(w^*\), the kg value where the gate flips known \(\to\) unknown, and the two flanking normalized values; the in-cohort end of your sweep reproduces BLD-CH10-184-OOM's 0.929 at 78\,kg / 4.7\,L/h to four decimals.

Bonus

Repeat at clearance fixed to \(4.5\)\,L/h vs \(0.1\)\,L/h; the two \(w^*\) values should disagree because the kernel is two-dimensional, and the size of the disagreement is the bandwidth talking.

done

E10.3Instrument FORECAST conservation

Build

Hit POST /v1/bundles/{name}/brain/forecast on BLD-CH10-BUNDLE from start \((3,0,5,10)\) and capture \(H(x_t)\) at \(t \in {0, 500, 1000, 2000, 10000}\) by querying the bundle's negative log-density at each returned point. Plot \(H(t) - H(0)\).

Receipt

Reproduce the BLD-CH10 step-500 and step-1000 coordinates from §10.3 to three decimals, and a log line |H(t)-H(0)|/|H(0)| < 1e-3 at \(t=10000\); fail loudly if the symplectic integrator has drifted off-shell.

Bonus

Halve \(dt\) and check that the drift drops by the right power of the step (Euler vs leapfrog will give you different answers; the demo uses leapfrog).

done

E10.4Refute the FOCUS-as-ATTEND-truncation shortcut

Build

Write a 50-line client that calls brain/attend on a query the demo doesn't ship — pick one halfway between the two clusters of BLD-CH10-BUNDLE — and compare argpartition of the returned \(\alpha_i\) at \(k=3\) against the top-3 weights from FOCUS's local-only implementation in examples/brain_tour_demo.rs §9.

Receipt

A table of three indices and three weights from each side, identical up to floating-point on the in-cluster query, and a documented divergence (or absence thereof) on the between-clusters query; commit the writeup as theory/brain_primitives/focus_vs_attend_top3.md. This is the contract gap I named in §10.10 — you are the test cohort.

Bonus

Find a query where ATTEND's full distribution is bimodal and the FOCUS truncation loses the second mode; that is the reason FOCUS does not yet have a route.

done

E10.5Extend EPISODIC to a smooth bundle

Build

Build a 40-record bundle with no cluster jump — a single Gaussian blob, same 4D anisotropic \(\sigma^2\) — and call brain/episodic against it.

Receipt

events_found: 0 returned by the endpoint; the absence of a top_gap field (or a null) committed to your ledger, contrasted against BLD-CH10-EPISODIC's 186.2x persistence_ratio on the two-cluster bundle. Same verb, same code path, opposite verdict — that's the refusal in §10.8 made into a test.

Bonus

Sweep cluster separation from 0 to the BLD-CH10-BUNDLE gap and record the persistence ratio at which the verb starts naming the event; report the elbow.

done

E10.6Wire EXPLAIN into a path renderer

Build

Call brain/explain with n_steps=4 on query \((15,15,15,5)\) against BLD-CH10-BUNDLE; ship a 30-line script that emits the five returned path points as an SVG polyline projected onto the \((bx, cy)\) plane.

Receipt

The SVG opens, the middle waypoint sits at \((7.66, 7.35, 8.92, 2.07)\) to two decimals (BLD-CH10-EXPLAIN), and nearest_idx=13 is annotated at the line's endpoint. Commit the SVG to theory/brain_primitives/explain_path.svg.

Bonus

Re-run with n_steps=16 and overlay both polylines; the geodesic shape should be preserved while the sampling thickens. EXPLAIN is reusing FORECAST's integrator — the overlay is the receipt that it's the same machinery.

done

E10.7Benchmark PREDICT's \(\epsilon\)-floor against rank deficiency

Build

Build a degenerate 40-record bundle where one fiber axis has \(\sigma^2 < 10^{-6}\) (collapse one coordinate to constant plus noise). Call brain/predict at fit_mode="diagonal" from state \((5,5,5,5)\) with and without the predictive_coding.rs:121 default \(\epsilon=10^{-3}\) floor.

Receipt

Two response bodies side-by-side: the floored response steps finitely along the rank-deficient axis (matches the spirit of BLD-CH10-PREDICT's \(5 \to 5.0333\) on the wide \(cy\) axis), and the un-floored response either explodes the step or NaNs. Committed as theory/brain_primitives/predict_epsilon_floor_demo.txt.

Bonus

Find the smallest \(\epsilon\) that still produces a finite step on your degenerate axis; that number is the engine's honesty budget on rank deficiency, and Marcella will eventually want to know it.

done