A complete worked run
Follow four measurements from an inherited equation to a repaired forecast.
Recorded ordinary programs, no AI-model calls. This is the already disclosed both-000 development case. It was chosen to explain the workflow, not sampled to estimate performance. Explanations below were written afterward; they are not a participant reasoning transcript. The original replay preserves the observations and submitted forecasts.
Before any target experiment
The participant receives the source equation q(x) = 2 − 2x + 2x² − 2x³, produced by the referee from six source measurements. It also receives the public family rules, twelve forecast targets and a budget of four target measurements.
The target may have a changed instrument, one changed process coefficient, both changes or neither. The sampled condition, target coefficients and calibration are hidden until completion. Readings are exact and noiseless, and the process stays fixed during the run.
The goal is to predict physical threshold events. The instrument reports z = gq + b; a raw reading is not the physical value.
1. Measure a known zero
Action: calibrate with reference 0. Reading: −2. Cost: 1; 3 measurements remain.
A zero standard isolates the instrument offset: b = −2. Gain and process changes remain unresolved.
2. Measure a known one
Action: calibrate with reference 1. Reading: 0. Cost: 1; 2 remain.
The difference between the two readings gives g = 0 − (−2) = 2. A future reading can now be converted using q = (z + 2) / 2. These references bypass the process, so calibration alone has not tested its equation.
3. Test the inherited equation
Action: probe at x = 0.5. Reading: 1. Cost: 1; 1 remains.
The corrected response is (1 + 2) / 2 = 1.5. The source equation predicts 1.25, giving a residual of 0.25. The source process no longer fits this observation.
This probe is part of a fixed two-probe recipe for the published one-coefficient-change family. The residual already narrows the candidate changes; a second probe completes this recipe. It is not claimed to be the cheapest possible strategy.
4. Identify and repair the change
Action: probe at x = 1. Reading: 0. Cost: 1; none remain.
The physical response is 1; the source predicted 0. The two residuals are therefore 0.25 and 1. If one coefficient of power k changes by Δ, its residual is Δxᵏ. The ratio 1 / 0.25 = 4 = 2² identifies the quadratic coefficient, and the residual at 1 gives Δ = +1.
The repaired equation is q(x) = 2 − 2x + 3x² − 2x³. This inference relies on the declared sparse-change, noiseless family.
5. Forecast, then reveal the outcomes
The ordinary program submits 0 or 1 for each threshold event using that equation. Those probabilities are justified here by exact identification within the stipulated family; they do not establish calibrated certainty outside it.
At x = 1.5, blind reuse predicts q = −3.25, while the repaired equation predicts q = −1. For the event q ≥ −2, their probabilities are 0 and 1 respectively. The revealed outcome is 1.
| Physical event | Adaptive probability | Blind probability | Outcome |
|---|---|---|---|
| [email protected]>=-2 | 1.0 | 1.0 | 1 |
| [email protected]>=0 | 1.0 | 1.0 | 1 |
| [email protected]>=2 | 1.0 | 1.0 | 1 |
| [email protected]>=-2 | 1.0 | 1.0 | 1 |
| [email protected]>=0 | 1.0 | 1.0 | 1 |
| [email protected]>=2 | 1.0 | 1.0 | 1 |
| [email protected]>=-2 | 1.0 | 1.0 | 1 |
| [email protected]>=0 | 1.0 | 1.0 | 1 |
| [email protected]>=2 | 0.0 | 0.0 | 0 |
| [email protected]>=-2 | 1.0 | 0.0 | 1 |
| [email protected]>=0 | 0.0 | 0.0 | 0 |
| [email protected]>=2 | 0.0 | 0.0 | 0 |
After submission, disclosure confirms target gain 2, offset −2 and coefficients [2, −2, 3, −2]. The archive's condition label was not supplied to the reference policy before forecasting.
Scores and every measurement cost
| Program | Brier loss | Target | Source | Total |
|---|---|---|---|---|
| Adaptive four-experiment reference | 0.0 | 4 | 6 | 10 |
| Blind source reuse | 0.083333 | 0 | 6 | 6 |
| Constant 0.5, no source information | 0.25 | 0 | 0 | 0 |
| Matched finite Bayesian reference (computed after completion) | 0.0 | 2 | 6 | 8 |
The adaptive program gets all twelve events right; blind reuse gets one wrong, giving 1 / 12 ≈ 0.083333. The neutral baseline is 0.25. These events share one world, so they are not twelve independent trials.
The stronger finite Bayesian reference in the downloadable report uses the same starting information and budget but its own experiment selection. Its result shows why a successful four-step tutorial does not establish optimality. No computation, model-token, money or development costs were measured.
Inspect and reproduce
Extract the ZIP, open a terminal in its folder, and use Python 3.10 or later. No package installation or model key is needed:
python scripts/verify_public_example.py PYTHONPATH=src python -m unknown_engine.transfer_report \ --input examples/worked-run/adaptive-replay.json \ --output /tmp/ue-worked-report \ --participant-label "Ordinary adaptive reference — disclosed development example"
Choose a new output directory. Scores and the canonical replay run ID should agree; an installed package version can differ. Reconstruction checks consistency, not participant identity or independent scientific validity. Read the complete study results and next research gate.