SCIENCE · INVESTIGATE AND EXPLAIN

Defend a constrained design choice with evidence

Connect requirements, alternatives and limits in a reviewable decision brief.

Learning outcome: Justify a candidate under stated priorities while retaining failed scenarios and separating local model evidence from wider claims.

Starting recap

Feasibility precedes preference; a nondominated choice is not a universal best design.

All lessons are open directly. Your saved experiments remain when you leave and return.

Try

Nominal standard gain 2 uses 1821.035 J at 3 tokens; insulated gain 12 uses 1515.221 J at 5 tokens.

Open the experiment

Predict

Predict whether a nominal lower-energy choice can justify a claim that it is robust across all four scenarios.

Your prediction and reason

Experiment

Capture a baseline and two alternatives under the same nominal conditions, state a preference rule, then inspect the chosen candidate across all scenarios without changing its correction. Write a claim/evidence/limit table.

Compare failures and constrained design tradeoffs

Worked teaching model · synthetic values · Twelve fixed candidates and four public deterministic cases reuse engineering-device-v1. Keep hardware, gain and correction fixed across each four-case suite. Case pass counts are coverage of supplied conditions, not field reliability, probabilities, independent trials or physical validation. Feasibility requires every supplied criterion; energy and assigned token cost are separate conditional objectives. An empty robust feasible set is a supported result, not permission to relax requirements silently.

Fixed candidate: gain, hardware and correction: Gain 2 W/K; Standard enclosure; subtract 0 degC sensor correction Scenario for conditional tradeoffs: Nominal

Reset keeps your prediction, captures and practice history.

Keep the candidate fixed while changing the test condition

1: gain 2 W/K · Standard enclosure · subtract 0°C. Each matrix row retains one gain, hardware and subtracted correction across all four public scenarios. The selected detail scenario is Nominal. Changing the scenario selector inspects a different condition; it does not retune this candidate.

These are 48 deterministic model combinations, not 48 manufactured devices or independent trials. Passing a fraction of these four selected cases describes only this public suite; it is not a field reliability probability. All outcomes are development evidence with known public exposure.

Compare all twelve candidates across four scenarios

Every supplied criterion is retained. A cell passes only when all four pass.
Fixed candidate	Nominal	Two-sample delay (20 s)	Sensor offset +2 degC	Heater limited to 8 W	Cases meeting all criteria
1: gain 2 W/K · Standard enclosure · subtract 0°C (selected)	Tail 29–31°C at 90–120 s: pass Peak ≤32°C: pass Input ≤2000 J: pass Cost ≤6 tokens: pass	Tail 29–31°C at 90–120 s: pass Peak ≤32°C: pass Input ≤2000 J: pass Cost ≤6 tokens: pass	Tail 29–31°C at 90–120 s: fail Peak ≤32°C: pass Input ≤2000 J: pass Cost ≤6 tokens: pass	Tail 29–31°C at 90–120 s: fail Peak ≤32°C: pass Input ≤2000 J: pass Cost ≤6 tokens: pass	2 / 4 Not feasible across all four
2: gain 2 W/K · Standard enclosure · subtract 2°C	Tail 29–31°C at 90–120 s: fail Peak ≤32°C: pass Input ≤2000 J: fail Cost ≤6 tokens: pass	Tail 29–31°C at 90–120 s: fail Peak ≤32°C: pass Input ≤2000 J: fail Cost ≤6 tokens: pass	Tail 29–31°C at 90–120 s: pass Peak ≤32°C: pass Input ≤2000 J: pass Cost ≤6 tokens: pass	Tail 29–31°C at 90–120 s: fail Peak ≤32°C: pass Input ≤2000 J: pass Cost ≤6 tokens: pass	1 / 4 Not feasible across all four
3: gain 2 W/K · Insulated enclosure · subtract 0°C	Tail 29–31°C at 90–120 s: fail Peak ≤32°C: pass Input ≤2000 J: pass Cost ≤6 tokens: pass	Tail 29–31°C at 90–120 s: fail Peak ≤32°C: fail Input ≤2000 J: pass Cost ≤6 tokens: pass	Tail 29–31°C at 90–120 s: pass Peak ≤32°C: pass Input ≤2000 J: pass Cost ≤6 tokens: pass	Tail 29–31°C at 90–120 s: fail Peak ≤32°C: pass Input ≤2000 J: pass Cost ≤6 tokens: pass	1 / 4 Not feasible across all four
4: gain 2 W/K · Insulated enclosure · subtract 2°C	Tail 29–31°C at 90–120 s: fail Peak ≤32°C: fail Input ≤2000 J: pass Cost ≤6 tokens: pass	Tail 29–31°C at 90–120 s: fail Peak ≤32°C: fail Input ≤2000 J: pass Cost ≤6 tokens: pass	Tail 29–31°C at 90–120 s: fail Peak ≤32°C: pass Input ≤2000 J: pass Cost ≤6 tokens: pass	Tail 29–31°C at 90–120 s: fail Peak ≤32°C: pass Input ≤2000 J: pass Cost ≤6 tokens: pass	0 / 4 Not feasible across all four
5: gain 6 W/K · Standard enclosure · subtract 0°C	Tail 29–31°C at 90–120 s: pass Peak ≤32°C: pass Input ≤2000 J: pass Cost ≤6 tokens: pass	Tail 29–31°C at 90–120 s: fail Peak ≤32°C: pass Input ≤2000 J: pass Cost ≤6 tokens: pass	Tail 29–31°C at 90–120 s: fail Peak ≤32°C: pass Input ≤2000 J: pass Cost ≤6 tokens: pass	Tail 29–31°C at 90–120 s: fail Peak ≤32°C: pass Input ≤2000 J: pass Cost ≤6 tokens: pass	1 / 4 Not feasible across all four
6: gain 6 W/K · Standard enclosure · subtract 2°C	Tail 29–31°C at 90–120 s: fail Peak ≤32°C: pass Input ≤2000 J: fail Cost ≤6 tokens: pass	Tail 29–31°C at 90–120 s: fail Peak ≤32°C: fail Input ≤2000 J: fail Cost ≤6 tokens: pass	Tail 29–31°C at 90–120 s: pass Peak ≤32°C: pass Input ≤2000 J: pass Cost ≤6 tokens: pass	Tail 29–31°C at 90–120 s: fail Peak ≤32°C: pass Input ≤2000 J: pass Cost ≤6 tokens: pass	1 / 4 Not feasible across all four
7: gain 6 W/K · Insulated enclosure · subtract 0°C	Tail 29–31°C at 90–120 s: pass Peak ≤32°C: pass Input ≤2000 J: pass Cost ≤6 tokens: pass	Tail 29–31°C at 90–120 s: fail Peak ≤32°C: fail Input ≤2000 J: pass Cost ≤6 tokens: pass	Tail 29–31°C at 90–120 s: fail Peak ≤32°C: pass Input ≤2000 J: pass Cost ≤6 tokens: pass	Tail 29–31°C at 90–120 s: fail Peak ≤32°C: pass Input ≤2000 J: pass Cost ≤6 tokens: pass	1 / 4 Not feasible across all four
8: gain 6 W/K · Insulated enclosure · subtract 2°C	Tail 29–31°C at 90–120 s: fail Peak ≤32°C: fail Input ≤2000 J: pass Cost ≤6 tokens: pass	Tail 29–31°C at 90–120 s: fail Peak ≤32°C: fail Input ≤2000 J: pass Cost ≤6 tokens: pass	Tail 29–31°C at 90–120 s: pass Peak ≤32°C: pass Input ≤2000 J: pass Cost ≤6 tokens: pass	Tail 29–31°C at 90–120 s: fail Peak ≤32°C: pass Input ≤2000 J: pass Cost ≤6 tokens: pass	1 / 4 Not feasible across all four
9: gain 12 W/K · Standard enclosure · subtract 0°C	Tail 29–31°C at 90–120 s: pass Peak ≤32°C: pass Input ≤2000 J: pass Cost ≤6 tokens: pass	Tail 29–31°C at 90–120 s: fail Peak ≤32°C: pass Input ≤2000 J: pass Cost ≤6 tokens: pass	Tail 29–31°C at 90–120 s: fail Peak ≤32°C: pass Input ≤2000 J: pass Cost ≤6 tokens: pass	Tail 29–31°C at 90–120 s: fail Peak ≤32°C: pass Input ≤2000 J: pass Cost ≤6 tokens: pass	1 / 4 Not feasible across all four
10: gain 12 W/K · Standard enclosure · subtract 2°C	Tail 29–31°C at 90–120 s: fail Peak ≤32°C: pass Input ≤2000 J: fail Cost ≤6 tokens: pass	Tail 29–31°C at 90–120 s: fail Peak ≤32°C: fail Input ≤2000 J: fail Cost ≤6 tokens: pass	Tail 29–31°C at 90–120 s: pass Peak ≤32°C: pass Input ≤2000 J: pass Cost ≤6 tokens: pass	Tail 29–31°C at 90–120 s: fail Peak ≤32°C: pass Input ≤2000 J: pass Cost ≤6 tokens: pass	1 / 4 Not feasible across all four
11: gain 12 W/K · Insulated enclosure · subtract 0°C	Tail 29–31°C at 90–120 s: pass Peak ≤32°C: pass Input ≤2000 J: pass Cost ≤6 tokens: pass	Tail 29–31°C at 90–120 s: fail Peak ≤32°C: fail Input ≤2000 J: pass Cost ≤6 tokens: pass	Tail 29–31°C at 90–120 s: fail Peak ≤32°C: pass Input ≤2000 J: pass Cost ≤6 tokens: pass	Tail 29–31°C at 90–120 s: fail Peak ≤32°C: pass Input ≤2000 J: pass Cost ≤6 tokens: pass	1 / 4 Not feasible across all four
12: gain 12 W/K · Insulated enclosure · subtract 2°C	Tail 29–31°C at 90–120 s: fail Peak ≤32°C: fail Input ≤2000 J: pass Cost ≤6 tokens: pass	Tail 29–31°C at 90–120 s: fail Peak ≤32°C: fail Input ≤2000 J: pass Cost ≤6 tokens: pass	Tail 29–31°C at 90–120 s: pass Peak ≤32°C: pass Input ≤2000 J: pass Cost ≤6 tokens: pass	Tail 29–31°C at 90–120 s: fail Peak ≤32°C: pass Input ≤2000 J: pass Cost ≤6 tokens: pass	1 / 4 Not feasible across all four

No candidate meets all four scenarios in this finite suite. In particular, the 8 W case fails the finite-time tail requirement even for insulated hardware. Its constant-input equilibrium is 20 + 8/0.5 = 36°C, but its 200 s time constant means the 20°C start reaches only about 27.219°C after 120 s. This is a finite-time service failure, not proof that insulation makes 29°C permanently unreachable. Standard hardware instead has an 8 W equilibrium of 28°C.

Selected candidate: separate requirements in each condition

Same candidate, same initial temperature and 120 s horizon; scenario changes are explicit
Scenario	Tail samples at 90, 100, 110, 120 s (°C)	Peak (°C)	Applied input (J)	Assigned cost	All criteria
Nominal	29.359, 29.542, 29.673, 29.766 Pass	29.766 at 120 s Pass	1821.035 Pass	3 tokens Pass	Pass
Two-sample delay (20 s)	30.341, 30.359, 30.294, 30.201 Pass	30.359 at 100 s Pass	1922.517 Pass	3 tokens Pass	Pass
Sensor offset +2 degC	28.187, 28.324, 28.422, 28.492 Fail	28.492 at 120 s Pass	1607.588 Pass	3 tokens Pass	Fail
Heater limited to 8 W	24.747, 25.057, 25.337, 25.590 Fail	25.590 at 120 s Pass	960.000 Pass	3 tokens Pass	Fail

Temperature judgments use full precision, not rounded display values. Held-input exact one-node intervals are monotonic toward their interval equilibria, so endpoint samples bound their peaks and the intervening tail temperatures here. This is not a general claim about physical temperature fields. A passing energy budget cannot compensate for a failed temperature requirement.

Cost and input energy within one feasible scenario

For Nominal, feasible means meeting all four supplied requirements. The comparison then minimizes only assigned token cost and applied heater energy. A candidate is nondominated if no other feasible candidate is no worse on both and strictly better on at least one. Equal pairs do not dominate each other. This conditional comparison excludes other priorities and is not a universal best design.

Feasible candidates only · fixed axes: cost 3–5 tokens, input 0–2400 J

Circles: feasible pairs. Outer squares: nondominated pairs. Identical or nearby points can overlap; the table retains every candidate. Points outside the fixed scale are omitted with a notice, never moved onto the boundary.

Nominal: retain rejected candidates and their failed criteria alongside the feasible comparison
Candidate	Cost (tokens)	Applied input (J)	Failed criteria	Cost–energy status
1: gain 2 W/K · Standard enclosure · subtract 0°C	3	1821.035488	None	Feasible and nondominated
2: gain 2 W/K · Standard enclosure · subtract 2°C	3	2012.930200	Tail 29–31°C at 90–120 s; Input ≤2000 J	Excluded: infeasible
3: gain 2 W/K · Insulated enclosure · subtract 0°C	5	1624.624719	Tail 29–31°C at 90–120 s	Excluded: infeasible
4: gain 2 W/K · Insulated enclosure · subtract 2°C	5	1809.091605	Tail 29–31°C at 90–120 s; Peak ≤32°C	Excluded: infeasible
5: gain 6 W/K · Standard enclosure · subtract 0°C	3	1887.808894	None	Feasible, dominated on cost/energy
6: gain 6 W/K · Standard enclosure · subtract 2°C	3	2130.915020	Tail 29–31°C at 90–120 s; Input ≤2000 J	Excluded: infeasible
7: gain 6 W/K · Insulated enclosure · subtract 0°C	5	1558.581071	None	Feasible, dominated on cost/energy
8: gain 6 W/K · Insulated enclosure · subtract 2°C	5	1790.699641	Tail 29–31°C at 90–120 s; Peak ≤32°C	Excluded: infeasible
9: gain 12 W/K · Standard enclosure · subtract 0°C	3	1893.370525	None	Feasible, dominated on cost/energy
10: gain 12 W/K · Standard enclosure · subtract 2°C	3	2153.177644	Tail 29–31°C at 90–120 s; Input ≤2000 J	Excluded: infeasible
11: gain 12 W/K · Insulated enclosure · subtract 0°C	5	1515.220813	None	Feasible and nondominated
12: gain 12 W/K · Insulated enclosure · subtract 2°C	5	1757.975786	Tail 29–31°C at 90–120 s; Peak ≤32°C	Excluded: infeasible

Selected run: all thirteen true states

1: gain 2 W/K · Standard enclosure · subtract 0°C · Nominal
Time (s)	True temperature (°C)
0	20.000000
10	21.903252
20	23.625385
30	25.183636
40	26.558649
50	27.541112
60	28.243095
70	28.744670
80	29.103051
90	29.359119
100	29.542083
110	29.672812
120	29.766220

Selected run: all twelve observation, command and energy receipts

Commands occur at 0–110 s; 120 s is the final state, not a new observation command. The delayed scenario requests t − 20 s. Negative requested times use the held initial state at effective time 0, not a measured prehistory. Raw indication adds the scenario bias to the selected true observation; corrected indication subtracts the candidate correction of 0°C. A nonzero correction is not automatically appropriate in an unbiased scenario.

Held input for each 10 s interval; positive ambient energy is outward
Step / interval (s)	True start → end (°C)	Requested / effective observation (s)	Raw / subtracted correction / corrected (°C)	Error (K)	Requested / applied (W)	Clipping	Input (J)	Stored change (J)	To ambient (J)	Residual (J)
0: 0–10	20.000000 → 21.903252	0 / 0	20.000000 / 0 / 20.000000	10.000000	30.000000 / 20.000000	Upper	200.000000	190.325164	9.674836	0.00e+0
1: 10–20	21.903252 → 23.625385	10 / 10	21.903252 / 0 / 21.903252	8.096748	26.193497 / 20.000000	Upper	200.000000	172.213330	27.786670	0.00e+0
2: 20–30	23.625385 → 25.183636	20 / 20	23.625385 / 0 / 23.625385	6.374615	22.749230 / 20.000000	Upper	200.000000	155.825065	44.174935	0.00e+0
3: 30–40	25.183636 → 26.558649	30 / 30	25.183636 / 0 / 25.183636	4.816364	19.632729 / 19.632729	None	196.327288	137.501302	58.825986	0.00e+0
4: 40–50	26.558649 → 27.541112	40 / 40	26.558649 / 0 / 26.558649	3.441351	16.882703 / 16.882703	None	168.827028	98.246365	70.580663	0.00e+0
5: 50–60	27.541112 → 28.243095	50 / 50	27.541112 / 0 / 27.541112	2.458888	14.917775 / 14.917775	None	149.177755	70.198232	78.979523	0.00e+0
6: 60–70	28.243095 → 28.744670	60 / 60	28.243095 / 0 / 28.243095	1.756905	13.513811 / 13.513811	None	135.138108	50.157497	84.980612	0.00e+0
7: 70–80	28.744670 → 29.103051	70 / 70	28.744670 / 0 / 28.744670	1.255330	12.510661 / 12.510661	None	125.106609	35.838146	89.268463	0.00e+0
8: 80–90	29.103051 → 29.359119	80 / 80	29.103051 / 0 / 29.103051	0.896949	11.793898 / 11.793898	None	117.938980	25.606795	92.332185	0.00e+0
9: 90–100	29.359119 → 29.542083	90 / 90	29.359119 / 0 / 29.359119	0.640881	11.281762 / 11.281762	None	112.817621	18.296369	94.521252	0.00e+0
10: 100–110	29.542083 → 29.672812	100 / 100	29.542083 / 0 / 29.542083	0.457917	10.915835 / 10.915835	None	109.158347	13.072980	96.085368	0.00e+0
11: 110–120	29.672812 → 29.766220	110 / 110	29.672812 / 0 / 29.672812	0.327188	10.654375 / 10.654375	None	106.543751	9.340804	97.202947	0.00e+0

Whole-run balance: 1821.035488 J applied input = 976.622047 J stored change + 844.413440 J signed ambient transfer. Residual -3.41e-13 J. Display rounding can create a small apparent discrepancy.

Original fictional one-node device and assigned costs. Uniform temperature, constant heat capacity/conductance/ambient, held heater input and exact exponential propagation within each sample. No spatial gradient, evaporation, radiation law, random noise, active cooling, integral control or physical safety/efficiency/reliability certification. Public cases are exposed teaching practice. The 2000 J requirement is an acceptance criterion, not an automatic cutoff. Token cost is fictional; heater input is not a measured wall-plug consumption. No averaging of these indicators repairs a failed requirement.

Your investigation: predict the scenarios a fixed candidate will fail, inspect its receipts and retain a failure explanation. Compare a second candidate without changing the criteria. Explain one tradeoff and one condition outside this finite public suite before recommending a design.

Selected fixed candidate meets all criteria in 2 of 4 supplied public cases. Nominal: all requirements met.

Selected case: 1821.035 J applied heater energy; 3 assigned tokens. 5 feasible candidates in this scenario; 2 nondominated on cost and energy. This case count is not field reliability. Changing correction between scenarios would define different candidates.

Observation to attach to a capture

Captures preserve recipes and replay their calculated results. They are synthetic model evidence, not physical measurements.

Understand

Lead with a claim whose conditions are visible

An engineering argument connects a decision with requirements, comparisons and limits. “This design is best” conceals the question being answered. A stronger claim names the scenario and preference: “Among the nominal candidates that meet every supplied criterion, this option uses the least modeled heater energy, at a higher token cost.” It leaves room to identify where that choice fails.

Start with the suite’s fixed requirements: tail samples from 90 through 120 seconds in 29–31°C, peak no higher than 32°C, input energy no more than 2,000 J and cost no more than six fictional tokens. Write your priority among feasible candidates before choosing one. A priority is a decision rule, not another observed property of the device.

Build a baseline and two alternatives

Use standard hardware, gain 6 and zero correction as a nominal baseline. Capture it, then compare standard gain 2, zero correction and insulated gain 12, zero correction under the same nominal conditions. Keep all runs at the same 20°C start, ambient and 120-second horizon. Record cost, energy, tail compliance and peak separately.

The baseline uses approximately 1,887.809 J at three tokens. Standard gain 2 uses 1,821.035 J at the same cost while still satisfying the nominal criteria. Insulated gain 12 uses 1,515.221 J at five tokens. The latter saves about 305.815 J relative to standard gain 2 while adding two fictional tokens. Neither of those two choices improves both cost and energy relative to the other.

If you choose minimum tokens, explain why you prefer the feasible three-token option. If you choose minimum input energy, explain the additional token allowance. Do not turn the assigned costs into a currency estimate or claim that the input-energy difference measures lifecycle environmental benefit. The widget contains no manufacturing, disposal or grid-emissions inventory.

Test the scope of the claim

Inspect the selected candidate across all four scenarios without changing its gain, hardware or correction. Standard gain 2, zero correction passes nominal and delayed operation but fails offset and limited operation. No candidate passes all four supplied scenarios. A defensible report must preserve those failures even if the decision is restricted to nominal operation.

Distinguish three statements: the requirement passed, the mechanism explains why, and the choice suits an intended use. The first follows from the bounded model calculation. The mechanism requires assumptions and comparison with alternatives. Suitability for an actual intended use needs evidence outside this synthetic suite. NASA’s product-realization guidance distinguishes verification of requirements from validation for intended use; this course does not confer either physical certification or NASA process compliance.

Connect the local device to a wider problem carefully

A local heater can illustrate resource tradeoffs relevant to wider energy use. Explain that connection without pretending a 120-second fictional enclosure represents a building, factory or community. Scaling requires evidence about duty cycles, numbers of devices, boundary conditions, service needs and upstream impacts. Reduced input during one modeled run is not by itself a societal emissions estimate.

Make a three-column table: claim, supporting evidence, limitation or alternative. For a cool endpoint, compare sensor bias with insufficient actuator capacity. The public scenarios give separate examples of each; an actual unexplained device would need discriminating measurements. For a preferred nominal candidate, list a worsened indicator and the conditions under which your recommendation should be reconsidered. Return to design tradeoffs if feasibility and preference are being mixed.

Transfer: repair an overextended recommendation

A paper recommendation reads, “The insulated gain-12 candidate is environmentally superior because it uses 1,515.221 J and therefore must work reliably everywhere.” Identify two unsupported parts and rewrite a bounded claim. Keep the actual modeled number rather than discarding inconvenient detail.

Check the bounded-claim transfer

The suite supplies neither a lifecycle environmental comparison nor operation in every environment. A bounded revision is: “Under the nominal model and stated criteria, insulated gain 12 with zero correction is the lowest-input-energy feasible candidate, using about 1,515.221 J at five fictional tokens. Other scenarios and actual environmental impacts require separate evidence.” Preserve its failed cases and the chosen cost-energy priority. The public rewritten example is guidance, not an independent evaluation of a learner's report.

Finish a short decision brief containing the question, criteria, baseline, two alternatives, selected priority, evidence, failure and next measurement. This lesson prepares project evidence without requiring a project interface to be available. Continue to review and revision to evaluate the reasoning rather than rewarding its length or presentation.

Apply

Public practice checks a specific claim. It does not establish independent mastery.

Identify an alternative explanation, a worsened indicator and the additional evidence needed to connect the local model to a wider energy-use problem.

Your explanation and limitations

Continue

Completion requires a saved prediction, at least one capture and a reflection. Presence checks do not grade your reasoning.

Skipping retains experiments and awards no mastery.

Previous: Make a result reproducible from its evidence Next: Revise reasoning without erasing the first attempt

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