SCIENCE · INVESTIGATE AND EXPLAIN

Plan evidence for an unfamiliar failure

Use a new paper condition to identify model limits before retuning a candidate.

Learning outcome: Prepare a discriminating investigation and distinguish public suite development from human-reviewed unfamiliar transfer.

Starting recap

The suite exposes public model cases; selecting one does not create a sealed or immutable final assignment.

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

Try

An insulated device limited to 8 W approaches 36°C at constant input but reaches only about 27.219°C by 120 s.

Open the experiment

Predict

Predict whether missing a finite-time requirement necessarily means the target is permanently unreachable.

Your prediction and reason

Experiment

Keep one candidate fixed across its public suite and record a pre-result plan for the separate paper sensor packet. State hypotheses, requested reference checks and what evidence would invalidate the assumed correction.

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

A new label is not an unfamiliar investigation

The suite exposes all twelve candidates and all four scenarios. Capturing a recipe, changing the scenario selector or reopening a row does not create a sealed test. These are public development comparisons. Use them to practice identifying failures and planning measurements, while preserving what you already know.

Before inspecting a chosen row, write a prediction and a method in your working notes. Keep gain, hardware and correction fixed when describing the selected candidate’s four-scenario performance. If you have already seen the output, say so. The current ordinary captures retain recipes and notes; they are not an immutable project submission binding a human-assigned unfamiliar case. That separate review workflow belongs to the cumulative project.

Diagnose the meaning of a missed deadline

A low final temperature can arise from different constraints. Standard hardware limited to 8 W has G = 1 W/K and ambient 20°C. Its constant-input equilibrium is 20 + 8/1 = 28°C, below the required 29°C lower boundary. Starting at 20°C, it cannot reach that boundary under the stated constant maximum input.

Insulated hardware has G = 0.5 W/K and the same 100 J/K capacity. Its maximum-input equilibrium is 36°C, but its time constant C/G is 200 seconds. After 120 seconds at 8 W, its temperature is 20 + 16[1 − exp(−120/200)] ≈ 27.219°C. It misses the deadline even though the long-time limit is above 29°C.

On paper, the constant-input insulated case would first reach 29°C when exp(−t/200) = 7/16, giving t = 200 ln(16/7) ≈ 165.34 seconds. This is outside the widget’s 120-second horizon. It is a held-input calculation, not a claim that the controller was simulated for longer or that every later criterion would pass. Record which part of a conclusion follows from the time-dependent calculation and which would need new evidence.

Prepare a discriminating plan for a new sensor packet

Suppose a human supplies a separate hypothetical instrument packet: exact reference temperatures 20, 30 and 40°C give indicated readings 22, 33 and 44°C. Before reading the worked answer below, state at least two explanations and a useful next check. Could one constant correction account for the data, or might the scale be wrong? Identify the units and preserve the raw reference/indication pairs.

The existing suite allows corrections of zero or two degrees. Do not force this new packet into that limited choice and then call the residual a heater failure. A model can be inadequate for the new condition, and identifying that inadequacy is a meaningful transfer outcome. NIST’s traceability guidance supports documenting the reference relationship and its limitations; these exact paper pairs are not an actual calibration certificate.

Transfer: test the constant-offset explanation

Calculate each indication minus reference. Predict what subtracting two degrees would do at the 40°C reference, then propose a relation consistent with all three supplied pairs. State what extra evidence is needed before adopting that relation for other temperatures.

Check the unfamiliar-sensor transfer

The differences are 2, 3 and 4°C, so one additive offset does not fit. Subtracting 2 from 44 leaves 42°C, still 2°C above the 40°C reference. The supplied exact pairs are consistent with indication = 1.1 × reference for this Celsius-based paper mapping; dividing by 1.1 fits them. This is an empirical mapping between the stated scale readings, not a claim that absolute thermodynamic temperature is multiplied that way. Additional reference points, uncertainty and stability checks are needed before generalizing. The packet is public practice, not an unseen assessment.

Describe what a genuine transfer handoff needs

A human-assigned unfamiliar case should identify the device boundary, conditions, available measurements, uncertainties, resource limits and question to answer. Record assignment identity, prior familiarity and assistance before submitting the response. If evidence is insufficient to distinguish mechanisms, explain which additional observation would help instead of inventing a fault or outcome.

Tuning after seeing the new result makes subsequent runs development evidence. Keep the first prediction and failed reasoning available for review. NASA’s verification and validation guidance helps distinguish checking specified behavior from establishing suitability for intended use. Neither the public matrix nor these paper packets establishes physical prototype proficiency or independent mastery.

Return to diagnosis limits for competing explanations or failure logs for a reproducible record. The aim is an evidence-seeking plan that can recognize when its current model is insufficient.

Apply

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

Explain how human assignment identity, help and exposure should accompany future reviewed transfer without claiming that the present captures provide that workflow.

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: Compare feasible designs before ranking preferences Next: Make a result reproducible from its evidence

Save a science backup or import one

Science work is stored locally in this browser, separately from mathematics and AI. It does not sync automatically. Use this science-only backup; this checkout's older all-subject export does not include science.

A legacy file is available only when the complete snapshot fits the 36 MB limit. For larger snapshots, prepare a complete file set below; never discard notebooks to make a smaller file.

Choose a science backup (maximum 36 MB)

Matching imported notebook drafts replace their current drafts. Omitted lessons and known first attempts remain. Export your current work first if you want to retain both drafts.

Complete file sets and course backups

A file set can hold more work than one science file. Keep its manifest and every part together. Each file is limited to 36 MB. This format needs this version of LearnAI or a compatible newer version; older versions can use only the legacy single-file backup above.

Export scope

The set includes every saved science course and global continuation at this moment. Later edits need a new export. A conflicting tab exports its own visible work, which may differ from saved work in another tab.

Choose the manifest and all parts together

0 file(s) selected. File order and filenames do not determine identity. Missing, changed or conflicting parts block the entire restore; no good part is applied by itself.

Science storage: loading. No account or remote computation is required.