TCLab: retained exploratory comparison

Status: 2026-09-21. One bounded exploratory comparison is complete. physical_status=not_admitted; measurement_verdict=not_assessed. The user authorized an initial approximation despite unresolved physical admission. This note owns that experiment; the execution plan owns next actions and the source review owns alternative datasets. No production dynamics or defaults changed. This is a retained experiment, not an active acquisition or refitting plan. Any follow-up requires admission through that sole queue; the dated results and frozen specification below remain unchanged.

1. Question, source and physical boundary

Does a declared driven nodal model with latent heater states predict two recorded sensor temperatures better than a smaller measured-state model when both are calibrated on the same files and frozen before reserved comparison? This is a conditional model comparison, not a derivation of thermodynamics or an experiment on autonomous NFR formation. Both model families also admit a classical linear thermal-network interpretation; their comparison cannot establish a uniquely TNFR explanation.

The authors' TCLab description distinguishes heater and sensor temperatures. The data directory is pinned at d250c5b0625afb35007c075df1e0f7125e74017d; repository license is BSD-3-Clause. No author-fitted coefficients were imported. Git blob identities bind all five downloaded files (132,055 bytes total).

The historical acquisition notebook uses hardware TCLab(), nominal one-second scheduling and 900-second runs. Its active loop includes 25-minute cooldowns and sets heater-1 maximum-power configuration to 200, not 200 watts. The saved notebook does not reproduce every file: step/five-minute generation is incomplete, heater-2 settings are not assigned, and env_2 is unexplained. This supports intended hardware acquisition, not a complete per-run device/reset/calibration record.

Independent ambient temperature, command-to-watt conversion, sensor/clock uncertainty and physical repeat independence remain unverified. The model's nominal time and temperature chart do not resolve those omissions.

2. Model frozen before response inspection

EPI is provisionally represented in degrees Celsius; the declared structural clock is the recorded clock in seconds. Set a=leak rate, k=inter-heater coupling rate, c=heater-to-sensor backreaction coefficient, r=sensor response rate and g=command gain. All are positive effective coefficients, with g in degrees Celsius per second per command percentage point. They are not independently measured heat capacities or conductances.

For i=1,2 and the other assembly j, the four-state candidate is

H_i' = a*(Ta-H_i) + k*(H_j-H_i) + c*(S_i-H_i) + g*Q_i
S_i' = r*(H_i-S_i).

This follows from the selected graph realization of the extended nodal row, not from the uncompleted nodal identity alone. On support (H1,H2,S1,S2,B), use weights w(Hi,Si)=1, w(H1,H2)=k/c, w(Hi,B)=a/c; the unit edge fixes an arbitrary common conductance scale. Set nu_H=a+k+c, nu_S=r, nu_B=0, B=Ta. Then the shared isolated-EPI pressure p=-L_rw*x and explicit source Gamma_Hi=g*Qi yield the displayed equations. All other pressure channels are inactive; there are no operator events. The fixed bath and supplied heater input are premises, not emergent sources.

The smaller, three-parameter comparison is

S_i' = a*(Ta-S_i) + k*(S_j-S_i) + g*Q_i.

It is another grounded nodal graph, not a claim that the real sensor pair is a complete state. Both candidates assume exchange symmetry, linear commands, constant coefficients and a constant bath. Before each prediction set Ta to the mean of the first sensor pair and each hidden heater to its corresponding first sensor value. These are initialization approximations, not measured ambient/heater states. The entire recorded command schedule is supplied; the forecast is conditional on those inputs, with no later temperature updates.

Within the four-state model, equal current sensor readings can have different future derivatives when hidden heater temperatures differ. Eliminating the heaters therefore introduces memory/hidden-initial-state terms, consistent with the existing memory derivation. This identity does not establish that four states are the minimal physical TCLab state.

Variable contract for this approximation

This 2026-09-23 clarification applies the plan's definition/identification/evolution contract to the already frozen models. It changes neither their equations nor the reported forecasts, calibration or physical-admission status. The table details the four-state candidate. The two-state baseline retains only sensors and bath, with its separately specified rates and no heater states.

Quantity	Mathematical definition in this model	Operational identification	Prospective law / remaining premise
EPI	Real scalar temperature chart, nominal degrees Celsius, on the declared nodes	CSV T1,T2 observe sensors; heater states are hidden; the bath is an initial-sensor proxy. Independent sensor calibration, ambient and hidden initialization remain open.	The equations above evolve heaters/sensors; bath EPI is held. Initialize once, without subsequent sensor correction.
nu_f	Nonnegative rate per recorded second; heater/sensor values derive from the fitted coefficients as specified above; bath rate is zero	Calibration fits effective rates conditional on the pressure normalization and clock. It does not independently measure a physical reorganization capacity or heat capacity.	Rates are held throughout each run and shared across acquisitions; that constancy is a model premise.
DeltaNFR	Isolated EPI transport -L_rw*x, in the chosen temperature unit	Computed from the supplied graph and modeled state; hidden heater temperatures prevent direct reconstruction from the two sensors alone	Evaluate the frozen graph law on predicted states. No evaluated temperature derivative determines pressure.
Clock	Increasing recorded timestamps, nominal seconds	CSV Time; calibration, synchronization and clock uncertainty remain unverified	Left-held commands on actual recorded intervals; no fitted structural-to-physical clock correction.
Support and weights	Fixed reciprocal graph; common weight scale is a normalization convention	Chosen exchange/bath topology; absolute conductances are not measured or identified by the normalized transport fit	Graph and weights remain fixed. The node/edge realization is a constitutive approximation.
Input Gamma	Additive heater rate g*Q_i, in degrees Celsius per recorded second	Recorded percent commands and calibration-fitted gain; no independent command-to-watt conversion	Entire command schedule is conditioned on; gain is frozen. No output-dependent source correction.
Phase and history	No phase channel or additional independent history coordinate is consumed	No physical phase measurement is claimed; hidden heaters carry the model's internal state	Full-state evolution is Markovian; eliminating heaters produces the conditional memory described above.

Definitions and executable closure are specified for this approximation. Limited predictive adequacy is assessed in section 4; physical identification remains open. Resolving the table's physical gaps does not follow automatically from lowering forecast error, and the existing scored files remain inspected.

3. Split, fitting and numerical realization

Only these two named files calibrate each model:

• validation_experiment_env_2_step_50_run_2.csv;
• validation_experiment_env_2_sin_5_50_run_2.csv.

Reserve whole files step_50_run_3, sin_2_50_run_3, sin_50_50_run_3 under the same prefix. The acquisition code maps sin_50 to a 0.5-minute input, not a 50-minute period. Forecasting uses recorded commands, not inferred filename periods. Source aliases identified by the inventory are excluded. Different file identities do not prove independent physical preparations.

Fit all post-initial calibration samples of both sensors with equal residual weight. Use five parameters for the latent model, three for the smaller model, each bounded to [1e-6,1] in its declared units. These bounds are numerical search settings, not physical constants. Three initializations and a maximum of 200 evaluations per initialization were frozen before loading responses. All six fits converged without active bounds; select the minimum calibration cost separately for each model. No evaluation result selected coefficients, bounds, initial conditions, horizon, smoothing or a new model. Persistence at each initial sensor temperature is also scored as a trivial control.

The benchmark constructs its generator through structural_diffusion_operator and propagates the affine system using the shared matrix_exponential with left-held recorded commands on each actual timestamp interval. This is a detached, approximate matrix forecast, not a live engine trajectory or an exact-real interval certificate. All forecast files were saved and content-hashed before converting reserved post-initial temperatures into scored observations. Whole CSV bytes were available locally; this is not externally blinded or independently timestamped prospective acquisition. No missing rows were interpolated.

4. Observed comparison

RMSE below combines both sensors and all post-initial samples in degrees Celsius; per-channel results prevent the larger response hiding the other.

Reserved file suffix	Scored times	Four-state RMSE	Two-state RMSE	Persistence RMSE	Four-state RMSE by sensor (S1,S2)
step_50_run_3	900	1.285	1.545	22.356	(1.792, 0.303)
sin_2_50_run_3	900	2.434	3.061	21.342	(3.286, 1.023)
sin_50_50_run_3	898	2.446	2.664	20.980	(3.314, 0.994)

The latent model reduces joint RMSE by approximately 16.8%, 20.5% and 8.2% relative to the two-state baseline. Its calibration RMSE is 0.642 C versus 1.358 C. These are descriptive comparisons, not confidence intervals or an independence-adjusted significance test. The larger model has two additional fitted parameters; this experiment does not prove a universal need for memory.

An important remaining error is a positive sensor-1 bias of approximately 1.466, 2.972 and 3.025 C respectively. Sensor-2 MAE is slightly worse than the two-state baseline on both oscillatory tests, despite lower RMSE. Retain those mixed results: improvement is not uniform across metrics. Possible effects of ambient/initialization, symmetry, input conversion and omitted physics are unresolved explanations, not measured diagnoses or a license to refit.

The selected latent coefficients (a,k,c,r,g) are approximately (0.00695545,0.00275190,0.01143465,0.04570218,0.00679360). The smaller model's (a,k,g) are (0.00443295,0.00182855,0.00447633). The latent-state observability rank is 4 within its supplied model. This does not identify separately every physical primitive or establish noise-robust reconstruction. Heater 2 remained unexcited in the reserved inputs; its gain equality remains an untested symmetry premise.

An independent SciPy matrix-exponential propagation differs from the retained predictions by at most 7.4e-13 C across both models/all reserved runs. Thus this solver comparison does not explain the degree-scale residuals; it is not a rigorous error bound or sensor calibration. The synthetic tests cover analytic and independent ODE solutions, input boundaries, duplicate splits, exclusion of future responses and an actual weighted-pressure/Gamma/shared-integrator step. All 26 checks passed.

5. Evidence and next decision

The local retained bundle is artifacts/research/tclab_exploration_2026_09_21/: original source files, frozen specification, executed benchmark snapshot, calibration, issued forecasts, scores and numerical check. The inspected six-panel plot is reserved_comparison.png (also SVG). These are ignored local artifacts, not a published independently audited evidence bundle.

• Dataset revision: d250c5b0625afb35007c075df1e0f7125e74017d.
• Engine base: f27413a0a29dddc132e5aafea081b0caee0b0135; dirty source hash sha256:da7c03dbb402ae560b5fdd0bd8d039836b4b620fde83e79befdcae2e710e2be6.
• Python 3.13.6, NumPy 2.5.3, SciPy 1.18.1; deterministic fixed starts, no RNG.
• Raw specification SHA-256: b8582e565b5523a864a3fa69f2e029c5a0fd8abe500c61990d9b1a367b458b55. The pre-data console hash c271ba2f... identified logical LF text; Windows saved CRLF. Both retained raw specification copies agree; no policy changed.
• Forecast hash: sha256:c0d8219f925ada27b2b79f316ef0e9961afa19a57fb270297aaab15579536299.

The implementation corrected a capacity attribute and CSV admission before calibration; later graph metadata/formatting changes do not alter the matrices or retained forecasts. Replaying into a fresh directory is permitted but does not create new reserved evidence:

python benchmarks/tclab_nodal_exploration.py --spec artifacts/research/tclab_exploration_2026_09_21/spec_before_responses.json --data artifacts/research/tclab_exploration_2026_09_21/data --output artifacts/research/tclab_exploration_2026_09_21/replay

The useful conclusion is that a specified nodal transport/input model transfers some response structure across these files, and the latent version improves the predeclared quadratic metric. Physical admission and the stronger TNFR ontology remain open. If the sole plan admits another comparison, establish independently which initialization/ambient/input premises can be supported and declare any model revision explicitly. Preserve the present residuals; these three runs are now inspected and cannot serve as fresh reserved tests for that revision.