Thermal Observability Limits in Reconstructing Full Thermogravimetric Curves from Partial Measurements

<jats:p>Reconstructing the unmeasured part of a thermogravimetric (TG) curve could support adaptive measurement, but low mass-path error is useful only when the available observations also identify terminal residue and derivative thermogravimetric (DTG) events. We evaluated this information requirement using open numerical TGA data while keeping curves, material groups, and studies intact. Development comprised 40 inert-atmosphere curves in 10 groups from four studies. A held-out CC BY 4.0 Chilean Oak study supplied 20 curves in five groups for rule-frozen external validation; one Eucalyptus curve was retained only as stress evidence. The observation design crossed four prefixes, five isolated 100 °C windows, and uniform or training-only variance-greedy sets of 4, 8, or 16 measurements. Strong physical and functional baselines were selected inside group-held-out folds, projected to monotone mass paths, and evaluated under leave-one-curve-out, leave-one-group-out, leave-one-study-out, and external-study tests. Success jointly required hidden TG error, terminal-residue accuracy, DTG detection and location, multi-event F1, physical validity, calibrated uncertainty, and non-abstained coverage. No observation-model cell passed the complete joint gate in all four development studies and the external study. Nevertheless, native-protocol observability ranking transferred strongly to the external study (Spearman rho = 0.943 across 14 common cells), and the non-worsening 4-to-8-to-16 uniform sparse-budget order reproduced in all five cohort studies. The no-joint-pass boundary persisted in all 243 locked threshold combinations. Early-prefix conditions produced 932 foldwise collisions at the 1-percentage-point observed/10-percentage-point hidden definition, with a mean observed-neighbor-to-oracle gap of 5.16 percentage points. Conversely, 343 curve-condition predictions achieved hidden TG RMSE at or below 10 percentage points but failed the joint event-aware gate. No training-only abstention threshold met accuracy, event, calibration, width, and coverage requirements; the resulting external policy abstained throughout. Partial TGA observability is therefore task dependent. Sparse measurements distributed across the protocol can reconstruct the mass path accurately, but do not necessarily recover DTG events, while early prefixes remain empirically non-identifying across studies. The supported output is a bounded thermal-observability map and an abstention boundary, not a universal full-curve predictor or an experimental early-stopping rule.</jats:p>