Objective function and search strategy

The physical model predicts an absolute two-band transient response. Fitting compares that response with observed total fluxes while keeping the host baseline and the selected model family explicit.

1. What is actually minimised?

F^RT includes escaping dust emission and the transmitted source term. H_b is the fixed per-band host. The likelihood uses 22 epochs in each band, with the effective errors supplied in the canonical input table. These already include the adopted additive floor, described approximately as 1.10 mJy; the solver does not add it again. The input guide distinguishes that rounded description from the exact archived error columns.

There are no additional penalties or weights for lag, width, colour, fluence, peak luminosity, flux–flux slope or late-time structure. Those are diagnostics to compare with the fitted light curves, not extra observables secretly added to the objective. The dust column and radiative transfer set the transient amplitude: W1 and W2 do not receive independent fitted normalisations.

The effective errors are treated as independent between measurements. The host values remain fixed, so their uncertainty is not part of the reported conditional parameter uncertainty. Using a different baseline, error floor or time window changes the statistical problem and must be stated explicitly.

2. Profile the event epoch

For each physical configuration, the code shifts the response relative to the observed MJD values and minimises over t₀. It scans MJD 56500–57500 at 10-day spacing, then applies bounded local minimisation around candidate minima. The implementation uses linear interpolation of the response and zero transient flux outside its support.

The best epoch is saved together with a boundary flag. A minimum near the search edge deserves investigation; it is not evidence that the event is known precisely. The archived value, t₀ = 57063.03166038865 MJD, aligns the unsmoothed fallback peak with the observation calendar. It is not a measured disruption time, optical maximum or dust-emission maximum.

3. Continuous parameters and discrete choices

The six continuously refined physical quantities are η, τ_visc, τ_C, τ_E, the opening angle and inclination. With t₀ this gives seven continuous fitted quantities. Within a local candidate, the STARS history, radial boundaries and density exponents, grain composition, size range and q are fixed.

Archived Case A has χ² = 58.95064072368716, split into 19.487984248108464 for W1 and 39.46265647557869 for W2. Quote χ² and the nominal conditional degrees of freedom separately. Selecting among discrete driver histories and geometry choices, parameter boundaries and correlations complicates a formal goodness-of-fit interpretation; subtracting seven is not a correction for the whole model-selection process.

4. Staged search, not exhaustive exploration

The retained staged workflow schedules 64 balanced configurations for each of 141 STARS histories, or 9024 initial candidates. Subsequent stages add selected configurations and refine a shortlist of up to 20 candidates. This is a finite search design, not all combinations of all continuous parameters and not a proof of a global minimum.

python -u scripts/run_v48_staged.py --workers 12

Run an expensive search only after reproducing a single case and understanding the numerical cost. The actual scheduled axes and restrictions are in configs/v48_staged_domain.json. A printed BEST χ² is the cumulative best result; an unchanged value does not mean all models have identical χ² or that the process has stopped.

A candidate marked unsupported_sublimation crosses the static-opacity temperature gate. It has not been simulated with dust destruction and must not be interpreted as a physical zero-MIR solution. Numerical failure, an unsupported physical domain and a valid but poor photometric fit are different outcomes.

5. Local refinement and stopping rules

The retained V48_PAPER_FINAL/run_parallel.py workflow uses bounded coordinate polls and saves accepted states. It expects project-specific baseline files or checkpoints and is not the public quick-start entry point. Stopping when tested coordinate steps no longer improve the objective establishes local stationarity at those steps and bounds, not uniqueness or a global optimum. Reaching an evaluation budget is a different stopping condition.

Changes in driver identity, geometry family or fixed dust prescription should be treated as comparisons between model assumptions. A similar minimum χ² for two candidates does not by itself select a unique physical interpretation, especially with only two photometric bands.

6. Conditional parameter variation and profile intervals

The later V4.8 analysis estimates approximate conditional one-parameter intervals for η, τ_visc, τ_C, τ_E, opening angle and inclination. These ranges describe parameter variation within the adopted source history, dust prescription, photometric error model and baseline numerical resolution. They are not calibrated 1σ uncertainties with demonstrated 68.3% coverage, and they do not include the full physical-model uncertainty.

For each parameter, its trial value is fixed while the other five physical parameters and the event epoch t₀ are reoptimised using an approximation to the saved radiative-transfer responses. Candidate limits near Δχ² = 1 are then checked with the direct radiative-transfer solver. In these direct checks, t₀ is reoptimised for each response; the other physical parameters remain fixed at the values selected by the response approximation. This checks the objective at the selected physical configurations, not a fully reoptimised direct-solver profile.

The adopted refined Case A direct reference has χ² = 58.83195387879388. Its twelve checked physical-parameter endpoints have Δχ² = 0.957856–1.041510, measured from this direct reference. Trial points and superseded endpoint candidates are not additional final intervals.

The Δχ² = 1 threshold has a nominal single-parameter likelihood interpretation under regular statistical assumptions. Here, the reported result is the approximate conditional range itself. The endpoint checks do not establish repeated-sampling coverage, complete nuisance-parameter minimisation with the direct solver, or convergence of interval endpoints under increased numerical resolution. A deviation of 0.042 in Δχ² is not a 4.2% accuracy statement about parameter uncertainties.

The intervals keep the selected STARS history, black-hole mass, radial geometry, grain composition and size law, host fluxes, observational-error prescription and baseline discretisation fixed. They are not joint confidence regions, posterior credible intervals, or uncertainty from selecting a different model. Numerical-resolution tests are separate from statistical coverage checks; the Case A endpoint evaluations do not certify resolution convergence of the intervals.

Computational scope. This version supports direct V4.8 radiative-transfer evaluations, response-approximation-assisted parameter exploration, fixed-configuration endpoint checks and separate numerical-resolution tests. These calculations were organised around a finite single-PC computation budget. More hardware can increase the number of independent evaluations or permit finer sampling, but it does not by itself establish profile convergence, statistical coverage or a more complete physical model. Existing historical workflows already support cache reuse and controlled parallel evaluation. Possible further development includes profiling and optimising expensive code paths, improving documentation and scaling of those mechanisms, more complete direct nuisance-parameter optimisation, and expanded numerical/coverage tests. These further improvements and validation steps have not been completed or benchmarked in this audit; no hardware requirement or performance gain has been established by a new benchmark.

Browse the refined Case A reference, its twelve checked endpoints and original profile-update scripts. For the reproducible example and the prerequisites for variation checks, follow the expanded Case A walkthrough.

7. Diagnostics are useful, but definitions matter

Light-curve moments, interband offsets, fluence ratios and colour tracks help interpret a fitted response. They depend on baseline subtraction, integration limits and treatment of sampling or negative excess. A measured W2–W1 offset is not automatically the central-source-to-dust light-travel time. A luminosity-weighted response radius is not necessarily the inner radius of either radial population.

Keep empirical diagnostics and physical-fit conventions separate. In particular, the fixed hosts used here derive from the first two NEOWISE epochs, whereas a combined AllWISE+NEOWISE baseline may appear in other empirical analyses. Comparing results without preserving those definitions can create an apparent model discrepancy that is actually a baseline or window change.

8. Numerical and physical uncertainty remain separate

The convergence checks establish that a discretised solution meets its numerical criteria. Resolution tests ask whether the result changes under refined sampling. Statistical profiles ask how parameters vary within the adopted likelihood and fixed modelling assumptions. None substitutes for the others.

The archive includes a record of a prior Case A reproduction. It does not establish completed validation of the full parameter search or every physical assumption, and this documentation expansion does not constitute a new radiative-transfer run.

Two-band data do not uniquely determine an arbitrary three-dimensional density field, a grain mixture and an unobserved illuminating history simultaneously. Report the adopted source, geometry, dust, baseline, error model and resolution alongside any inferred parameters. See Data & parameters and References for the exact inputs and provenance.