[Montana]

Part of #961: lifts the item "A function that reads the time and that nothing in the dynamics reads" (minutes := time/60, BIOMD0000000498, 739, 951, and a time-indexed table nothing reads).

What was refused

#710 refuses steady_state() for any model where some function reads the time (NetworkModel.functions_use_time, one flag for the whole function block). A function that only reports, like minutes := time/60, doesn't touch f(y), so the state those models settle to was refused for no reason. On main:

BIOMD0000000739: SimulationError: steady_state() is not supported for this model: it reads the time ...

The same happens for seen() = 2*time() beside A -> B at k (the existing test test_a_reported_function_that_reads_the_time_is_refused).

The change

Core:

• RateDeps (the dependency walk behind reaction_rate_reads_time) gains a clock flag. It is set by time and by a time-indexed table, and not by a rateOf, which reads the running derivatives (0 at a steady state).
• NetworkModel::rate_laws_read_clock(): does any reaction's rate read the clock.
• NetworkModel::functions_reading_clock(): which functions' values move with the clock, through other functions and derived parameters (via expression_support).
• find_steady_state refuses on rate_laws_read_clock() in place of functions_use_time(). In its result, each clock-reading function's value and output-sensitivity row are NaN: what was read is its value at t = 0, and it has no steady value.
• Both predicates are bound, and added to the stub.

Python (_raise_if_no_steady_state_to_solve_for and the new _ss_reads_the_time): still refuses when the time reaches what is reported as a state:

• a rate law;
• a rule an assignment-rule species is reported through (S := B*(1 - exp(-time)), via _ar_report_map);
• a compartment size (C := 1 + time/(1+time), via compartment_size_params).

Otherwise the state is solved for.

Reporting: SteadyStateResult records the clock-reading functions, and output_sensitivities("expression:seen") refuses by that reason ("it reads the time, so it has no steady value ... issue #961") instead of "its value is nan".

Unchanged: the early stop of run(steady_state=True) (the next #961 item), which still uses functions_use_time.

Tests

In test_steady_state_of_a_model_that_reads_time.py, #710's file:

• Changed: test_a_reported_function_that_reads_the_time_is_refused becomes ..._only_reports_is_nan, under integration and newton. It checks the state is [0, 1], seen is NaN, and kt is 1.
• New:
  • the sensitivity row is NaN while the state's column is right, and output_sensitivities refuses with the reason;
  • a batch;
  • a function reading the clock only through another;
  • a time-indexed table that only reports;
  • an SBML minutes := time/60 (A, B = 1/3, 2/3);
  • the core solver directly.
• Kept and passing: every steady_state() and steady_state_batch() evaluate f(0, y) for every convergence, Newton and sensitivity step, and their march never fires events. Time-dependent models and models with events report converged=True at a state the dynamics... #710 refusal (a rate on the time, directly, nested, in a later reaction, through a table, bare time, in SBML; an assignment-rule species on the time; a compartment sized on the time; events; size jumps), and the rateOf control.

Mutation tests (the core rebuilt for each C++ mutant): all 10 are killed.

mutant	killed by
core gate back to functions_use_time	the lifted tests
no NaN for the value	7 tests
no NaN for the sensitivity row	the sensitivity test
rateOf counted as the clock	the rateOf control
rates never read the clock	the 7 "a rate reads the time" tests
clock functions not followed through other functions	the nested test
a time table not the clock	both table tests
no assignment-rule species check	the rule-on-time tests
no compartment check	the compartment test
no named reason	the sensitivity test

Corpus

178 of 1,323 BioModels read the time and have no event.

• 171 have a rate that reads it: refused, as before.
• 3 read it through an assignment-rule species or a compartment: refused, as before.
• 4 are lifted:

model	reads the time in	result here	check
BIOMD0000000739	time_minutes	converged, residual 4e-30	matches run() to t = 1e9 to 2.8e-7 at rtol 1e-12 (0.1 at 1e-8, 4e-4 at 1e-10)
BIOMD0000000498	parameter_1 (a pulse nothing reads)	converged=False	the run still drifts 31% between t = 1e6 and 1e7
BIOMD0000000951	minutes	converged=False	the run still drifts between 1e6 and 1e7
BIOMD0000000305	V_ave	converged=False, naming 4 write-only accumulators and suggesting mask=	with that mask the state matches run() at t = 1e6 to 1.5e-15, though converged stays False (residual 1.96)

Every model that ran before takes the same path: the NaN mask applies only where functions_use_time is set, and all such models were refused.

Checks (macOS arm64)

• python/tests: 16,943 passed, 0 failed.
• parity_checks/tests: 1,015 passed. The 2 failures (test_bngsim_provenance and the reference-archive replay) also fail on main here: their subprocess can't import bngsim without my local import shim.

pre-commit run --all-files, sphinx -W, and ci/changelog.py check/required are clean (changelog.d/961.changed.md).

Not verified

• Linux: this change does no floating-point root finding; CI is the check.
• Documentation: docs/user-guide/steady-state.md is updated. The Tracking: forward-sensitivity runs that are refused where a derivative exists (refusals to lift) #961 checkbox is left for a maintainer to tick.