The two zero-E branches inside the solve read the previous candidate's temperature

[dfalster]

Found while fixing #105, which covers the same defect at the two exits outside the solve. This is the half that is inside the objective function, so it moves the argmax rather than just the reported state — hence a separate issue.

The gap

set_leaf_states_rates_from_psi_stem has three branches. The transpiring one derives the operating point's leaf temperature and re-derives the Farquhar block at it:

Tleaf_ = use_energy_balance_ ? leaf_temp_from_E(transpiration_) : leaf_temp_;
if (use_energy_balance_) {
  update_temperature_dependent_params(Tleaf_);
}

The two zero-transpiration branches — psi_upstream >= psi_stem, and the inner assim_max_ < 0 — write Tleaf_ and stop:

ci_ = gamma_*umol_per_mol_to_Pa_;
transpiration_ = 0;
stom_cond_CO2_ = 0;
Tleaf_ = use_energy_balance_ ? leaf_temp_from_E(0.0) : leaf_temp_;

So ci_ is read off gamma_, and assim_colimited_ = assim_colimited(ci_) at the bottom of the function is evaluated, at whatever temperature the block currently holds.

Why this is sharper than #105, not milder

At the exits #105 fixed, the block held the Tair baseline — wrong, but at least a fixed wrong temperature. Here it holds whatever the previous candidate left, because the transpiring branch mutates the block per candidate and by design (update_temperature_dependent_params bypasses the cache). So these branches read neither Tair nor their own temperature: they read the last psi the optimiser happened to probe.

That makes the objective history-dependent — the value at a given psi depends on the order candidates were visited. Hazard 3 is about the argmax varying smoothly with inputs, and an objective whose value depends on evaluation order is a mechanism for exactly the kind of non-smoothness that hazard describes.

Why it was not folded into #105

profit_psi_stem_TF calls this function, so this is inside the function the collar solve maximises. Changing it moves the argmax on the PM path, where #105 only moved the reported state at exits the optimiser never reaches. Different blast radius, different evidence needed.

What is needed

• Whether psi_upstream >= psi_stem is reachable during a collar solve at all, or only at bracket endpoints and through the standalone optimise_psi_stem_* entry points. The inner assim_max_ < 0 looks unreachable from find_root_collar_psi — prepare_collar_solve returns early on that condition before the optimiser runs — but it is reachable from the single-layer optimisers.
• The measured effect on the argmax and on profit over the PM-path grid, since operating_points.tsv runs gate-off and cannot see it.
• ⚠️ It adds transcendentals to a branch of the hot path (~10³ candidates per solve), so hazard 5's interleaved A/B applies. The branch is presumably cold, but that should be measured rather than assumed.

[dfalster]

Update: #93 deleted one of the two branches, so this issue is now about one branch, not two — and the remaining one has grown a second dimension.

Gone: the inner assim_max_ < 0 exit

#93 removed it, for a better reason than the one filed here: it zeroed transpiration_, which on that path is the hydraulic supply and does not depend on whether there is carbon to be had. Its replacement comment records that where assim_max_ < 0 the ci root-find takes its compensation-point fallback and returns exactly the state the branch used to set by hand. Nothing left to fix.

Stands: psi_upstream >= psi_stem

if (psi_upstream >= psi_stem){
  ci_ = gamma_*umol_per_mol_to_Pa_;
  transpiration_ = 0;
  stom_cond_CO2_ = 0;
  Tleaf_ = use_energy_balance_ ? leaf_temp_from_E(0.0) : leaf_temp_;
  } else{

ci_ is read off gamma_, and assim_colimited_ = assim_colimited(ci_) at the bottom of the function is evaluated, at whatever temperature the block currently holds — which on the PM path is the previous candidate's, because the transpiring branch re-derives per candidate by design. So this branch reads neither Tair nor its own temperature.

New: it now applies to vpd_leaf_ as well

#93 added the leaf-to-air deficit and seats it in the transpiring branch (set_leaf_vpd(Tleaf_)), immediately below update_temperature_dependent_params(Tleaf_). The zero-E branch above it does neither. So the same branch is now inconsistent in two derived quantities rather than one, and #93's own argument for why the deficit must follow the stored Tleaf_ applies to it verbatim.

For reference, #111 fixes exactly this pair of omissions at the two shut-down exits outside the solve, where it only moves the reported state. Here it is inside the objective, which is why it is still separate.

Unchanged from the original filing

• The objective becomes evaluation-order dependent, which is hazard 3's mechanism.
• Reachability needs establishing: bracket endpoints and the standalone optimise_psi_stem_* entry points, most likely, since prepare_collar_solve has its own earlier exit.
• ⚠️ It adds transcendentals to a hot-path branch (~10³ candidates per solve), so hazard 5's interleaved A/B applies rather than an assumption that the branch is cold.
• operating_points.tsv runs gate-off and cannot see any of it.

[dfalster]

Fixed by #117, which landed both this and #110 as one change — the two turned out to be the same branch, so a single reordering (Tleaf_ first, then update_temperature_dependent_params, then set_leaf_vpd, all above the assignments that read the block) closes both.

Not auto-closed because the PR body only names #110 and #112 after an amend; recording the resolution here rather than relying on the link.

What was established, against what this issue asked for:

• Reachability: yes, and on an argmax. prepare_profitmax's scan calls set_leaf_states_rates_from_psi_stem(psi_soil, psi_soil) at i == 0 on every run, and records that A as a profit candidate — so this branch selects operating points, it does not merely report them. Also reachable as the final state on the prescribed-collar path (profit_at_collar_psi clamps to bound_a = root_zero_E, where psi_stem == bound_a exactly), and at maximise_profit_over_collar's golden-section fallback and two-pin exit. find_root_collar_psi's normal path does not reach it — dprofit_at_collar_psi has its own reversed-gradient exit.
• The order-dependence was real and measurable. One fixed operating point at Tair 30 read A = −1.9888 on a cold object and −2.5355 after a single transpiring candidate, against a correct −3.0978; the deficit read 1.5000 / 2.7368 against 4.3714.
• The argmax moves in both directions: Tair 40 flips two soils from shut to interior (at higher profit), Tair 50–55 flip from barely-open to exactly shut.
• Hazard 5: no cost. ≤1% on the branch itself over four interleaved rounds, no signal on the PM collar solve, the ProfitMax optimiser, or gate-off. The branch is cold enough that the transpiring candidate sharing each iteration dominates — but that is now measured rather than assumed.

The assim_max_ < 0 half of the original filing stays gone: #93 deleted that branch, for the better reason recorded in its replacement comment.