fix(n_prov_destiny): make the processed-item substitution conserve N

[lbm364dl]

Summary

Targets alice/typologies so it lands inside #416. Three files, one concern: the processed-item substitution added in 96bcbe9 does not conserve nitrogen.

The commit message for 96bcbe9 says it "correctly conserve[s] production N". Measured against the real pins, it does not — and it fails in both directions, not only the zero-N one the PR already flags as an open question.

The measurement

Running the PR's own .prepare_prod_data() + .convert_fm_dm_n() against a no-processing baseline, total production N moves by:

year	1860	1930	1961	1980	2000	2020	2022
ΔN	−1.10%	+2.27%	+3.77%	+4.31%	+3.69%	−1.56%	0.00%

Worst single year +7.84%, net +1.875 Mt N (+1.56%) over 1860–2023.

Why

.expand_processed_items() applies every output row's cf to the same processed_fm. Summed per input item for Spain in 2000, those factors reach:

input item	Σ cf	n outputs
Maize and products	5.22	3
Wheat and products	5.11	4
Barley and products	4.90	3
Oilcrops, Other	2.38	2
Olives (including preserved)	0.24	1

So one tonne of maize sent to processing yielded 5.22 t of product. This is not a defect in the pin: R/supply_use.R:33-39 already documents these as the outputs of a virtual process ("a virtual process like 'Wheat and products processing', giving all its possible outputs"), i.e. not co-product shares of one physical process. Beer and starch are water-diluted, which is why the factors are large. Meanwhile grapes → wine, olives → oil and sugar beet → sugar destroy N, because those outputs are nearly N-free.

The fix

Nitrogen is an element: processing moves it between products but cannot create or destroy it. .processing_n_scaling() computes two factors per province-year and primary item:

• output_scale caps the outputs at the N actually available in the input, scaling all of an input's outputs by the same factor so their relative mix is untouched.
• removal_scale removes from the primary item only the N its named outputs actually account for.

Verified on the real pins — N removed from primaries now equals N credited to processed items to 2.1e-16 relative error, every year 1860–2023:

year	1860	1961	2000	2021
N removed (MgN)	1293.00179877	16183.23353365	48626.28109086	41638.54279214
N added (MgN)	1293.00179877	16183.23353365	48626.28109086	41638.54279214

A missing product N coefficient now drops that substitution and warns via cli, instead of silently pricing a real flow at zero. The special_items list shared with .convert_fm_dm_n() is extracted to .special_biomass_items() so the conservation pricing and the final FM→N conversion cannot drift apart.

What this deliberately does not decide

removal_scale is the conservative half. When outputs are N-poor the unaccounted N stays with the primary item rather than disappearing. Physically that residue is by-product (grape pomace, olive cake, beet pulp) or an agro-industry loss, so attributing it to the primary item's destinies is an approximation — it keeps the balance honest without choosing where the residue belongs. Routing it to explicit by-product items is a methodological decision for the model owners, tracked in #432.

Also not addressed here, by design: processing_coefs ends in 2021 while production runs to 2023, so 2022–23 still get no processing at all (#433).

Test plan

• 5 new unit tests: N-poor outputs conserve exactly; N-rich outputs are capped and never create N; the output mix is preserved under scaling; a missing coefficient drops the substitution and warns; an exactly balanced substitution is a no-op.
• R CMD check --as-cran — 0 errors, 0 warnings, 1 pre-existing NOTE
• devtools::test() — 4575 passing, 0 failures
• lintr — 0
• air format . — clean

Related

Found while reviewing #416. Separate follow-ups, none of them blocking this PR:

• Reuse build_supply_use()'s national processing definition in create_n_prov_destiny() instead of bespoke cf arithmetic #428 — reuse build_supply_use()'s national process definition, so this class of bug cannot recur
• Finn flow matrix is built transposed, so FCI uses outflow instead of inflow as throughflow #430 — Finn flow matrix built transposed (bug in new code; worth fixing before Reconcile with main, add typology sensitivity/decomposition analysis, processed-item accounting change #416 merges)
• plot_typology_indicators_panel() fails unless patchwork is attached (bare + / operators mask-dependent) #431 — plot_typology_indicators_panel() fails unless patchwork is attached (same)
• Zero-N processed items (wine, olive oil, sugar): decide where the unaccounted primary-crop N goes #432 — where the unaccounted N from zero-N outputs should go (methodology)
• processing_coefs ends in 2021 while production runs to 2023, so 2022-23 silently get no processing #433 — processing_coefs ends 2021, so 2022–23 get no processing
• 16.5 MB Europe_FAO_completed.xlsx ships in the package for 253 rows (2.8%) of it #434 — 16.5 MB workbook shipped for 2.8% of its rows
• All 33 exported functions added by #416 have non-runnable examples (27 commented out, 6 missing) #435 — all 33 new examples are non-runnable
• Typology decision rules are duplicated across two files, and the two specialised-cropping branches leave a gap #438 — typology rules duplicated across two files, plus a gap between the cropping branches
• n_soil_inputs_nue grafts Excreta from a stale _old pin, inflating manure N ~2x and zeroing 2022-23 #440 — stale _old Excreta graft, which this branch's pin bump widens