build_n_percapita() may double-count biological N fixation

Problem

The planned SJOS-N build_n_percapita() implementation appears to count biological nitrogen fixation (BNF) twice in the default synthetic_bnf framing.

The coefficient is defined as:

syn_tot_agri_ratio = (109 + 33) / (0.85 * 109)

and the country total is calculated as:

anthropogenic_n_t = synthetic * syn_tot_agri_ratio + bnf

At the calibration values, agricultural synthetic N is 0.85 * 109 = 92.65 Tg N. Multiplying it by the ratio already gives 142 Tg N (109 + 33). Adding the 33 Tg N BNF term again produces 175 Tg N.

Impact

This can inflate:

• build_n_percapita() results;
• the normalized per-capita nitrogen boundary axis from build_n_boundary_percapita();
• the SJOS-N scatter output that consumes that axis.

The code is currently on the unpublished SJOS-N work rather than main.

Methodological decision required

Define the intended system boundary and equation before changing the implementation. In particular:

• Does syn_tot_agri_ratio already convert agricultural synthetic N to total synthetic + BNF?
• Or should synthetic N be scaled independently (for example for its agricultural share) and observed agricultural BNF then added once?
• Should the packaged food_agri_share enter this calculation, and at which stage?
• Does the gridded bnf input represent the same agricultural/system boundary as the Campbell calibration value?

Acceptance criteria

• Document the system boundary and derivation of every scaling factor.
• Count synthetic fixation and BNF exactly once.
• Add a calibration test using 109 Tg synthetic, 33 Tg BNF, and the 0.85 agricultural share, asserting the explicitly chosen expected total.
• Add a downstream test for the per-capita and normalized-boundary outputs.
• Update coefficient descriptions and function documentation to match the selected equation.

Evidence

• R/n_percapita.R: .n_percapita_anthropogenic()
• data-raw/sjos_n_coefficients.R: syn_tot_agri_ratio