feat(analysis): make the two explanations of the N change reproducible

[WesIngwersen]

Both of these tables had been produced by hand and quoted in write-ups. Nobody could re-run them after a rebuild, which is how an explanation goes stale without anyone noticing. They are now one script, and both come from a single derivation of B and A — deriving them takes minutes, and the two views have to describe the same build or they are not comparable.

Table 1 — which input moved N

Holds one of A / B at the baseline and moves the other. This is the only way to say whether a change in N came from the IO rebuild or from the GHG regeneration.

what moves	median change in N	previous run
both B and A	−8.05%	−10.64%
A only, B held at v0.3	−4.58%	−8.30%
B only, A held at v0.3	−2.74%	−1.73%
direct intensity D = 1'B	−6.35%	−1.59%

D is the control on the B row: if B moves D and N alike the emissions change is a level shift; if D moves much more, it sits in sectors nothing else depends on and never propagates. It now moves more than twice what B-only moves N, which is a real change in character from the previous run.

Table 2 — the mechanism, in units you can say out loud

N factors exactly, per sector:

N_j = sum_i d_i L_ij
    = (sum_i L_ij)      x  (sum_i d_i L_ij / sum_i L_ij)
    = output multiplier x  average intensity of what is pulled

quantity	v0.3 baseline	nowcast 2024	change
intermediate input per $ output (col sum of A)	0.5033	0.5030	−1.55%
output multiplier (col sum of L)	2.0064	1.9629	−2.69%
avg intensity of what a $ pulls (kg CO2e/$)	0.0930	0.0860	−4.94%
N (kg CO2e/$)	0.2024	0.1746	−8.05%

Validation that this reproduces the hand method rather than something adjacent: the baseline column lands on 0.5033 / 2.0064 / 0.0930, matching the figures quoted by hand last week to four decimals.

The emphasis has flipped since then. The multiplier effect halved (−4.0% → −2.69%) because the merged stack brought the median column sum of A back to 0.5030 against v0.3's 0.5033 — the export re-splits, purchaser-value margin anchor and EC conditioning restored intermediate input intensity the earlier build had lost. Meanwhile the intensity effect grew to −4.94%. The fall in N is now mostly a cleaner mix rather than a shorter supply chain. Table 1 agrees independently: A's contribution halved while B's grew.

⚠️ Neither table is an identity

• N is not additive in A and B, so table 1's middle rows do not sum to its first; the remainder is their interaction.
• Medians are taken per row, so table 2's components do not multiply to its N row.

Both report the size of an effect, not a decomposition that closes. The script prints that under each table so a reader cannot take the sum.

Testing

Analysis script, so no unit tests per repo convention. The reproduction check is the baseline column matching the hand figures, and it prints on every run alongside the MUT vintage and sector count, so a replay states what it ran on.

uv run python -m bedrock.analysis.nowcasting.results.n_change_decomposition --csv
uv run black --check . ; uv run ruff check .    # clean

🤖 Generated with Claude Code

[bl-young]

this comes from _ef_smoke_lib which still pints the v0.3.1 model, which doesn't include the MECS update. We need to bump that to v0.3.2.

There may be other related updates as well needed alongside this