diff --git a/bedrock/analysis/nowcasting/results/n_change_decomposition.py b/bedrock/analysis/nowcasting/results/n_change_decomposition.py
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+"""Why N moved, two complementary ways.
+
+Both tables come from one derivation of B and A, because deriving them takes
+minutes and the two views have to describe the same build.
+
+**Table 1 - which input moved it.**  ``N`` changes for two independent reasons
+and the headline number cannot tell them apart: **A**, the technology matrix
+the nowcast rebuilds from annual data, and **B**, the emission intensities that
+move when the GHG FBS series is regenerated.  Holding one at the baseline and
+moving the other separates them.
+
+⚠️ The two middle rows do not sum to the first.  ``N = 1'B (I-A)^-1`` is not
+additive in A and B, so the remainder is their interaction: emissions moving in
+sectors whose input structure also moved.  Quote the rows, not a sum.
+
+``D = 1'B`` 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, the change sits in
+sectors nothing else depends on, so it never propagates.
+
+**Table 2 - the mechanism, in units you can say out loud.**  ``N`` factors
+exactly into two parts, 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
+
+So a fall in N is either "a dollar drags less of the economy behind it"
+(multiplier) or "what it drags is cleaner" (average intensity), and this says
+how much of each.  The median column sum of ``A`` is reported alongside as the
+thing the multiplier is built from.
+
+CLI::
+
+    uv run python -m bedrock.analysis.nowcasting.results.n_change_decomposition
+    uv run python -m bedrock.analysis.nowcasting.results.n_change_decomposition \\
+        --year 2023 --baseline v0_3_1 --csv
+"""
+
+from __future__ import annotations
+
+import argparse
+import typing as ta
+from pathlib import Path
+
+import pandas as pd
+
+from bedrock.analysis.nowcasting.results._ef_smoke_lib import (
+    NOWCAST_COMPARE_YEAR,
+    V03_SNAPSHOT,
+    _as_float_series,
+    activate_live_config,
+    config_stem,
+)
+from bedrock.utils.math.formulas import (
+    compute_d,
+    compute_L_matrix,
+    compute_M_matrix,
+    compute_n,
+)
+from bedrock.utils.snapshots import releases
+from bedrock.utils.snapshots.loader import load_snapshot
+
+OUT_DIR = Path(__file__).resolve().parent
+
+
+class Build(ta.NamedTuple):
+    """Baseline and live matrices on one shared sector axis."""
+
+    B_old: pd.DataFrame
+    B_new: pd.DataFrame
+    A_old: pd.DataFrame
+    A_new: pd.DataFrame
+    vintage: str
+    sectors: pd.Index
+    dropped: int
+
+
+def _n_from(B: pd.DataFrame, A: pd.DataFrame) -> pd.Series:
+    """``N`` for one (B, A) pairing, through the formulas the model uses."""
+    L = compute_L_matrix(A=A)
+    return _as_float_series(compute_n(M=compute_M_matrix(B=B, L=L)))
+
+
+def _median_pct(new: pd.Series, base: pd.Series) -> float:
+    """Median percent change, dropping sectors the baseline puts at zero."""
+    both = new.index.intersection(base.index)
+    rel = (new.loc[both] - base.loc[both]) / base.loc[both].replace(0.0, pd.NA)
+    return float(pd.to_numeric(rel, errors='coerce').dropna().median() * 100.0)
+
+
+def load_build(year: int, baseline_key: str) -> Build:
+    """Derive the live build once and align it to the baseline's sector axis."""
+    from bedrock.transform.eeio.derived import (  # noqa: PLC0415
+        derive_Aq_usa,
+        derive_B_usa_non_finetuned,
+    )
+
+    B_old = load_snapshot('B_USA_non_finetuned', baseline_key)
+    Adom_old = load_snapshot('Adom_USA', baseline_key)
+    Aimp_old = load_snapshot('Aimp_USA', baseline_key)
+
+    vintage = activate_live_config(year)
+    B_new = derive_B_usa_non_finetuned()
+    aq = derive_Aq_usa()
+
+    # One sector axis for every combination, or the mixed pairings compare
+    # different economies rather than different builds.
+    sectors = (
+        Adom_old.index.intersection(aq.Adom.index)
+        .intersection(B_old.columns)
+        .intersection(B_new.columns)
+    )
+    dropped = len(aq.Adom.index) - len(sectors)
+
+    def sq(frame: pd.DataFrame) -> pd.DataFrame:
+        return frame.reindex(index=sectors, columns=sectors).fillna(0.0)
+
+    def cols(frame: pd.DataFrame) -> pd.DataFrame:
+        return frame.reindex(columns=sectors).fillna(0.0)
+
+    return Build(
+        B_old=cols(B_old),
+        B_new=cols(B_new),
+        # The model's L uses domestic plus imported requirements together.
+        A_old=sq(Adom_old) + sq(Aimp_old),
+        A_new=sq(aq.Adom) + sq(aq.Aimp),
+        vintage=vintage,
+        sectors=sectors,
+        dropped=dropped,
+    )
+
+
+def ab_decomposition(b: Build, label: str) -> pd.DataFrame:
+    """Table 1: hold one of A / B at the baseline and move the other."""
+    base = _n_from(b.B_old, b.A_old)
+    return pd.DataFrame(
+        [
+            {
+                'what moves': 'both B and A',
+                'median change in N': _median_pct(_n_from(b.B_new, b.A_new), base),
+            },
+            {
+                'what moves': f'A only, B held at {label}',
+                'median change in N': _median_pct(_n_from(b.B_old, b.A_new), base),
+            },
+            {
+                'what moves': f'B only, A held at {label}',
+                'median change in N': _median_pct(_n_from(b.B_new, b.A_old), base),
+            },
+            {
+                'what moves': "direct intensity D = 1'B",
+                'median change in N': _median_pct(
+                    _as_float_series(compute_d(B=b.B_new)),
+                    _as_float_series(compute_d(B=b.B_old)),
+                ),
+            },
+        ]
+    )
+
+
+def multiplier_intensity(b: Build) -> pd.DataFrame:
+    """Table 2: N as output multiplier x average intensity of what is pulled."""
+
+    def parts(B: pd.DataFrame, A: pd.DataFrame) -> dict[str, pd.Series]:
+        L = compute_L_matrix(A=A)
+        N = _as_float_series(compute_n(M=compute_M_matrix(B=B, L=L)))
+        multiplier = L.sum(axis=0).astype(float)
+        return {
+            'a_colsum': A.sum(axis=0).astype(float),
+            'multiplier': multiplier,
+            'avg_intensity': N / multiplier.replace(0.0, pd.NA),
+            'N': N,
+        }
+
+    old, new = parts(b.B_old, b.A_old), parts(b.B_new, b.A_new)
+    rows = [
+        ('intermediate input per $ of output (col sum of A)', 'a_colsum'),
+        ('output multiplier (col sum of L)', 'multiplier'),
+        ('avg intensity of what a $ pulls, kg CO2e/$', 'avg_intensity'),
+        ('N, kg CO2e/$', 'N'),
+    ]
+    return pd.DataFrame(
+        [
+            {
+                'quantity': label,
+                'baseline': float(pd.to_numeric(old[key], errors='coerce').median()),
+                'nowcast': float(pd.to_numeric(new[key], errors='coerce').median()),
+                'change %': _median_pct(new[key], old[key]),
+            }
+            for label, key in rows
+        ]
+    )
+
+
+def main() -> None:
+    ap = argparse.ArgumentParser(
+        description='Explain the change in N: A vs B, and multiplier vs intensity.'
+    )
+    ap.add_argument('--year', type=int, default=NOWCAST_COMPARE_YEAR)
+    ap.add_argument(
+        '--baseline',
+        default=V03_SNAPSHOT,
+        help='snapshot key to hold the other side at (default: the v0.3 release)',
+    )
+    ap.add_argument(
+        '--csv', action='store_true', help='also write CSVs beside this file'
+    )
+    args = ap.parse_args()
+
+    baseline = getattr(releases, args.baseline, args.baseline)
+    b = load_build(args.year, baseline)
+    short = str(baseline)[:7]
+
+    print(f'\nnowcast {config_stem(args.year)} vs snapshot {baseline}')
+    print(
+        f'MUT vintage {b.vintage}   {len(b.sectors)} sectors on both sides'
+        + (f'   ({b.dropped} dropped)' if b.dropped else '')
+    )
+
+    t1 = ab_decomposition(b, short)
+    print('\n--- which input moved N ---')
+    print(
+        t1.to_string(index=False, formatters={'median change in N': '{:+.2f}%'.format})
+    )
+    print(
+        'The middle two rows do not sum to the first: N is not additive in A '
+        'and B,\nso the remainder is their interaction.'
+    )
+
+    t2 = multiplier_intensity(b)
+    print('\n--- the mechanism: N = output multiplier x average intensity ---')
+    print(
+        t2.to_string(
+            index=False,
+            formatters={
+                'baseline': '{:.4f}'.format,
+                'nowcast': '{:.4f}'.format,
+                'change %': '{:+.2f}%'.format,
+            },
+        )
+    )
+    print(
+        'Medians are taken per row, so the two components do not multiply to '
+        'the N row\nexactly; they are the size of each effect, not an identity.'
+    )
+
+    if args.csv:
+        for name, table in (('ab', t1), ('mechanism', t2)):
+            path = OUT_DIR / f'n_change_{name}_{args.year}.csv'
+            table.to_csv(path, index=False)
+            print(f'wrote {path}')
+
+
+if __name__ == '__main__':
+    main()