Fit S3's interpolation form, and build the materials seed (#698)

[WesIngwersen]

Stacked on #714.

S3's last open item was the interpolation form. It is fitted, and ❌ the
candidate this plan named is not the answer.

First, two different questions were being called "interpolation"

The materials level is observed every year (ASM→2021, AIES 2023), so it never
needed interpolating — §4 rules out doing so. The commodity mix is observed
only at 2017 and 2022, and nothing observes its interior: the fuels share of
the census universe stays between 0.98% and 1.14% across the span, so the coarse
annual partition constrains the mix hardly at all.

❌ The price-carried path is rejected

frame	best θ	gain over frozen
direct + group	−0.25	+0.4%
unsuppressed, direct + group	0.00	0.0%

The level moves with price; the mix does not.

⚠️ The summary panel cannot arbitrate the form

The obvious test — interpolate between two summary years, score the years
between — is circular, and its answer must not be used. BEA carries the last
benchmark forward, so every interior year of a summary span is itself an
interpolation. And since BEA has not incorporated the 2022 Economic Census,
its 2022–2024 tables are still 2017-benchmark carries, so a span ending
anywhere in the nowcast horizon is contaminated at the endpoint as well.

✅ The benchmark detail panel can arbitrate it — a second use for what S0a
built. 2007, 2012 and 2017 are three independent Economic-Census-anchored
observations. Interpolate 2007→2017, score at the observed 2012:

form	manufacturing	whole table
frozen at 2007	0.0889	0.1323
linear	0.0764	0.1190
geometric	0.0710	0.1164
endpoint — adopt 2017 at once	0.1216	0.1712

✅ Interpolating beats freezing by 20.1%, geometric beats linear by 7.1%,
and ❌ adopting the newer observation immediately is worse than freezing — so
"just seed every year from the 2022 census" loses to doing nothing.

❌ But do not extend the trend past the last observation

form	manufacturing	whole table
hold the 2012 mix	0.1232	0.1733
linear trend extended	0.1569	0.2455
geometric trend extended	0.1513	0.2546

27.4% worse on manufacturing, 41.7% on the whole table. A mix trend does not
persist.

What ships

An asymmetry, every leg measured: geometric between the censuses, 2022 held
flat for 2023–24. materials_seed(year) is an index on the share (not the
level — §The 2017 anchor) with the column total held, since Step 3 owns the level
through GO − VAPRO.

year	treatment	moved from frozen
2017	census observed	0.0000
2018–2021	interpolated	0.0192 → 0.0770
2022	census observed	0.0979
2023–2024	held at 2022	0.0979

The 0.0979 sits alongside §The mix score's independently-computed 0.0949 — the
construction checking out.

⚠️ One clean interior observation on a ten-year span, transferred to the
census's five-year one. It settles which form; it does not prove the form right.

New CLI: --form, --seed. Gates: ruff check . clean, mypy bedrock clean
(bar 4 pre-existing Windows-only resource errors), pytest 795 passed.

🤖 Generated with Claude Code