Test the government function bridge, and reject it (#578)

[WesIngwersen]

Stacked on #713.

The plan sequenced S5's government leg behind a go/no-go: does Census
govslocalfin's function × object split bridge to a commodity mix for the
G* columns? It has been run. ❌ No.

The bound that decides it

The bridge means one model — stable within-function input mixes, moving function
weights: s_c(t) = Σ_f w_f(t)·m_{c|f}. Hold m fixed and

d(s(t), s(0)) ≤ ½ Σ_f |Δw_f| = d(w(t), w(0))

because each m_{c|f} sums to 1 over commodities. The function-mix movement is
an exact ceiling on the commodity-mix movement the bridge can deliver — so the
question is answerable without building the bridge, which is what made gating it
worth doing.

Three measurements

function mix moves, 2017 → 2022	0.0464 — against a 0.201 commodity drift in the same columns
government functions overlap	36% (mean pairwise dissimilarity 0.639 on BEA's own G* columns) → realistic ceiling 0.030, 14.7% of what needs explaining
reweighting BEA's real 3-function split	+2.4% (0.1946 → 0.1899)

⚠️ 97.6% of the drift is movement within a function. A finer function list
does not help — BEA's 3-function split moves 0.0453 where govslocalfin's 33
functions move 0.0464, so disaggregating does not move more dollars between them.
For scale, the inflation carry and ORE's built seed both get ~4.5%, which the
plan already calls at the bar rather than over it.

Two defects that would also have sunk it

• ⚠️ Current Operations by function exists only for 2022-2024 — one
  economy-wide number for 2017-2021. No 2017 anchor at the seed year. The
  137→232 row jump the source note flagged is exactly this.
• ⚠️ The only continuous function series, Total Expenditure, is a 0.062
  proxy for it — larger than the 0.0385 of movement it would have to transmit.
• ⚠️ State and local only. Federal is 43.1% of the block's misplaced dollars,
  and S00500 (83,851 $M at 0.383, worst column in the table) is out of reach.

What this does not close

#578 stays open. The G* columns still drift 230-258 $B and the drift is
within-function. This closes govslocalfin as the route to it, not the problem.

Two by-products belong elsewhere and are not claimed here: Salaries and Wages
is Step 2's government V00100, and Capital Outlay by function does run
2017-2024, which makes it the check on the FD government investment columns.

Contents

• gov_function_bridge.py — the probe, with --reach/--coverage/--movement/--bound and a --check that regresses every documented finding.
• Plan: new §The government function bridge; S5, the S4 verdict table, the source table and the two-problems table all updated off the result.
• annual_survey_expense_sources.md — corrects two claims now known wrong: that G* needs a total rather than a mix, and that Current Operations by function runs for every year.

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

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