Implement §3.3.2 power generation (Eqs. 71–138)

[vahid-ahmadi]

All 68 equations of the power sector, clean-room from the published manual. With §3.2 and §3.3.1 the registry is now Eqs. 21–138, contiguous with no gaps.

The headline finding is not an equation

§3.3.2 as published cannot be simulated forward.

Six parameters are absent from Table 5 — the intercepts in the investment, green-share and credit-rationing equations — and two variables, r_KNFF and r_KFF, are never defined anywhere in the manual. At explicit zero defaults:

• credit rationing collapses to a constant (0.939)
• the green investment share degenerates to 50:50 against a tabulated 69:31
• a one-period solve returns power-sector investment of −0.021 against a tabulated +2.15

This is the section the climate-policy scenarios run through, so it is the one that most needs the authors' answer.

Fourteen identities disagree with Table 6, several decisively

Thirty hold within four-significant-figure noise. Fourteen do not; each is implemented as printed and pinned with its measured gap. The corroborated ones:

Eq. (84) — marginal cost × (1 + mark-up) gives 0.9725 against a tabulated 0.3198, a factor of 3.04. Both inputs check out independently: Eqs. (82)+(83) reproduce the marginal cost to 4.5e-5, Eq. (74) reproduces the price to 3.7e-4. So the manual's two chains meet at a contradiction rather than one side being mistranscribed. The tabulated price implies a mark-up of −0.267 — electricity sold below marginal cost — which the tabulated gross operating surplus of −4.479 independently supports.

Four sign contradictions in the financial-transfer block (Eqs. 107, 112, 113, 116) need no lag to falsify. Table 6 is the corroborated side: Eqs. (90)/(118) imply the same lagged interest-bearing assets to 1.4e-4, and (91)/(119) agree to 3.6e-5. Aggravating: Table 5 marks the parameters involved "model-constrained — calculated from Eq. (…)", meaning they were derived so these equations would reproduce these values.

Eq. (131) tabulates nominal power-sector capital equal to its own real value to four digits — impossible at any deflator ≠ 1 — and Table 6 then propagates that error consistently through its own Eqs. (134) and (135).

A family of four gaps at ~3.9e-3 is one systematic finding: Table 6's whole capital block is tabulated at a deflator near 1.031 while the equations prescribe 1.035.

Two structural findings

• Eq. (88)'s printed inequality points opposite to its own prose. As printed, fossil capacity is retired when the ban date is beyond the horizon rather than within it. The printed form is implemented, with the baseline switch set so the no-ban case behaves as the manual annotates.
• The price block is undefined at full decarbonisation. Eqs. (81), (82) and (85) all divide by fossil quantities that go to zero on exactly the path Eq. (88) exists to simulate. The guards raise rather than invent a limit.

A third witness for the §3.3.1 fuel-price finding

Table 6 tabulates the power sector's fuel input at 15.75 both nominally and in real terms — only possible if the fuel price is 1, as Table 5 states and as Eq. (61) contradicts. It reaches no identity here, but in simulation it moves the electricity price by a third.

Status

229 tests pass, 72 new. Milestone 2 still needs §3.3.3 and the oracle comparison.

Manual defects surfaced by reimplementing rather than reading the R: now well past twenty, including two — the missing parameters and the undefined variables — that block forward simulation of the published specification entirely.

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