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The correction that prices most of the atlas is fit outside the density range it is applied to (2026-08-16)

LARGELY CLOSED as of 2026-08-17 -- re-verified 2026-08-20, see update below

No number below has been changed and nothing has been withdrawn -- they are kept as measured on 2026-08-16 for reproducibility (scripts/trust_gate_density_audit.py recomputes them exactly from the saved per-building tables of that date). But the reach this page is about has since shrunk dramatically, not because of any fix aimed at it, as a side effect of bahawalnagar_rural (124 bldg/km2) crossing into the trust gate's rate_ratio band sometime between 2026-08-16 and the 2026-08-17 parcel-label refit. Re-running the audit script against both the 27-quadrat (2026-08-17, pre-Box 18) and the current 30-quadrat (2026-08-20, Box 18) fits gives:

2026-08-16 (as measured below) 2026-08-17 (27 quadrats) 2026-08-20 (30 quadrats, current)
sparsest quadrat in the fit 872 bldg/km2 (Multan) 124 bldg/km2 (Bahawalnagar Rural) 124 bldg/km2 (unchanged)
in-domain buildings sparser than every fit quadrat 84.1% 13.5% 13.5% (unchanged)
roofclf half priced out of calibration range 54.3% 5.5% 5.3%
as a share of published Best estimate 54% 5% 5%

The short version, updated: the multiplier is still fit on urban/semi-urban land and applied to sparser cells nationally, and the trust gate still selects on density as a side effect of selecting on precision (Spearman(density, rate_ratio) is -0.36 on the current 30-quadrat fit, versus -0.58 as measured 2026-08-16) -- so the mechanism this page describes is real and unfixed. But the practical reach of that mechanism dropped an order of magnitude between 2026-08-16 and 2026-08-17, apparently from Bahawalnagar Rural's own rate_ratio moving (2.19 → 1.78 → 1.70 across the three fits above) rather than from any deliberate widening of the gate. The three Box 18 peri-urban quadrats folded in 2026-08-20 (Attock, Layyah, Lodhran) did NOT move this finding further -- the sparsest passing quadrat, the out-of-range building share, and the out-of-range MWp share are all within measurement noise of the 2026-08-17 figures. Whether Bahawalnagar Rural's rate_ratio crossing the gate on 2026-08-17 was itself examined and intentional, or a side effect of the parcel-label refit that nobody checked against this page, is not recorded anywhere and is worth asking the owner about.

Figures in the body of this page below are left as originally measured on 2026-08-16 for reproducibility; read them as history, not as the current reach.

What the multiplier is and how much rides on it

The roofclf half of the atlas is two components that share one formula:

est_kwp = roof_area_m2 * DEFAULT_KWP_PER_M2_MODULE * coverage_ratio / area_recall
component published
sub-400 m2 rooftop (central) 7,890.2 MWp
>= 400 m2 roofclf rooftop replacement 7,189.4 MWp
total 15,079.6 MWp, 83% of the 18,218.4 MWp Best estimate

coverage_ratio and area_recall come from sub400_capacity.coverage_ratio_by_size_and_density and area_recall_by_size_and_density, both fit on the quadrats that select_calibrated_quadrats returns. So that selection is not a side detail of the calibration; it sets the multiplier on five sixths of the published figure.

The trust gate selects on density, not only on precision

select_calibrated_quadrats keeps quadrats whose roofclf rate_ratio (predicted over true adoption rate) falls in [0.5, 2.0]. Measured across the 25 quadrats that have a building density on file:

Spearman(density, rate_ratio) = -0.577. roofclf over-predicts adoption in sparser settlements, so an upper bound on rate_ratio removes the sparse end by construction rather than by accident.

density tercile n range (bldg/km2) median rate_ratio gate pass rate
sparse 9 124 to 1,366 2.19 0.44
middle 8 1,428 to 2,109 0.97 1.00
dense 8 2,119 to 5,258 0.76 0.50

Five quadrats are dropped that are sparser than every survivor, and all five fail in the same direction, above the ceiling rather than below the floor:

quadrat bldg/km2 base_rate rate_ratio
bahawalnagar_rural 124 0.016 2.19
khairpur_rural 141 0.005 4.41
muzaffargarh_rural_wide 278 0.008 3.10
sundar 553 0.091 2.24
muzaffargarh_rural 639 0.009 2.29

There is a case that this is backwards. The coverage ratio is defined as true mapped PV area over flagged roof area, which is precisely the quantity that prices over-flagging. Excluding a quadrat because roofclf over-predicts there removes the observation that would have measured the over-prediction, and then applies a ratio measured where roofclf is well behaved. That is an argument, not a finding, and it is not the reason this page exists; the reach below is.

A second, independent blocker

nasirabad_rural and tank_rural have no n_buildings value in results/calibration_quadrats.csv, so quadrat_building_density_km2 cannot place them in a density band and they can never enter the coverage-ratio fit no matter how the gate is set. nasirabad_rural is the quadrat that set density.CALIBRATED_BLDG_DENSITY_KM2's floor of 48.5 bldg/km2, so the quadrat that justifies including the sparsest cells in the domain is structurally unable to contribute to the correction applied inside it. Both counts are cheap to backfill: measured in-boundary against VIDA they are 189 and 225 buildings over 4.00 km2, giving 47.3 and 56.3 bldg/km2.

Reach: the fit and the deployment barely overlap

The sparsest quadrat in the shipped fit is Multan at 872 bldg/km2, itself passing at rate_ratio 1.96 against a 2.0 ceiling. The calibrated density domain runs from 48.5, and the cells inside it look nothing like Multan:

  • in-domain buildings in cells sparser than every quadrat in the fit: 60,276,228 of 71,662,822 (84.1%), across 2,894 of 2,957 cells
  • their building-weighted density: p25 161, median 252, p75 374 bldg/km2, roughly a factor of 3.5 sparser than the sparsest calibration point

Carried through to capacity:

component published priced out of calibration range
sub-400 m2 rooftop 7,890.2 MWp 4,637.9 MWp (58.8%)
>= 400 m2 roofclf rooftop 7,189.4 MWp 5,204.1 MWp (72.4%)
roofclf half 15,079.6 MWp 9,842.0 MWp (65.3%)

9,842 MWp is 54% of the published Best estimate.

The density stratification does not currently absorb this

DEFAULT_N_DENSITY_STRATA = 2, and the band edges are quantiles of the quadrats' own densities, while national cells are assigned to a band by their own density. With the shipped quadrat set the split lands at 1,822.5 bldg/km2, which puts:

  • band 0: fit from 8 quadrats spanning 872 to 1,758 bldg/km2, applied to 99.6% of national cells and 92.1% of national buildings, covering everything in the domain from 48.5 up to 1,737 bldg/km2
  • band 1: fit from 8 quadrats spanning 1,887 to 4,195, applied to 19 cells and 7.9% of buildings

So a village cell at 50 bldg/km2 and a peri-urban cell at 1,700 receive the identical coverage ratio and the identical area recall. The stratification is real in the code and close to degenerate at deployment, because the quadrat density distribution and the national cell density distribution overlap only at their extreme ends.

The rural quadrats that could populate a sparse band do exist, and they are empty of signal. At the deployment threshold they flag, in total, nine buildings: bahawalnagar_rural 0, khairpur_rural 1, muzaffargarh_rural 2, muzaffargarh_rural_wide 6. The trusted set flags 18,839. Only sundar (553 bldg/km2, 660 flagged) carries any weight below 872, and it is a semi-industrial estate rather than farmland.

What the gate is worth, measured

Refitting both multipliers under a widening ratio_hi and recomputing both components exactly. The ratio_hi = 2.0 row is the shipped configuration and reproduces both published totals to the digit, which is the check that the rest of the table means anything:

ratio_hi quadrats sparsest band split sub-400 >= 400 roofclf half vs shipped
2.0 (shipped) 16 872 1,822 7,890.2 7,189.4 15,079.6 0.00%
2.5 19 124 1,717 7,262.5 6,634.6 13,897.0 -7.84%
3.0 20 124 1,737 7,466.1 7,121.2 14,587.3 -3.26%
3.5 21 124 1,717 7,188.3 6,621.5 13,809.8 -8.42%
5.0 22 124 1,715 7,189.0 6,620.2 13,809.2 -8.42%
no ceiling 22 124 1,715 7,189.0 6,620.2 13,809.2 -8.42%

Two things to read off it. The gate is worth about -1,270 MWp, or -8.4% of the roofclf half and -7.0% of the published Best estimate, which is 20 times the 61.7 MWp component that was dropped from the atlas on 2026-08-15 for being unmeasured where applied. And the response is not monotone: 3.0 recovers half of what 2.5 gave up, because admitting a quadrat moves the band split and reshuffles which side of it the other quadrats fall on. A calibration whose output jumps by 5 percentage points depending on which single quadrat crosses the median is not stable, and with two bands and a handful of quadrats near the split it cannot be.

What this does and does not mean

It does not mean the published figure is 8% too high and should be adjusted down. Relaxing the gate admits quadrats where roofclf is measurably miscalibrated, which is what the gate is for, and even the fully relaxed fit has almost no support at 150 to 400 bldg/km2, the building-weighted centre of the under-calibrated mass. Both settings are poorly evidenced there; the sweep measures the sensitivity, not the correct answer.

It does mean three things that are not currently stated anywhere:

  1. The density domain (48.5 to 5,258) is roughly 18 times wider at its sparse end than the correction's own support (872 to 4,195). CLAUDE.md already warns that the domain gate and the precision gate are independent and must be checked separately for each new quadrat. It does not say how far apart they have drifted, and the drift is the whole exposure.
  2. The published 90% credible interval (14,346 to 21,768) does not contain this. The coverage-ratio bootstrap resamples calibration quadrats, and every quadrat it can resample sits in the wrong density band, so the interval measures sampling noise within the dense stratum and is silent about transfer to the sparse one.
  3. By the project's own 2026-08-15 precedent, a component not measured where it is applied does not get published. Applied strictly here, that would mean restricting the roofclf domain to >= 872 bldg/km2, withdrawing 9,842 MWp of roofclf-priced capacity. The published total would not fall by the full amount, because atlas.py's per-cell blend hands the >= 400 m2 rooftop estimate back to segmentation's own est_mwp_rc_roof outside the domain; the sub-400 m2 half (4,637.9 MWp) has no fallback at all and would go to zero, since the out-of-domain extrapolation was itself dropped on 2026-08-15. Either way the headline moves by thousands of MWp, which is the point.

What would fix it

Map low-density quadrats, targeting 300 to 600 bldg/km2 first. Inside the under-calibrated population, 150 to 300 bldg/km2 holds 40.8% of the buildings and 300 to 600 holds 27.5%, so those two bands are two thirds of the exposure. Start at the upper end: flagged buildings, which is what the fit consumes, accumulate several times faster at 500 bldg/km2 than at 124.

Be honest about the cost. All 27 existing quadrats together cover 80 km2, and the existing rural boxes yield on the order of 1.5 flagged buildings per km2. Matching the dense stratum's 18,839 flagged buildings at rural densities is not achievable by hand mapping. It is also not necessary: a few hundred flagged buildings in band would convert this from unmeasured to measured-with-a-wide-interval, and the existing quadrat bootstrap would then widen the published interval honestly instead of understating it.

Three cheaper things are worth doing first, and none of them need new mapping:

  • Backfill n_buildings for nasirabad_rural and tank_rural (189 and 225). It does not fix the gap, but it removes a silent second exclusion and lets those quadrats participate the moment the gate question is settled.
  • Record the fit's own density support alongside the domain in sub400_central_summary.json and ge400_roof_summary.json, and warn when the domain extends past it, the same way density.py already warns about a calibration table with no placement_bins.
  • Decide the gate question explicitly, with the sweep above as the evidence, rather than leaving [0.5, 2.0] as an unexamined default whose density confounding is now measured.

This is the concrete, quantified instance of the standing caveat in Open questions that the quadrats are purposive rather than a probability sample. The general form of that caveat cannot be closed without a national sampling frame; this specific form can be narrowed a long way by mapping in one identified density band.