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Per SAP 10.2 Appendix N, PDF p.101 footnote 43 (line 7053):
"For the efficiency values, the interpolated efficiency is the
reciprocal of linear interpolation between the reciprocals of the
efficiencies."
i.e. 1/η_interp = (1 − t)·1/η_low + t·1/η_high, the weighted harmonic
mean at t = (PSR − PSR_low) / (PSR_high − PSR_low). Cascade was using
**linear** interpolation directly on η — a +0.15..+0.25% over-estimate
in the typical PSR range (1.2..1.5) for ASHPs in the cohort.
Cohort fixture: cert 3336-2825-9400-0512-8292 (Mitsubishi PUZ-WM50VHA,
PCDB 104568). MIT/η-zone cascade matches worksheet EXACTLY (every line
86..92, every month), but η_main_heating cascade 225.443 vs worksheet
224.923 → main_heating_fuel +5.24 kWh/yr too high → ECF 1.5474 vs ws
1.5503 → SAP +0.04 vs worksheet 78.3739. Back-solving the worksheet's
η_main implies η_space_1 = 224.923 / 0.95 ≈ 236.76.
Closed form at PSR=1.40151, bracketing PCDB rows PSR 1.2
(η_space_1=253.9) and PSR 1.5 (η_space_1=229.2):
Linear (pre-slice): 253.9 + (229.2 − 253.9) × 0.6717 = 237.31 ✗
Reciprocal (footnote 43): 1 / ((1 − 0.6717)/253.9 + 0.6717/229.2)
= 1 / 0.004224 = 236.74 ✓
The harmonic mean is curvature-aware: linear interpolation under-
penalises efficiency drops at higher PSR (η typically falls off as
PSR increases past the system's design point) by averaging on η
rather than 1/η. SAP 10.2 footnote 43 is explicit about which side
of the reciprocal the interpolation sits.
Outcome:
Cohort-2 Summary path (38 certs):
exact (<1e-4): 23 → **33** (+10)
≤±0.07: 15 → **5** (-10: HP certs close to exact)
±0.07..0.5: 0 → 0
±0.5..1: 0 → 0
±1+: 0 → 0
RAISES: 0 → 0
Cohort-2 HP cluster post-slice:
0100 +0.00003 ← was +0.00283
0320 -0.00001 ← was +0.01801
0330 -0.00004 ← was +0.01772
2336 +0.00003 ← was +0.01778
3336 +0.00001 ← was +0.04005 (worst residual closes exact)
4536 -0.00002 ← was +0.01312
9036 -0.00003 ← was +0.02159
9796 +0.00000 ← was +0.00174 (post-S0380.27)
2536 +0.00072 ← was +0.00163
2800 +0.00068 ← was +0.00436
4800 +0.00068 ← was +0.02939
9370 +0.00002 ← was +0.00174
9421 +0.00001 ← was +0.00117
Cohort-1 ASHP cohort (7-cert cohort + new chain test certs):
cert 0380: +1e-6 ← was +0.034 (Mitsubishi PUZ-WM50VHA, the
canonical first-HP cohort cert)
cert 3800: -2e-5 ← was +0.021
cert 9418: -3e-7 ← was +0.00004
cert 9285: -3e-5 ← was +0.021
cert 2636: -0.015 ← was +0.003 (cantilever fixture; remaining
residual is non-η in nature)
5 of 7 cohort-1 ASHP certs now hit delta < 1e-4 vs worksheet — the
+0.04 spec-precision-floor cluster diagnosed in
HANDOVER_CERT_0380_MIT_CASCADE.md is the linear-vs-reciprocal η
interpolation bug, not a spec-floor at all. The handover doc's "no
public spec or BRE data field would distinguish these" claim was
incorrect — SAP 10.2 footnote 43 is the resolution.
API path (golden fixtures): 6 ASHP cohort residuals updated to reflect
the cascade closure:
cert 0380 PE: -14.7865 → -14.6848 kWh/m²; CO2: +0.2774 → +0.2780 t/yr
cert 0350 PE: -7.9281 → -7.8741; CO2: +0.1697 → +0.1701
cert 2225 PE: -11.9175 → -11.8557; CO2: +0.2617 → +0.2621
cert 2636 PE: -9.7153 → -9.6692; CO2: +0.2189 → +0.2193
cert 3800 PE: -9.7551 → -9.6838; CO2: +0.2598 → +0.2603
cert 9285 PE: -8.1110 → -8.0466; CO2: +0.1559 → +0.1564
All SAP integer residuals unchanged (cascade tracks the EPC integer
SAP at residual 0 across the cohort).
PSR interpolation unit test (`test_interpolate_heat_pump_efficiency_at
_cert_0380_psr_per_sap_app_n`) updated to reflect the reciprocal
formula with the SAP-10.2-footnote-43 spec citation and closed-form
asserts (η_space_1 ≈ 234.5235; η_water_3 ≈ 285.0861 at PSR=1.43).
Pyright net-zero (1 → 1 across touched files: pcdb/parser.py,
tests/test_pcdb_table_362_lookup.py, rdsap/tests/test_golden_fixtures.py).
Tests: 710 pass (was 710 pre-slice with linear interp + un-updated
pins; net-zero because the 6 golden pin updates + 1 interp test update
exactly offset the 6 + 1 failures the formula change introduced), 10
expected fails unchanged.
Co-Authored-By: Claude Opus 4.7 <noreply@anthropic.com>
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