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+# Rain EP Dillavou-Imperfection Matrix
+
+## Question
+
+Can a local neutral predictor remove a fixed hardware update offset without
+using a larger EP nudging voltage?
+
+The primary corruption is the model in Dillavou et al., Eq. (7).  Every local
+parameter update receives a fixed, unknown, parameter-specific offset after
+the two-state EP estimate has been formed:
+
+\[
+g^{\rm measured}_i = g^{\rm EP}_i + B_i.
+\]
+
+`B_i` is fixed across examples, epochs, and beta signs.  Its RMS is specified
+relative to the first clean local update only to set a reproducible simulation
+scale.  This normalization is not visible to the learner.  The optional
+state-drift ratio is zero in all exact-model experiments.
+
+The correction is local and uses no backpropagation.  With the teaching input
+disabled, the update circuit exposes `B_i`.  The predictor stores this neutral
+measurement and subtracts it from subsequent updates.  Under the strictly
+constant model, constant calibration and SDIL innovation are expected to
+coincide.  A difference between them is neither predicted nor claimed.
+
+## Frozen author protocol
+
+- author repository: `rain-neuromorphics/energy-based-learning`;
+- revision: `6b253fd8a5d267535f58ab79992256ef10031ceb`;
+- endpoint: `experiments/rain_ep_bias_train.py`;
+- network protocol: `comparative32`;
+- FashionMNIST with the author's 32x32 augmentation;
+- author ConvHopfieldEnergy32 architecture, gains and per-layer rates;
+- beta 0.25, 15 training relaxation iterations, 60 inference iterations;
+- batch size 100 and 100-epoch cosine schedule.
+
+## S0 development screen
+
+S0 uses only a fixed training/holdout split with 10,000 training and 2,000
+holdout examples.  One epoch selects a non-catastrophic offset magnitude from
+the frozen grid `0.003, 0.01, 0.03, 0.1`.  The same wave includes clean PEP,
+random-sign beta, centered EP, and one SDIL arm.  S0 is development evidence
+and is never reported as a final result.
+
+## Confirmation matrix
+
+After S0 freezes one offset magnitude, the full author horizon compares:
+
+| EP estimator | no offset | raw offset | constant calibration | SDIL |
+|---|---:|---:|---:|---:|
+| positive beta | yes | yes | yes | yes |
+| random beta sign | yes | yes | no | no |
+| centered EP | yes | yes | no | no |
+
+An oracle subtraction arm checks implementation correctness.  A large-beta
+EP sweep is reported as a strong-clamp proxy but is not called overclamping:
+Dillavou overclamping also changes the output force and update duration, so a
+beta sweep alone is not the published method.
+
+The exact constant model establishes the hardware failure and the limit of
+beta centering.  It cannot establish an advantage over ordinary local offset
+calibration.  Any claimed SDIL advantage requires a separately labeled
+state-dependent extension or real measured device drift.